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A Systems analysis of optimal manpower utilization in health maintenance organizations

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Title:
A Systems analysis of optimal manpower utilization in health maintenance organizations
Creator:
Schneider, Donald Paul
Publication Date:
Copyright Date:
1973
Language:
English
Physical Description:
xx, 276 leaves. : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Diseases ( jstor )
Health care costs ( jstor )
Health care services ( jstor )
Health maintenance organizations ( jstor )
Human resources ( jstor )
Integers ( jstor )
Modeling ( jstor )
Nurses ( jstor )
Pediatrics ( jstor )
Physicians ( jstor )
Dissertations, Academic -- Industrial and Systems Engineering -- UF
Health facilities -- Personnel management ( lcsh )
Industrial and Systems Engineering thesis Ph. D
Medical care -- Mathematical models ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 266-274.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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14204169 ( OCLC )
ADB3879 ( NOTIS )

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A SYSTEMS ANALYSIS OF OPTIMAL MANPOWER
UTILIZATION IN HEALTH MAINTENANCE ORGANIZATIONS











By



Donald Paul Schneider


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA
1973















ACKNOWLEDGMENTS


I wish to acknowledge the considerable contribution to this work

by Dr. Kerry E. Kilpatrick who acted as the Chairman of my Supervisory

Committee. His direction and insight contributed to both the form and

content of this dissertation.

I also thank the remainder of my committee, Dr. H. Donald Ratliff,

Dr. Thom J. Hodgson, Dr. Frank R. Sloan and Richard C. Reynolds, M.D.,

for their efforts which contributed to the completion of this work. I

would also like to thank Dr. Stephen D. Roberts for his guidance and

support in several stages of this research; Dr. Barney L. Capehart for

his guidance in the early stages of my graduate studies; Dr. Donald R.

Miller for his aid and helpful suggestions, and Dr. M. E. Thomas for

his support throughout my stay at the University of Florida.

I would also like to thank the members of the health care community

who provided valuable advice, criticism, and the facilities so that the

research could be developed, tested and validated. These include Dr.

Douglas Fenderson, Director of the Office of Special Programs, Bureau

of Health Manpower Education, National Institutes of Health; Mr. John

Braun, Chief, Physician's Assistant Staff, Office of Special Programs,

Bureau of Health Manpower Education, National Institutes of Health;

Dr. L. F. Krystynak of the University of Florida, Mr. Richard Bohn,

President of the Metropolitan Health Council of Indianapolis, Indiana;

Dale R. Benson, M.D., director of the Southeast Health Center of Indi-

anapolis; Mr. Tim Payne, administrator of the Southeast Health Center;









Mr. Dave Norton, consultant to the Florida Health Care Plan, Inc.; Mr.

Richard Freeman, Special Assistant to the Deputy Secretary of Health,

Education and Welfare; Mr. Dave Whelan, President of Health Management

Group, Inc.; and Dr. Judith Liebman of the University of Illinois.

Finally, I thank my wife Ester for her encouragement and patience

throughout the course of this work.

This dissertation was supported in part by the Health Systems Re-

search Division of the University of Florida.
















TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . . . . . . .

LIST OF TABLES . . . . . . . . .

LIST OF FIGURES . . . . . . . . .

KEY TO SYMBOLS . . . . . . . . . .

ABSTRACT . . . . . . . . . . .

CHAPTER

1 INTRODUCTION . . . . . . . .

Background . . . . . . . . .

Scope and Purpose . . . . . . .

Research Objectives . . . . . . .

Organization of Dissertation . . . . .

2 BACKGROUND AND LITERATURE REVIEW . . . .

Health Maintenance Organizations . . . .

General Terminology . . . . . .
Legislative Background . . . . .
Research Viewpoint . . . . . .

Allied Health Manpower . . . . .

Physician Extenders . . . . . .
Physician Extenders in Primary Care . .
Physician Extender Utilization: The Team
Delegation of Medical Services . . .

Motivation for Mathematical Modeling . . .

Previous Studies . . . . . .


Systems Analysis as
Process . . .
Planning the Benefit
Proposed BMO Design


Page

iii

ix

xiii

xiv

xviii


. .














. . .


an Aid to the HMO Design
. . . . . . . . 27
s To Be Provided by an HMO 28
Process . . . . ... 30









Page

3 DEVELOPMENT OF ANALYTICAL MODELS . . . . .. .35

Preliminary Models . . . . . . . . ... 35

Introduction . . . . . . . . ... 35
System Schematic for Model Development . . .. .36
Tradeoff Decisions To Be Incorporated in the
Models . . . . . . . . ... . 38
Preliminary Model Development . . . . .. 41
Development of the Medical Care Aspects of the
Model . . . . . . . . . . . 44
Further Development of Financial Aspects of the
Model . . . . . . . .. . . . 51
Additional Model Refinements . . . . .. 58
A Comparison of Models Ml, M2, and M3 ...... 64

Development of Planning Models . . . . . ... .66

Development of the Overall Planning Model .... .66
Minimum Cost Model for Fixed Services . . ... .69
A Special Case of the Minimum Cost Model ... .72
Subscriber Maximization Model . . . . .. 75
Minimal Use of Professional Manpower ...... .77
Concluding Remarks ... . . . . . . 79

4 DATA COLLECTION AND ANALYSIS . . . . . ... .81

Introduction . . . . . . . . .. . . 81

An Overview of Health Care Data Collection . . 81
Purpose of the Chapter . . . . . ... .81

Medical Classification Systems . . . . . ... .83

The Criteria for a Medical Classification System 83
A Review of Existing MCS . . . . . ... .84
A Formulation of a New MCS . . . . ... .90

Time Requirements, Delegation and Utilization Data . 93

Time Requirements . . . . . . . ... 93
Delegation Guidelines . . . . . . ... .99
Utilization of Services . . . . . ... .108

Medical Cost Data . . . . . . . .... 113

Introduction . . . . . . . . . 113
Cost Calculations . . . . . . . ... 115
Concluding Remarks . . . . . . ... .120









Page

5 NOMINAL SOLUTIONS AND VALIDATION OF THE MODELS . . .. .122

Introduction . . . . . . . . . . . 122

Solution Process for Linear Programming and Mixed
Integer Programming . . . . . . . ... 122

Validation Process . . . . . . . . . 124

Problems Involved in the Validation Process .... .124
Formulation of a Validation Process . . . ... .125
Steps Taken To Validate the Models . . . ... .126
Implications of the Model Assumptions . . ... .131

Nominal Solutions . . . . . . . .... . .134

Comparison to the Prepaid Group Practice . . .. .134
Presentation of Nominal Solutions . . . ... .136
Comparison of Nominal Solutions to an Existing
Prepaid Plan . . . . . . . . ... 145

Case Examples . . . . . . . . ... . . 147

Use of the Models in the Design of an HMO in
Indianapolis, Indiana . . . . . . ... 147
Evaluation of the Indianapolis HIO Case Study . . 163
Case Study of the Design of an HMO in Daytona
Beach, Florida . . . . . . . ... 166
Evaluation of Daytona Beach HMO Study . . ... 173

Concluding Remarks . . . . . . . .... . .175

6 PARAMETRIC AND SENSITIVITY ANALYSIS OF POLICY
QUESTIONS . . . . . . . . ... ..... 176

Introduction . . . . . . . . ... . .176

Sensitivity Analysis . . . . . . . . ... 177

Facility Costs . . . . . . . . ... 177
Physician Extender Salary . . . . . . .. 179
Indirect Supervision Guidelines . . . . .. 182

Parametric Analysis . . . . . . . . ... 190

PE Utilization As a Function of Subscriber Levels
and the Integer Restrictions . . . . .. 190
Optimal Delegation With a Scarcity of PE's .... .195
Maximum Subscribers Per Physician Under a Scarcity
of PE's . . . . . . . . ... . .201









Page

Remarks . . . . . . . . . . . . 202

7 SUMMARY OF RESULTS AND CONCLUSIONS . . . . .. 206

Introduction . . . . . . . . .. . . 206

Results and Conclusions . . . . . . . .. 206

Development of the Models and Data Base . . .. .206
Results From the Models . . . . . ... .209
Results of the Validation Process . . . ... .213
An Overview of the Results and Conclusions . 215

Areas fcr Further Research . . . . . . ... .216

APPENDICES

A MEDICAL CLASSIFICATION SYSTEMS . . . . . .. 222

B PHYSICIAN EXTENDER DELEGATION DATA . . . . ... .235

C PRINCIPAL MODEL INPUTS AND NOMENCLATURE FOR PROBLEM
VARIABLES . . . . . . . . . . . 254

D DATA COLLECTION FOR THE INDIANAPOLIS, INDIANA HMO . 261

REFERENCES . . ... . . . . . . . . . 266

BIOGRAPHICAL SKETCH . . . . . . . . ... . .275


viii















LIST OF TABLES


Page
TABLE

1 Example of Personnel and Time Requirements ...... 47

2 Relative Sizes of Models Ml, M2 and M3 . . . ... 65

3 Sample Output for Analysis of Utilization, Time
Requirements and Delegation . . . . .... 95

4 MD and RN Time Requirements for Medical Services . .. 100

5 MD, PE and RN Time Requirements for Medical Services .102

6 Maximum Percent of Visits Under Indirect Supervision
for Four Delegation Assumptions . . . . .. 109

7 Comparison of Demographic Characteristics for the
Kaiser Sample and the PGP ............ 111

8 Percent Utilization for Adult Medicine, Pediatrics
and OB/GYN in the KCBDCS . . . . . . 112

9 1972 PGP Budget. . . . . . . . .... .115

10 Nonoffice Visit Expenses for PGP . . . . .... 117

11 Nonhospital Departmental Costs for Three Primary Care
Departments in PGP . . . . . . . .... 120

12 Cost and Manpower Comparison of PGP and the Overall
Planning Model . . . . . . . ..... .. 135

13 Comparison of OWM Nominal Solutions to PGP . . ... 139

14 Delegation Analysis for Nominal Continuous Variable
Solution . . . . . . . . ... ..... 141

15 Nominal Solutions for MC Model . . . . .... 143

16 Nominal Solutions for the SM Model . . . . .. 144

17 Parametric Results for Indianapolis HMO Design .... .151











TABLE

18 Variable Expenditures at Indianapolis HMO . . ... .156

19 Maximum Subscriber Levels for Indianapolis HMO As a
Function of Staffing Pattern . . . . . ... 161

20 Projected Demographic Characteristics for FHCP .... .168

21 Projected Utilization Rates Per Thousand Members for
FHCP . . . . . . . . . . . . 168

22 Continuous Optimal Solution for FHCP . . . ... 170

23 Integer Staffing Levels for FIICP . . . . ... .170

24 Parametric Results for Various Integer Staffing Levels
for FHCP . . . . . . . . ... .. .. . 172

25 Suggested Dynamic Hiring Plan for Adult Medicine at
FHCP -. . . . . . . . . . . . 173

26 Manpower Utilization Response to Increases in Facility
Cost . . . . . . . . .. . . . 178

27 PE Use As a Function of Salary Increment From the
Nominal . . . . . . . . .. . . 180

28 An Analysis of Six Different Indirect Supervision
Guidelines . . . . . . . . .. . . 184

29 Maximum Shifts From the Nominal in MD and PE Utilization
Caused By Changes in the Indirect Supervision Guide-
lines . . . . . . . . ... . . 186

30 PE Utilization As a Function of Basic MD Supervision
Time . . . . . . . . ... .. . .. 189

31 Results of Integer Manpower Restrictions For 8000-30000
Subscriber Levels . . . . . . . ... .193

32 Optimal Delegation and MD Requirements Under a
Scarcity of PE's . . . . . . . . ... 197

33 Marginal MD and Cost Savings As Additional PE's
Are Used . . . . . . . . ... .... . 199

34 Maximum Subscriber Sizes Per MD Under a Scarcity
of PE's . . . . . . . . .. .. . 203









Page

TABLE

A-I Principle Sections of the International Classification
of Diseases . . . . . . . . . ... . 222

A-2 California Relative Value Classification for Office
and Home Visits . . . . . . . . ... 223

A-3 Major Categories of a Medical Service Classification
System for General Practice . . . . . ... .224

A-4 Patterns of Medical Care for the Primary Care
Specialties . . . . . . . . ... .. . 225

A-5 Diagnostic Categories for which GEOMET Specifications
of Care Were Prepared . . . . . . ... 226

A-6 Sample Listing of Elements of Care for Pediatrics . 228

A-7 Sample Specifications of Care . . . . . .. 229

A-8 Assignment of Proxy Specifications of Care ...... .231

A-9 Clinical Subgroups in the Kaiser Clinical Behavior
Disease Classification System . . .... .. . .233

A-10 Ancillary Task Listing for General Medical Practice 234

B-1 Physicians' Willingness To Delegate Activities to a
Trained OB/GYN Assistant . . . . . .... 235

B-2 Summary of Tasks for a Physician Assistant ...... .236

B-3 Survey by Physicianh Specialty for Possible Duties of
Physician's Assistant . . . . . . ... .238

B-4 Physician Response for Delegation of Tasks to Physician
Assistants . . . . . . . .... ..... 240

B-5 Feasible Delegation of Elements of Care . . ... .251

C-l Names Assigned to Personnel Classes . . . ... .254

C-2 Names Assigned to the Medical Classification System . 255

C-3 Principal Input Data Coefficients for the Mathematical
Models . . . . . . . . ... .. .. . 258

D-l Age-Sex Breakdown for Potential Enrollees in SHC . . 261









Page
TABLE

D-2 Projected Visits Per Year for SHC as a Function of
Subscriber Level . . . . . . . . . 263

D-3 Fixed Expenditures at SHC . . . . . . ... .265


xii















LIST OF FIGURES


Page

FIGURE

1 Present Decision Process for Determining Benefits . 29

2 Proposed Decision Process for Determining Benefits . 29

3 Three-Stage Hierarchy in the Planning of HMO's .... .31

4 Present HHO Design Dynamics . . . . . . .. 32

5 Proposed 1MO Design Dynamics . . . . . . .. 33

6 A Schematic Representation of an HMO Structure .... .36

7 Medical Care Structure Showing Relation Between Re-
sources and Requirements . . . . . . ... .37

8 Tri-Level Classification System . . . . .... 91

9 Flow Diagram of the TLCS Computer Program . . ... 94

10 Subscribers Per MD As a Function of PE/MD Ratio . .. 204


xiii














KEY TO SYMBOLS


Subscripts:
i refers to type i personnel (including teams)
j refers to service j
k refers to health care teams
m refers to department m

aijm composite coefficient (see equation (3.56))


AD administrative costs (dollars per year)

AD administrative costs allocated to department m (dollars per year)
m

ADD composite coefficient (see equation (3.66))

B* upper limit on yearly budget for operating and salary expenses
for medical departments included in the optimization (dollars per
year)

b.. number of type j services a type i personnel can perform per year
for a given level of technology (medical services per man-year)

b* number of type j services a type iel* personnel can perform per
Year for a given level of technology (medical services per man-year)

c.. labor cost for one type i to perform one service j (dollars per
1 medical service)

CLT average cost per laboratory test (dollars per test)

CXR average cost per x-ray service (dollars per service)

d. demand for service J (dj = Sd') (medical services per year)

d'. demand for type j service per subscriber per year (medical services
per subscriber per year)

e' amortized cost for a type i personnel due to technological cost
(dollars per year)

e. initial cost for a type i personnel due to technological cost
S (dollars)

EXT external sources of revenue (dollars per year)


xiv









f. level of independence for type i personnel to perform service j


FTE full time equivalent professionals in department m (man-years)
m

g amortized construction cost (dollars per unit area per year)

g initial construction cost (dollars per unit area)

h. composite coefficient (see equation (3.61))
i



h* composite coefficient (see equation (3.62))


I set of all medical personnel including teams

I* set of professional manpower

I* ancillary manpower

Ip set of physician extender personnel including teams led by physician
extenders

I set of personnel excluding teams

It set of health care teams

Im set of all personnel in department m

I set of personnel whose productivity is enhanced by additional
technology

J set of services considered for provision or to be provided

J subset of J for which V = 1
m

Jm set of services considered for provision or to be provided in de-
partment m

J set of services class i*el* personnel supervise


j* supervisory services
m

K arbitrary, large constant

M set of all medical departments under consideration

MAN management and planning cost per FTE professional (dollars per man-
year per year)


xv









MAX.. maximum percent of service j that can be carried out by per-
sonnel i in the indirect supervision mode

MX. maximum fraction of type j services provided by nontypical means

N. number of type i personnel employed (man-year)
1

NLT number of lab tests ordered in department m per service provided
(tests per medical service)

NXR number of x-rays ordered in department m per service provided
(x-rays per medical service)

n, number of type j services demanded and not provided by ordinary
means (medical services per year)

o maintenance and utility costs per unit of area (dollars per unit
area per year)

OM other medical costs not included in the optimization (dollars per
year)

P yearly profit rate or rate at which capital fund accumulates

P amortization rate for initial capitalization

P. maximum number of type i personnel available (man-years)

PER personnel cost per FTE employee (dollars per man-year)

PV administrative cost per patient visit (dollars per patient visit)

qkij man-years of personnel type i per man-year of team k providing
service j (akij is defined to be one for the team leader)
'kij

R average yearly fee paid by subscribers for nonhospital. services
(dollars per year)

r. patient fee for service j (dollars per medical service)


S number of subscribers

s. yearly salary of type i personnel (includes overhead salary such
as retirement, vacation, insurance, etc.) (dollars per year)

SUi maximum fraction of time type i personnel will engage in super-
1 vision of ancillary personnel
l if N.>O
T. f\ iI'
i 0 if N. = 0
1









t'm amortized cost of equipment in department m per FTE professional
(dollars per man-year per year)

t initial cost of equipment in department m per FTE professional
(dollars per man-year)

u. per unit cost of providing type j service by extraordinary means
(dollars per medical service)

p. department m provided
Vm 0 department m not provided

w. space required per type i person (units of area per one man-
year)

x number of type i personnel assigned to service j (man-years)
ij

x*. number of supervisory level personnel assigned to the supervisory
service j* (man-years)

x! fractional part of personnel i group which are idle (man-years)
I

Y* maximum initial capitalization (dollars)

Y total floor space available (units of area)

Y floor space to be constructed for department m (Y = m w.N.)
S (units of area per department)

Pjm composite coefficient (see equation (3.58))

0'j composite coefficient (see equation (3.57))
jm
*jm composite coefficient (see equation (3.59))

yj composite coefficient (see equation (3.64))

Yjm composite coefficient (see equation (3.63))


ym composite coefficient (see equation (3.65))








Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy


A SYSTEMS ANALYSIS OF OPTIMAL MANPOWER
UTILIZATION IN HEALTH MAINTENANCE ORGANIZATIONS

By

Donald Paul Schneider

August, 1973


Chairman: Dr. Kerry E. Kilpatrick
Major Department: Industrial and Systems Engineering


Mixed integer programming and linear programming models are pro-

posed as aids to decision makers in the design and evaluation of health

manpower requirements in the office care setting of Health Maintenance

Organizations (HMO). Although special emphasis is given to the poten-

tial role of physician's assistants, nurse practitioners and nuise mid-

wives in HMO's,the staffing requirements for physicians, registered

nurses and licensed practical nurses are also investigated.

Four basic mathematical models are.developed to analyze in detail

the design relationships between resources and requirements in HMO's.

The models are used to examine the interaction between effective man-

power utilization, technology utilization, facility requirements and

local inputs such as available capital and existing health care facil-

ities. Another principal feature of the models is that they reflect

the total cost for outpatient medical care services delivered at the

HMO. The objectives used in the models pertain to either minimum cost

or the minimum feasible use of physicians through the substitution of

allied health personnel.


xviii









A new three-level hierarchial medical classification system is de-

veloped which relates to the following manpower planning considerations:

training and delegation, morbidity statistics, and manpower utilization.

The new medical classification system was used to define and collect

data regarding time requirements, delegation possibilities and patient

utilization. In addition medical cost data were collected at a major

prepaid group practice. Data relating to both direct and indirect costs

are presented to fulfill the data requirements of the models.

The models are validated through a seven-step process that in-

cludes: comparisons to two existing prepaid group practices; use of the

models in rhe design of two HMO's; face validity; sensitivity analysis;

parametric analysis; examination of internal validity; and an exami-

nation of data validity. Two detailed case studies are presented which

demonstrate the flexibility and usefulness of the models in actual HMO

planning. One case study was principally concerned with staffing re-

quirements, benefits to be offered and the capitation rate while the

other was chiefly concerned with the possible use of physician's assis-

tants and a dynamic hiring plan as the HMO subscriber size increased.

An extensive variety of results are presented relating to the use

of allied health personnel in the primary care specialties in HMO's.

An analysis of the potential cost and manpower effect extensive use of

allied health personnel would have on large HMO's shows a 4 to 10 percent

cost reduction and a 25 to 50 percent reduction in physician require-

ments depending on the medical specialty. An optimal delegation

analysis shows that routine examinations, well child care, chronic ill-

nesses, and diseases with a high emotional content are most economically

and medically suited for delegation to physician's assistant level personnel









sonnel. Results are also presented to show that one physician's assis-

tant level person can replace about .6 of a physician in an HMO and

that the optimal ratio of physician's assistant level personnel to phy-

sicians is 1.55, 2.10, and .47 in adult medicine, pediatrics, and ob-

stetrics/gynecology, respectively.

In addition, sensitivity analyses of physician's assistant utili-

zation as a function of facility cost, salary, and delegation guide-

lines are presented. Parametric analyses of physician's assistant

utilization as a function of the integer manpower restrictions and the

size of the HMO are also presented.














CHAPTER 1


INTRODUCTION



Background


The last decade has witnessed a growing national recognition that

the U.S. health care system has failed to meet the expectations of the

general populace (1). The plight of the rural poor and inner city poor

has been especially noticeable. The overall national shortage of phy-

sicians and trained health personnel plus the disinclination of the

professionals to settle in rural and impacted urban areas is creating

a doubly critical problem (1). In addition an increasing proportion

of physicians are not engaged in patient care at all but are engaged

in research, administration, teaching, government service or consul-

tation activities (1). Of those involved in patient care, the ratio

of family practitioners (general practitioners, internists, and pedi-

atricians) to the population fell by 33 percent from 1950 to 1965 (2).

The demand for health care is being stimulated by two additional

factors: a changed attitude toward health and health care and greater

financial support for health care. It has only been in the last two

decades when health insurance, Medicare, Medicaid, and many other

public and private financing programs became available and translated

medical needs into medical demand (1). Health care expectations have

risen to the point where many people believe health care is a right








rather than a privilege. In 1966 the American government in P.L. 89-749

assumed a commitment "to assure comprehensive health services of high

quality for every person."

Compounding these problems is the fact that too much of the phy-

sician's time is ineffectively utilized in routine and semi-clerical

tasks. Much of the work physicians and nurses do can be characterized

by routine tasks such as reading electrocardiograms, following a pa-

tient's vital signs manually, and administering and interpreting chem-

ical, biochemical and physical tests (3). In addition, large portions

of time and attention are devoted to the well or the so called "worried

well" (4).

Finally, costs of health care are rising rapidly. From 1965 to

1970 physician fees rose by an annual rate of from 5.4 percent to 9.2

percent (1). The average daily service charge for hospitals rose 279

percent from 1960 to 1970 (5). These cost increases are caused by

specific factors such as rising labor costs; the increasing employment

of more highly skilled personnel; the changing status and higher pay

of the house staff of hospitals; the rise in the cost of construction

and supplies; the increase in number and sophistication of diagnostic

tests and therapeutic procedures; the changing mix of the patient

population with a trend toward more serious illness; the persistence of

too many economically inefficient small units; and the rising costs of

administrative overhead (1).

Out of consideration for these signs and symptoms of failure of

the current health care system is the growing recognition that new

health care systems must be encouraged and developed. Thus in January,

1971, President Nixon called for a new health care system in America (6).








The central feature of his plan is the Health Maintenance Organization

(HMO) which is similar in concept to neighborhood health centers but

fundamentally embodies the principals of prepaid group practice (PPGP).


Scope and Purpose


This dissertation reviews the existing descriptive and conceptual

literature on HMO's and PPGP's and utilizes this information to model

mathematically HMO's. A systems analysis approach utilizing mixed in-

teger programming and linear programming models is proposed which pro-

vides an aid to decision makers in the design and evaluation of health

manpower requirements in the outpatient segment of the HMO.

To model the manpower needs a medical classification system was

developed to facilitate the development of the relationship between

the system requirements in terms of typical patient visits and system

resources in terms of trained health manpower. The models and medical

classification system are used to evaluate the potential role of a

physician extender (PE) in the HMO setting. There is a large number

of different types of PE's involved in health care and a few examples

include physician assistants, pediatric nurse practitioners, and nurse

midwives. The models are developed to examine the interaction between

effective manpower utilization, technology utilization, facility re-

quirements and local inputs such as available capital and existing

health care facilities. Another principle feature of the models is

that they reflect the total cost for outpatient medical care services

delivered at the HMO.

The analytical models introduced in this dissertation can be used

to evaluate staffing requirements for any type of medical service pro-





4

vided in the outpatient setting by an HMO. However, due to data limita-

tions the scope of the solutions presented are narrowed to the primary

specialties; adult medicine, pediatrics and obstetrics/gynecology

(OB/GYN). The manpower types considered are thus the physicians and

physician extenders commonly used in the above specialties as well as

registered nurses (RN) and licensed practical nurses (LPN). A principal

byproduct of a systems analysis and mathematical model is a systematic

framework in which data can be collected and analyzed. In the health care

setting such a framework is particularly needed (7). Thus within the

systems viewpoint developed in the models an extensive amount of data is

presented relating to the above specialties, manpower, and the cost of

medical care.

The overall result of this research is the presentation of a sys-

tems methodology which will aid in the evaluation and design of HMO's.

In audition, through use of the models and the data collected, definite

design guidelines for the utilization of medical manpower in HMO's are

established. Since the analytical models presented are very flexible,

they allow the comparison of an existing HMO to an optimal design which

incorporates many of the local inputs such as utilization rates, patterns

of medical care, salary structure and other items that are relevant to

the particular HMO being evaluated. The study compares two existing

prepaid group practices to the design given by the analytical models

and the models also are used to aid in the design of two HMO's. One of

the HMO's was in the process of converting from a neighborhood health

center to an MO and the other HMO was in its preoperational planning

stage. Through the comparison of results to existing HMO's and through

the use of the models in the design of emerging HMO's, the viability








and validity of the design approach was determined.

Overall, the goal is to carry out a research effort in which systems

analysis and operations research techniques are used and discussed, but

end with results and conclusions which can be utilized by persons not

necessarily acquainted with these techniques.


Research Objectives


This section briefly summarizes the specific research objectives

that are carried out in this dissertation. The objectives can be divided

into three principal areas: development of mathematical models to aid

in the design of IZO's; collecting the data required to solve the models;

and using the models to examine various policy questions and to aid in

the design of two emerging lMZO's.

Four mathematical models are developed to analyze in detail the

design relationships between resources and requirements in HMO's. These

four models solve the following basic types of problems:

(a) preoperational planning for which minimum

cost solutions are sought for the services

to be provided, manpower needed, delegation

policy, facilities needed and particular

technology innovations;

(b) preoperational planning for which the

optimal staffing, delegation policy and

facility is sought to minimize the capi-

tation rate;

(c) manpower planning for which the optimal

allied personnel policy is sought to








maximize the IMO subscribers per phy-

sician; and

(d) manpower planning for which the optimal

allied personnel policy is sought to

minimize the number of physicians re-

quired.

These four models are mixed integer programs (or linear programs if the

integer restrictions are dropped) and are developed in such a manner that

solutions are obtained at a relatively low cost.

The mathematical models were used to provide a framework in which

data were collected. As a first step in the data collection effort, a new

medical classification system is presented which relates to the following

manpower planning considerations: training and delegation, morbidity

statistics, and manpower utilization. In addition to previously pub-

lished data, an extensive amount of original data collected at a major

prepaid group practice is presented. In summary,data are presented for

the following areas:

(a) manpower time requirements;

(b) delegation possibilities to PE's;

(c) medical utilization by diagnosis;

(d) direct medical costs; and

(e) indirect medical costs.

The third major research objective involves the use of the models

and the data to derive solutions. As a first step in the validation

process the results of the models are compared to two major prepaid

group practices. In addition the models are used to derive solutions

for the following problems:








(a) an analysis of the potential cost and

manpower effect extensive PE utilization

would have on a major prepaid practice;

(b) an analysis of optimal delegation guide-

lines for PE's;

(c) a case study for the optimal manpower re-

quirements and resulting cost for a

neighborhood health center planning to

convert to an HMO in Indianapolis, Indiana;

(d) a case study for the possible utilization

of PE's in an emerging HMO in Daytona Beach,

Florida;

(e) a sensitivity analysis of PE utilization as

a function of facility cost, PE salary, and

PE delegation guidelines;

(f) a parametric analysis of PE utilization as

a function of the integer manpower restrictions

and size of the HMO; and

(g) a parametric analysis of the maximum subscribers

per physician in an HMO as a function of PE

utilization and HMO size.


Organization of the Dissertation


In Chapter 2 the two main components of the medical system under

study are presented. The concepts and properties of HMO's are discussed

and a more detailed look at health manpower is provided. Special emphasis

is given to a discussion of PE's. In addition a motivation for using








mathematical models to aid in the design of the HMO is presented. This

motivation includes the framework for HMO design that is carried out by

the models.

In Chapter 3 a system schematic and tradeoffs to be incorporated

are presented. Preliminary models are developed to show the basic

structural relationships in the HMO system. The preliminary models are

then enriched in a step-by-step fashion to the point where a detailed

model is presented. The detailed model provides the basis for the de-

velopment of four additional models which are aimed at specific HMO and

manpower planning questions.

In Chapter 4 a new medical classification system is presented. This

system is then used to present data relating to manpower time require-

ments, delegation possibilities and patient utilization. In addition,

both direct and indirect costs for prepaid medical care are presented.

In Chapter 5 the solution method for the models is briefly dis-

cussed and a detailed examination of the validation process is presented.

This includes a suggested sequence of steps which can be used to validate

a prescriptive mathematical model. Solutions from the models are pre-

sented and compared to two major prepaid group practices and an analysis

of the potential effect of PE utilization is explored. In addition two

case studies are presented which give additional data and demonstrate

some of the types of HMO analysis that can be carried out with the models.

In Chapter 6 sensitivity analyses and parametric analyses are pre-

sented. The sensitivity analyses include an examination of facility

costs, PE salary, and delegation and supervision guidelines. The para-

metric analyses include an examination of the integer manpower restric-

tions, HMO size, a scarcity of PE's and the maximum subscribers per






9

physician. In addition the potential national manpower implications are

briefly discussed.

A summary of the results and conclusions of this research and sug-

gestions for further research are presented in Chapter 7.















CHAPTER 2


BACKGROUND AND LITERATURE REVIEW



Health Maintenance Organizations


General Terminology

In many ways the Neighborhood Health Center (NHC) is a forerunner of

the R10 without the HMO financing system. NHC's employ nurses and para-

medical aids in expanded involvements, provide local employment for

neighborhoods, invite consumer participation in the decision processes,

affiliate with a hospital for referral and inpatient care, and provide

outreach services to the community for health education and family health

counseling (8). The NHC has been a very viable concept and is widely

accepted and used by the residents in its vicinity. However, although

the NHC's serve their communities well, they are in reality a separate

health care system and may be supplanted by HMO's in the near future.

Another concept central to HMO's is the relation between and defi-

nition of group practice and prepaid group practice. Group practice has

been described as "the application of medical services by three or more

full-time physicians formally organized to provide medical care, consul-

tation, diagnosis, and/or treatment through the joint use of equipment

and personnel, and with the income from medical practice distributed in

accordance with methods previously determined by the group." (9, p. 598)

Groups may be single disciplinary or multi-disciplinary in nature and









exist in the form of partnerships or as corporations.

Prepaid group practice (PPGP) is a version of group practice in

which the patient population prepays for health care at a specified

yearly or monthly rate. PPGP attempts to mutualize through capitation

the cost of comprehensive medical care for the population at risk and

removes the fee-for-service barrier to care. The large PPGP's include

teams of full-time physicians representing all of primary care and most

of the minor specialties so that comprehensive services can be provided

through an integrated single system (9). Services are not only available

at a hospital, but in neighborhood ambulatory care units which provide

primary care. Generally PPGP's have a scale of operation which permits

the extensive use of ancillary personnel, and the capitation method of

payment, it has been suggested, tends to provide an incentive for inte-

gration of physician extender health teams and to maintain the health of

the patient in an effort to deliver health care economically.

The claimed advantages of prepaid group practice are numerous and

include: provision of a comprehensive range of outpatient services;

continuity of health care in one setting; pooling of resources to make

possible the most efficient use of manpower, money, medical technology

and equipment; quick and efficient use of consultants; and an emphasis

on preventive medicine (10). Other authors point out additional ad-

vantages such as increased productivity and a better division of labor

(11) and peer review and better doctor-patient relationships (12). In

addition, capitation has been shown to be effective in decreasing sur-

gical rates for such procedures as tonsillectomies, adenoidectomies and

hysterectomies (13). Many of the above advantages have been observed in









the Kaiser-Permanente system which is the largest prepaid group practice

in the United States. As an example, the subscribers of Kaiser-Permanente

reported savings of 30-40 percent per family for medical care (14). Also

with the low surgical rates and the emphasis on ambulatory care, the

number of short term general hospital beds in the Kaiser system is about

1.6 per thousand members compared to the national rate of 4.1 per thous-

and population (13).


Legislative Background


As a result of a continuing dialog concerning the alternatives to

the present health care system, health care has again entered the national

political arena. In August, 1970, Senator Kennedy (D-Mass.) introduced

the Health Security Act (15). This bill called for sweeping changes in

the national health system revolving about a National Health Insurance

which would virtually replace private health insurance. This bill also

emphasized moving the medical care system toward organized programs of

health services, with special emphasis on teams of professional, tech-

nical and support personnel, and sought to move the health system toward

PPGP.

Partially because of Senator Kennedy's bill, health care came to

the forefront of national politics and in President Nixon's 1971 State of

the Union address (6), he set forth broad proposals for improving Amer-

ica's health care. These proposals included: a national health in-

surance program; increasing the number of doctors and other health per-

sonnel; making greater use of medical assistants to slow the rise in

costs; and new programs to encourage better preventive medicine. He

later followed this up with a paper to Congress detailing his health care









proposals (16). In this report, the President was highly complimentary

with regard to PPGP and made it a cornerstone of his health care pro-

gram under the name Health Maintenance Organization. The main objec-

tive of his HMO would be to foster cost consciousness in the group

practice setting. The cost savings would arise due to economics of

scale and the use of ancillary medical personnel where possible. His

plan called for a national commitment to help HMO's get started, along

with a restructuring of private health insurance to make HMO coverage

optional. It should be noted that the Administration's HMO plans are

broad enough to include individually practicing physicians and community

health facilities, bound together by contractual and professional agree-

ments and serving the enrolled population side by side with the fee-for -

service practice (17). This type of plan is exemplified by the San

Joaquin Medical Care Foundation. The President also asked for the repeal

of laws in 22 states which either limit group practice of medicine or the

use of physician's assistants. He also called for a greater number of

people in the allied health areas to help use existing medical manpower

more effectively and the Secretary of Health, Education, and Welfare was

directed to focus research in the field of health care services on new

techniques for improving the productivity of our medical system. In

addition to the health care legislation summarized above, there have been

several other major health care bills under consideration by Congress

(18-22) and further background material is given in reference (23).


Research Viewpoint


The HMO concept has been proposed as a potential cure for a number

of problems present in the American health care system. Among the most









frequently cited of these problems are rising costs, the episodic rather

than preventive nature of health care delivery, and maldistribution of

services which has resulted in inadequate access to care in inner city

and rural areas. Numerous viewpoints on the most desirable structure of

an HMO have baen expressed by spokesmen of the Nixon Administration (17,

24, 25), the American Public Health Association (26), the American Medi-

cal Association (27) and others. These structures differ in many impor-

tant details but are sufficiently similar to generalize for the purposes

of this research.

It is assumed that the precise concept of an HIO (or whatever term

may subsequently replace it) will be in continual flux. For present

purposes the following structural elements are taken as a minimum. An

HMO is an entity which

(a) serves an enrolled population who contract

with the delivery system for provision of a

range of health services;

(b) is managed in a manner to insure legal,

fiscal and professional accountability;

and

(c) provides prenegotiated comprehensive health

services to all subscribers directly through

its own staff and supporting resources or

through other health delivery entities for a

fixed payment paid on a periodic basis with-

out regard to the frequency,extent, or kind

of service actually provided during the

period.









The basic argument for the workability of HMOs is that with a fixed

annual capitation fee it is in the best interests of both the HMO and

the subscribers to maintain each subscriber in a high degree of health

to minimize the utilization of costly services such as inpatient hos-

pitalization. Other advantages offered by HMO's are expected to be:

(a) a continuity of care through a variety

of specialists in one location;

(b) lower cost to the patient (28-30);

(c) less physician involvement in clerical

and managerial details (31);

(d) regular working hours for physicians

(31); and

(e) continuing education and peer review of

physicians (31).


Allied Health Manpower


Physician Extenders


Although there are hundreds of kinds of manpower utilized in the

delivery of health services, the patient receiving medical care is in

most frequent contact with either a physician or a nurse. Recently a

new role has emerged which is intended to supplement the physician by

relieving him of routine duties not requiring his extended training. Al-

though these persons act under the supervision of a physician,they are

not usually involved in the type of direct patient nursing care associated

with the traditional nurses' role.

As of March,1971, at least 125 programs were in operation or in









advanced planning to train persons for this new role (32). The personnel

trained in these programs are known by a plethora of names; a partial

list follows:

(a) physician associate,

(b) physician assistant,

(c) family health practitioner,

(d) pediatric nurse associate,

(e) public health nurse practitioner,

(f) family nurse practitioner,

(g) opthalmic nurse,

(h) nurse midwife,

(i) nurse anaesthetist, and

(j) family nurse clinician.

Although some of these programs are relatively well-established, most are

quite new. To avoid the multitude of names, in this research the above

personnel categories will generally be referred to as physician extenders

(PE).


Physician Extenders in Primary Care


This dissertation deals principally with the delivery of primary

care in adult medicine, OB/GYN and pediatrics. Physician extender types

of importance to these areas are discussed in this section.

There are two general types of physician extender programs evolving

in the United States. One type is typically called a physician assistant

(PA) program and is principally aimed at persons with at least a high

school education and perhaps some college education and also with prior










health care experience such as a medical corpsman. The other type seeks

to expand the role of the nurse and is usually denoted by the term nurse

plus other modifiers such as practitioner, clinician, or midwife. These

programs generally accept RN's and give them further specialized training.

There are many different types of physician assistant programs in

existence. However a general definition of a TYPE A assistant was pro-

posed by the American Association of Medical Colleges' Task Force on

Physician's Assistants Programs.

Type A, within this definition of an assistant
to the physician, is capable of approaching the
patient, collecting historical and physical data,
organizing the data, and presenting it in such a
way that the physician can visualize the medical
problem and determine the next appropriate diag-
nostic or therapeutic step. He is also capable
of assisting the physician by performing diag-
nostic and therapeutic procedures and coordinating
the role of other more technical assistants. It
is recognized that he functions under the general
supervision and responsibility of the physician,
though he might, under special circumstances and
under defined rules, operate away from the immed-
iate surveillance of the physician. To properly
perform at this level, the assistant must possess
enough knowledge of medicine to permit a degree
of interpretation of findings and a degree of in-
dependent action within these defined rules and
circumstances. (33, p. 102)

The first PA training program was at Duke University (34) and Estes

(35) pointed out that the tasks physicians perform can be divided into

those requiring the complex judgement their education prepared them for

and those that require technical skills that can be learned by repi-

tition. It is these technical skills that Duke trained the PA's to

perform,with the additional goal to prepare the PA to "do anything which

the doctor can program him to do." (36, p. 33) The use of TYPE A or

generalist PA's has also been defined and analyzed in the University of









Washington's MEDEX program (37). Ex-corpsmen in this program follow a

three-month academic program followed by a twelve-month preceptorship

that includes three days of formal education per month. The Washington

MEDEX program has been used as a model to set up MEDEX programs in many

other universities (34). The use of ex-corpsmen as input to the PA

programs has to be considered as temporary due to the reduced future

supply of corpsmen; thus if PA's are to become a standard part of the

health care system, people without previous medical experience will have

to be trained or an increased number of nurses could be admitted to PA

programs (34).

An important example of the nurse expander type program is the

pediatric nurse practitioner (PNP). The first formal training program

was established by Silver and Ford (38) in Denver and since then the

American Nurses Association and the American Academy of Pediatrics have

issued a joint statement defining this concept and established guidelines

for programs of continuing education (39). Twenty-four training programs

for PNP's were listed in July 1971 (40). At the University of Colorado,

the PNP is a graduate nurse with a baccalaureate degree who has received

four months of intensive theory and practice in pediatrics at the Uni-

versity of Colorado Medical Center (41). During their training, emphasis

is placed on patient interviewing techniques, performing a complete phy-

sical, various aspects of parent-child relationships, child development

and counseling techniques (41). They also learn to assist in both the

management of healthy children and those with a variety of acute and

chronic disorders (42).

Another major category of the expanded role of the nurse is the









nurse midwife (NMW). According to the American College of Nurse Mid-

wifery definition, the NMW is "a registered nurse who, by virtue of her

added skill gained through an organized program of study and clinical

experience, recognized by the American College of Nurse-Midwifery, has

extended the limits of her practice into the area of management of care

of mothers and babies through the maternity cycle so long as progress

meets criteria accepted as normal." (43, p. 354)

Although there are many other types of training programs for many

medical specialties, the PA, PNP and NMW programs were specifically men-

tioned due to their involvement in the primary care areas: PA's are

usually trained to assist general practitioners or physicians in internal

medicine; PNP's are trained to assist pediatricians; and NMW's are

trained to assist physicians in 0B/GYN. These are the three primary care

areas focused on in this peper. Since many of the programs produce health

care providers with different titles but very similar capabilities, this

will be simplified by referring to all as PE's and recalling the three

primary care prototypes described above.


Physician Extender Utilization: The Team Concept


Utilization of auxiliary personnel in primary medical care delivery

is usually done in the context of a "health care team." At present,

tradition, licensing, registration, and practice act restrictions dictate

that the auxiliary personnel be supervised by an MD (44-51). Although it

is likely that this configuration will continue for some time to come,

some research (52) has been directed toward family health teams for HMO's

that are totally comprised of allied health personnel. Granting more









autonomy to allied health professionals raises questions of professional

acceptance, legal accountability, and patient acceptance. In recogni-

tion of these issues the AMA (27) has called for more research into the

questions of which type of assistant to develop, the tasks they can

assume, their acceptance by patients and physicians, and their impact on

costs and productivity.

This dissertation will explicitly consider three health care team

configurations:

(a) a team comprised of a physician, an RN, and

possibly an LPN;

(b) a team comprised of a physician extender,

an RN, and possibly an LPN; Pnd,

(c) a team comprised of a physician, a phy-

sician extender, and an RN.

A PE in the second type of team noted above would be acting under in-

direct supervision by an MD. Under that configuration the MD would

typically confer briefly with the PE regarding the patient and the PE's

findings, or the MD may briefly see the patient and read over the PE's

findings. In the third type of team, the PE would be acting unaer direct

supervision. This would not necessarily imply that the MD is in the room

at all times with the PE. However, it does imply that the MD has direct

control over the particular patient visit. The PE would typically take

the patient history and perform a preliminary workup or physical exam.

This portion of the visit is time consuming and does not require the

highly developed skills of the MD. The MD would then take these find-

ings and carry on from that point with the patient. It's possible the

PE would later be used to carry out tests, a treatment regimen, or to









explain a home treatment regimen to the patient.


Delegation of Medical Services


The question of which functions can be carried out by a physician

extender is at the core of the problem of PE utilization. For the pur-

poses of this study, a broad definition of the PE types is not enough to

fully analyze potential PE utilization. A more detailed answer of what

allied health personnel are prepared to do and what professional per-

sonnel are prepared to delegate to them is required.

Although the use of PE's is relatively new in the United States,

there has been considerable use of similar level personnel in other

countries. As far back as the 1700's "feldshers" were functioning in

Russia (44). In urban areas the feldsher works as an assistant to the

physician but in the rural areas the feldsher frequently performs in a

primary care role (53). An even more striking example of the utilization

of allied health personnel exists in China. China has several levels of

assistants for the physicians. One level of assistant, with a limited

formal training of about three months and on the job training, provides

certain elements of primary care in rural areas and another level is

typically comprised of housewives with ten or more days training who

work on a neighborhood level (54). With regard to health care teams,

a professor of orthopedics in China noted:

In the countryside--and I am sure this will
cause eyebrows to be raised--we made no distinction
between nurses and doctors....In fact, doctors and
nurses were in essence doing the same job to the
best of their abilities, and their abilities de-
pended as much on their adaptability and sense of
responsibility as on the type and duration of
training which they had undergone.(55, p. 192)









In Cuba, the nurses routinely give intravenous injections and make house

calls (56). In many other countries (most but not all are developing

nations) paramedical aids are an integral part of the health care system

(57-60).

However, within the United States the organized use of personnel on

the PE level is relatively new. As a consequence there has been some

uncertainty as to their possible function and the specific training pro-

grams needed. Since PE's will perform in a subsidiary capacity, several

surveys or studies to elicit the opinions of physicians have been per-

formed (33, 61-71). In a survey of 3,425 internists the American Society

of Internal Medicine found that internists believed many elements of their

practice could be delegated to an allied health worker (61). The Amer-

ican Academy of Pediatrics surveyed 5,799 pediatricians and found that

over 70 percent favored delegation of recording the patient history and

counseling on child care, feeding and development (62). About 25 percent

favored delegation of well child and sick child examinations. It has also

been reported that 50-65 percent of the physicians in Wisconsin indicate

a need for a physician assistant (63). Patient acceptance has been good

(64) and over 50 percent found the care provided by a pediatrician and

a pediatric nurse practitioner better than that received from a phy-

sician alone (65).

The major problem involved in utilizing the studies noted above is

their lack of a common medical classification system upon which dele-

gation can be analyzed. The studies used tasks, functions, services,

procedures, typical patient visits and sometimes a combination of these.

However, the modeling effort in this dissertation requires a single

consistent classification system in which delegation can be analyzed.









There are many classification systems for medical patients but unfor-

tunately few are useful for analysis of manpower and delegation decisions.

The most widely known is the International Classification of Diseases,

Abstracted (ICDA) but it is of more use in hospital admissions where

diagnosis is a feasible classification index. The California Relative

Value Units (CRVU) are also used to some extent, but it is too vague in

the area of patient office visits. There are several compilations of

tasks performed in the health care system (71, 72), but tasks do not lend

themselves well to viable patterns of delegation and analysis.

Instead of the above methods of medical classification the concept

of a medical service or typical patient visit will be used in this study.

This concept allows the model to concentrate only on viable patterns of

delegation, simplify the computational details and increases the in-

tuitive appeal of the results (73). Previous medical service listings

have been reported for general practice (73) and for the primary care

specialties (74). Since the former is limited to general practice and

the latter is too general, a new medical classification is presented in

Chapter 4 which enables the analysis of the relationship between train-

ing, delegation and manpower utilization to be fully explored.


Motivation for Mathematical Modeling


Previous Studies


Formal PE programs were started in the United States only a few

years ago. As a result there have been few studies which have analyzed

the use of PE's. Likewise the HMO proposal was first introduced in 1970

and also suffers from a lack of analysis. In both areas, discussions









regarding the concept behind paramedical personnel and HMO's are rela-

tively plentiful and,while these studies have guided the overall goal

of this paper, they do not provide a concrete basis on which to start

an analysis. However, there have been several exploratory studies per-

formed which are fairly directly related to the goals of this paper.

The research most useful to review was performed by Shuman (75,

76), Golladay, Smith and Miller (73), Reinhardt (77), and Gnldstein and

Horowitz (78). This collection of studies is of particular interest

since they represent the spectrum of techniques which have been used to

analyze health manpower usage. Shuman and Golladay et al. arrived at

totally different normative mathematical models to analyze manpower util-

ization, while Reinhardt used a descriptive model in the form of pro-

duction functions to analyze the increased efficiency resulting from the

use of paramedical aides. On the other hand, Goldstein and Horowitz took

a personnel management approach to increasing manpower efficiency in a

hospital. Each of these will be discussed in greater detail in the

following paragraphs.

Shuman's work dealt mainly with regional health manpower planning

and the substitution between various personnel classes. Both papers by

Shuman are of interest but since the aspects essential to this study are

contained in (76) only the latter work will be reviewed. Shuman con-

siders three ways by which productivity may be increased: introduction

of technology, transfer of tasks to less skilled personnel, and organi-

zational changes. A key point he makes is that the manpower problem is

part of a larger problem: the determination of an efficient means for

the delivery of health services. Only then can it be determined whether









shortages actually exist for MD's, nurses or allied health personnel.

This rather straight forward point has been largely neglected in most

manpower studies and casts doubt on many of their conclusions. In other

words the emphasis should be on the shortages of health services not on

a manpower shortage. Starting with this insight into the problems in the

health care system, Shuman then formulated an analytic model to attempt

to determine the proper mix of manpower to provide the services. Shu-

man's work was one of the first attempts to model analytically the

problem and consequently there are many problems left unanswered. The

principle shortcomings revolve around the size of the model as it is

structured and the lack of data and manpower analysis contained in the

study. Several aspects of Shuman's models are discussed in Chapter 3.

Golladay, Smith and Miller (73) investigated the optimal role for

paraprofessionals in the health care system and their potential impact on

the productivity of the physician. The study developed an analytical

model of primary care practice which enabled them to explore the impli-

cations of delegation for physician productivity, per patient costs,

and demands for all categories of medical workers. The most unique

feature of the study involved the data collection for task analysis in

medical practice. The analytic model was derived to answer these ques-

tions:

1) what is the optimal staffing pattern for a

practice and how is it related to the size

of the patient population;

2) how many hours of patient contact time would

be required to satisfy the medical demands

of a specified patient population; and,









3) which activities would be delegated in an

efficiently run practice?

Their model is described in Chapter 3. Golladay, Smith and Miller con-

cluded that

1) use of one PA may increase the productivity

of a physician by 74 percent; and

2) from a monetary standpoint, MD's would

profit from using PA's.

In contrast to the normative models proposed by Shuman and Gelladay et

al., Reinhardt derived a descriptive model utilizing a production function

approach. This type of approach is the most common quantitative technique

used to analyze manpower utilization and is frequently used by econo-

mists. Reinhardt set out to answer two questions:

1) to what extent is it possible to raise the

output per physician hour through use of

paramedical personnel; and

2) can physicians in group practice use aux-

iliary personnel more efficiently than

physicians in solo practice?

His conclusion was that MD's should employ 3-4 aides rather than the 1-2

aides they now employ and that this would increase medical production by

20 percent. He also concluded group practice resulted in 11 percent to

16 percent higher production per MD than solo practice. Note these fig-

ures are conservative since they represent the use of allied personnel

in 1965 and 1967 and not an optimal or even near-optimal task delegation.

His work does however firmly lead to the conclusion that allied personnel

will lead in practice to increased medical care production.









Goldstein and Horowitz used personnel management techniques in an

attempt at better utilization of medical manpower. Their study involved

establishing what tasks were performed in the hospital, what training

level was required to perform each of the tasks and what level personnel

were presently performing the task. The two major goals of the study

involved:

(1) study and analyze the hiring-in requirements

and the duties and functions of paramedical

personnel in a single hospital; and,

(2) to recommend changes to restructure occu-

pations and to improve the utilization of

manpower in that hospital.

Their study did not attempt any optimization but it did result in concrete

recommendations for better utilization of manpower. It is also an ap-

proach that is intuitively appealing to many people including those who

have an inherent distrust of mathematics and model building. Its prin-

cipal drawback is that it relies upon studying a well established insti-

tution such as a hospital in order to arrive at results. It also limited

itself to reshuffling tasks paramedical personnel perform, and not sub-

stituting paramedical personnel for MD's.


Systems Analysis as an Aid to the HMO Design Process


The approach taken by Shuman, Golladay et al., and Reinhardt and the

approach taken in this dissertation can be termed systems analysis. Sys-

tems analysis has been described by Kershaw and McKean as the "comparison

of alternative means of carrying out some function, when those means are

rather complicated and comprise a number of interrelated elements."









(79, p. 1) The essential feature of a systems analysis is thus the rec-

ognition of the interrelatedness of parts. The system should be defined

so as to encompass all parts that are related in a significant fashion

(79).

An HMO is a system that consists of staff, facilities and materials

and is organized to deliver medical care. However, the output of the HMO

is difficult to quantify. It can be argued, for example, that the out-

put of a medical system should be measured in terms of the improvement

or stabilization of the health of the patients. In practice however,

this concept is extremely difficult to apply and in this dissertation

the output is measured in terms of medical services provided. The math-

ematical models will allow an analysis of the interrelated factors to be

performed and will allow the examination of the substitution of various

alternative resource combinations. In addition to manpower, the models

should also permit the analysis of the effects of automation and tech-

nology upon output. An approach to incorporating technology into the

models is discussed in the next chapter. Although extremely important,

questions on the quality of care provided and the effects of alternative

system configurations on the general health of the population covered

are considered to be beyond the scope of this dissertation.


Planning the Benefits To Be Provided by an HMO


There are two basic approaches to examining the choice of services.

The first approach (see Figure 1) is the traditional method which is most

commonly proposed. This technique assumes that legislative groups in

consultation with various health personnel will decide what services an

IIO should provide. The principal weakness is that it is a decision made









without regard to the other variables in the planning process. Note that

Figure 1 denotes a system with no feedback loops.



Begin Local Services Staff Facilities Finish
Planning Inputs to be Required Required Planning
Offered



Figure 1: Present Decision Process
for Determining Benefits


The second approach recognizes the problems attendant to legislating

the variety of services an HMO must offer. This approach leads to the

best array of services tailored to the local situation (see Figure 2).

For example, it may be too expensive in a rural area to offer specialty

care to HMO subscribers, but at the same time an HMO might possibly pro-

vide many other services at a lower price and comparable quality than can

be found in the traditional mode of health service. The models are de-

signed to formulate a set of services based on the available capital and

on the level of fees the patients are willing to pay. The services of-

fered naturally depend very heavily upon the population base since a

large HMO, through economics of scale, may be able to offer many spec-

ialized services in an economical manner, whereas a small HMO may under-

utilize the manpower and facilities for that service, thereby making it

more expensive than the traditional system.

Services -- Staff

Begin Local Inputs tFs Finish
Planning Facilities Planning


Figure 2: Proposed Decision Process
for Determining Benefits









The models are designed such that they can be useful in the pro-

posed decision process depicted by Figure 2. The individual medical

services used in the models are detailed enough to distinguish between

time requirements and training requirements. Sets of these services can

be considered for the various medical specialties and the models are de-

signed so that the specialties can be included or excluded from the HMO

depending on economic factors. The models also allow the decision maker

to fix some or all sets of services as necessary for provision in the HMO

due to political or other conditions.


Proposed HMO Design Process


This research assumes a three-level hierarchy in the design of an

HMO (see Figure 3). The first level describes the financing, social

characteristic, incentives, generalities and overall objectives of HMO's.

This is the level that is most frequently discussed in the literature.

The second level deals with HMO's on a more specific basis. This level

of decision making would be concerned with the size of subscriber group,

levels of technology, general personnel guidelines, capitation rate, re-

lations with hospitals, etc. The third level examines NMO's on a micro-

scopic level. The decision on this level would be concerned with the

type and number of various personnel classes, specific technology utili-

zation, task allocation, patient flow, etc.

This three-level hierarchy completely specifies the design of an

HMO. Because the models developed in this dissertation can best be used

to analyze levels two and three they are presented as a systematic

technique to decision making on these levels.









Legislation
Level 1 Financing
Social Characteristics
Overall Objectives








Size of Relations
Level 2 s Services Personnel Capitation with
Level 2 MO's Guidelines Rate t
Hospitals







Specific Number of Specific Assignment
Level 3 type of each type Technology of Services
Personnel of Personnel Utilization
Needed



Figure 3 Three-Stage Hierarchy in the Planning of IMO's


Figure 3 showed the relationship which exists between the levels of

decision making for planning an HMO. Figures 4 and 5 present the dynam-

ics of the decision process. Figure 4 presents an approximation of the

dynamics involved in the present HMO design concept while Figure 5 pre-

sents the dynamic relationships which are modeled in this paper. Note

that Figure 5 portrays the strong interaction which exists between sub-

systems of the HMO while Figure 4 shows a weaker interaction which occurs

in the present design process.

As was noted previously, the research effort is primarily aimed at

effective manpower utilization. However, as Figure 5 shows, the manpower

utilization is strongly interactive with the other subsystems of the HMO.




















(t
ob
JC -


E



-4

p..












These other subsystems will be examined only as far as is needed to

perceive their input to the mathematical models. The optimal design, or

even design, of these other subsystems is beyond the scope of this re-

search.

In the next chapter, models are developed which will permit the

evaluation of alternative designs of 1MO's. To examine the design of

HO1's, three measures of effectiveness are utilized and developed by the

mathematical models:

1) minimizing cost to the subscriber;

2) using the least number of professional

manpower to serve a given set of sub-

scribers (and maintain quality); and,

3) using a given set of professionals such

that the number of services they provide

are maximized.

Using these objectives, the models can help optimally design certain

aspects of the HMO. Thus, they can be used to present design guidelines

and enable one to perform sensitivity analysis on the inputs.















CHAPTER 3


DEVELOPMENT OF ANALYTICAL MODELS



Preliminary Models


Introduction

In this chapter several models are proposed to answer some of the

questions which arise in the overall design process for HMO's. These

models are designed to represent a useful formulation for part of the

HMO system and to be solvable in a practical sense. Each of the models

involves the assignment of personnel to services and the staffing levels

required. Beyond this, the models can be dichotomized as:

(a) maximize subscribers by optimal allocation and mix

of professional manpower and facility resources,

and ancillary manpower, or

(b) minimize resources used to provide a fixed set of

services or requirements.

Initially, a very simple model is derived. A step by step motiva-

tion and refinement is then carried out; culminating in a more complex,

but more flexible and refined model. The complex model is then used to

derive four other principle models. Throughout the development new

notation will be introduced in the text; additionally, a complete listing

is given in the Key To Symbols.









System Schematic for Model Development

A recurring HMO theme, as expressed in the literature noted in the

first two chapters, is the cost-effectiveness through utilization of

group practice and the capitation incentives. To examine the cost-

effectiveness of HMO's one must examine the costs in the IMO structure.

A schematic of the structure of an HMO is given in Figure 6.





HMO





INPATIENT IC DENTAL
VISITS





MEDICAL CLERICAL ADMIN. LAB X-RAY OTHER ANCILLARY

REFLECTED BUT NOT EXAMINED


Figure 6 A Schematic Representation of the O10 Structure



The inpatient care and dental care portions of an HMO are major

problems in themselves and can be effectively isolated from the analysis

of office based medical care. This does not imply there are no relation-

ships between inpatient and ambulatory care, but only that the relation-

ships can be handled external to this analysis. For example, an increased

use of ambulatory care usually occurs in prepaid practice due to the

decreased use of inpatient facilities. However since utilization of

ambulatory care is an input to the models, this increase can be noted









and used to determine the input to the models which would then reflect

the ambulatory care manpower and costs resulting from the increased use

of ambulatory care facilities. Also, within the O10 structure there are

additional functions other than the medical care function. There are

support personnel, such as clerical, administrative, laboratory, x-ray,

and other ancillary aides, and management personnel for planning and

direction and these functions are reflected in the models. The models

focus on medical manpower, but to look at overall cost-effectiveness the

models should reflect the costs of non-medical care functions for two

principal reasons:

(a) to examine the effect the costs of these non-medical

functions have on the medical manpower; and

(b) to examine the full costs for medical services and

lIMO's as a whole (excluding inpatient and dental).

Within the medical care structure there are two main factions-those

who subscribe to the plan for medical services and those who work for the

plan and provide medical services. This is shown in Figure 7.




Demand
REQUIREMENTS: Subscribers serce
for services
Services
Provided

Medical Capability to
RSOURC: Personnel provide services


Figure 7 Medical Care Structure Showing Relation
Between Resources and Requirements









The upper loop must be expressed in some taxonomy of health care

delivery while the lower loop must be expressed in manpower types and

capabilities. In addition, to be combined in the last block, the man-

power capabilities must be expressable in terms of the taxonomy of health

care delivery. This is an extremely difficult concept to put into prac-

tice. In previous related studies Golladay, Smith and Miller (73)

approached this empirically for a small sample, Pondy (81) took a related

but more superficial approach and Shuman (76) did not attempt to put the

concept into practice.


Tradeoff Decisions To Be Incorporated in the Models

Chapter 2 presented a detailed view of IMO's and health manpower

and resulted in a systems viewpoint of the interactions between the two.

Figures 6 and 7 further helped to sharpen the focus to the point where

mathematical models could be developed. At this point the particular

decision making areas to be considered in the models will be explicitly

stated. When normative mathematical models make decisions, they make

them by trading off resources and requirements against each other in such

a way that the objective function reaches its extremum. The constraints

act to complicate the decision making to the point where mathematical

programming techniques must usually be used to solve the problem.

As a result of the systems development it has been determined that

several factors are important and should be considered by the mathemati-

cal models in their decision making. The major tradeoffs that are incor-

porated in the minimum cost models are summarized below.

1. The models tradeoff delegating a service to the lowest

cost person (who can perform the service) versus the

additional cost of supervision by the MD.









2. The models tradeoff delegating a service to the lowest

cost person (who can perform the service) versus the

supervision time required from the MD. Since supervision

time is usually a scarce resource this implies also

selecting those services to be delegated as well as to whom

to delegate the service,

3. The models tradeoff the cost of providing a service by an

MD and nurse versus the cost of providing the service by

an MD, PE and nurse versus providing the service by a PE

and nurse. In the second case, MD time decreases but MD

plus PE time is greater than in the first case. In the

third case, MD time for the service becomes zero, but

additional MD time is required for the indirect supervi-

sion of the PE.

4. The models tradeoff the cost of higher cost personnel

versus the integer restrictions on manpower levels. Thus

for example, if delegating a service that requires .2 man

years would require that one more PE would be hired with

the subsequent .8 man years of idleness; it may be better

to delegate the service to another, perhaps higher salaried

person.

5. The models tradeoff the total cost of a service in the HMO

versus what it can be purchased for outside the IN0. Note

that the total cost for a service in an HMO is interrelated

with all other services offered. This tradeoff can be









done on a service by service level or on a medical

specialty level.

6. The models tradeoff the cost for additional technology

versus the higher productivity or lower salary levels

required.

Only the major factors have been included in the tradeoffs summarized

above. There are other subsidiary factors such as capital requirements,

capability limitations, and scarcity of manpower that are potentially

involved in most of the above tradeoffs.

This chapter also includes models concerned with the minimal use of

MD's or for maximizing subscribers per MD for which the six tradeoffs

listed above are still relevant, but the key is minimal use of MD time.

In some cases the two give the same result, but there are many exceptions.

In addition this latter type of model includes two additional factors:

(a) as subscriber levels increase this means that more

patient visits are eligible for PE's to handle; and

(b) a budgetary limit is imposed, thus there may be ways

to add additional subscribers but they would be too

costly (in the models this is taken as the revenue =

expenses point not the marginal revenue = marginal

expenses point).

The above tradeoffs are explicitly designed into the models. There

may be other types of tradeoffs made depending on the exact use of the

models or the data used for solving the models, but these additional

tradeoffs are expressable in terms of the above tradeoffs.









Preliminary Model Development

Figures 6 and 7 represent two different but related structures in

the HMO. Figure 6 diagrams what could be viewed as a cost structure

while Figure 7 diagrams a medical care structure. On the most elemental

level Figure 7 could be modeled by viewing the subscriber demands as the

requirements vector and the medical personnel as the resources. Two

objectives present themselves for this model:

(a) minimize the medical manpower needs for a given

number of subscribers; or

(b) maximize the subscribers for a given number of

medical personnel.

The first objective takes the requirements as fixed and the resources to

be variable while the second objective is the converse of the first.

Use the definitions:

I set of medical personnel of type i,

I* set of MD's,

I* set of non-MD's,

J set of medical services of type j,

xij manpower type i performing service j (man-years),

d. demand for service j (medical services per year),

b.. rate at which manpower type i produce service j (medical

services per man-year),

N. number of manpower type i employed (man-years),
1

s. salary for type i personnel (dollars per year),

i=
i iel

S= e
J jeJ









With these definitions we can meet the medical care requirements with

the constraint



Z b..x.. > d. jeJ. (3.1)
i 1i 13 3


We can also define the number of manpower type i employed as



E x..-N. < 0 V icl (3.2)
S131 1
j i


and the first objective becomes


min Z N. (3.3)
i

or if constraint (3.2) is not used we have


min S x.. (3.4)
i11


The model given by (3.1) (3.4) will be called M1 and is a linear

programming model which essentially characterizes the models used by

Golladay, Smith and Miller (73) and by Pondy (81). To arrive at the

Golladay, Smith and Miller model the converse of the b.. coefficient is

used. The b.. coefficient in (3.1) converts resources to activities
13j

while Golladay, Smith and Miller use a coefficient in constraint (3.2)

to convert activities to resources. This allows them to define health

care teams or technologies in a straight forward manner but has the

undesirable property of forcing the inputs from each member of the team

to occur in fixed ratios-to change the ratios a new team must be defined.

In addition Golladay, Smith and Miller take the MD input as fixed and

seek to minimize the salary of ancillary personnel as their objective.









This places weighting factors in equation (3.4) and the summation is

taken over those i for non-MD's and constraint (3.2) is eliminated for

non-MD's. The resultant model (where k is the team or technology) is:


min E E siaikx (3.5)
iEl* k

subject to

Saikxk i N V iEI* (3.6)
k

E xk = n V jEJ (3.7)
kEK.


The Pondy model is very similar. Both can be efficiently solved as a

minimum cost network flow problem with nonnegative gains (80).

Thus both the Golladay, Smith and Miller model and the Pondy model

follow directly from the elementary constraints on resources and require-

ments. This structure does not allow a full exploration of the relation-

ship expressed in Figure 7. It also ignores the cost structure in which

the medical system operates. It can be noted that both models were

primarily focused on the fee-for-service setting.

The model resulting from the second objective easily follows if the

following definitions are made. Let

S number of subscribers,

d' services of type j demanded per subscriber.
J
Here the resources are fixed and the requirements are variable. Thus

the model is:

max S (3.8)









subject to

x.. Ni ieI (3.9)



Sb..xij d! S < 0 jeJ (3.10)
i 13 3j J -


This model arises from the implication that the present shortage of

medical manpower is an overriding concern in the health care setting

and thus seeks to provide medical care to the most people given the man-

power available. No corresponding model appears in the literature. The

weaknesses are the same as were noted above and in addition this model

ignores the economics of medical care entirely.


Development of the Medical Care Aspects of the Model

Several general weaknesses of the Ml model have been pointed out.

At this point the model will be developed further along the scope of

Figure 7. This further development will lead to a model which exhibits

greater flexibility and depth in its portrayal of prepaid group practice.

The concept of minimizing medical manpower cost will be used.

Medical care is provided either by individuals or by teams. Within

a health care team the leader would typically be an MDi however,teams of

PE's and nurses are also possible. In the former case, direct supervi-

sion by MD's is implicit within the team. However, in the latter case

indirect supervision by physicians would normally be required. The

Golladay, Smith and Miller model (73) and Pondy model (81) explicitly

consider teams but do not consider the latter problem. On the other hand

a model proposed by Shuman (76) considers indirect supervision but not

teams. With the following definitions, model Ml can be revised to pro-

vide the needed generality.









Let

I set of individual health care personnel,
It set of health care teams,
I set of manpower including teams,

qkij man-years of manpower type i per man-year of team k
providing service j,


k kIt '
-* t
I= I I v I

The particular introduction and definition of qkij is the key to the

generalization of the model. Using that definition (3.1) and (3.4) are

unaffected. The only change occurs in (3.2) which becomes


ij + s kijxkj Ni 0 V iel (3.11)
j kj


In addition, a method to view indirect supervision must be introduced,

not only for PE-nurse teams but also for PE's or nurses in an individual

capacity. This concept, as used by Shuman (76), provided for fixed

supervision levels regardless of the service being performed or the

health care personnel involved. The constraint can be modified to

reflect these considerations by defining:

f.. level of independence for type i personnel to perform

service j; fj = 0 implies no indirect supervision required

while f.. = 1 implies full indirect supervision,
*
Ji* set of services class i el personnel supervise,

xi*j* j* is the supervisory service provided by personnel i

The supervisory constraint involves the quality of health care in that

it constrains the number of personnel a professional staff member may

supervise and the level of independence exercised by the paramedical

assistants. The general supervisory constraint is given by









S E f..bx.. Sj bi j bi*j*xi*j* (3.12)
jeJi* iCI* 1

It is generally accepted that MD's do not want to be burdened by an

excessive amount of administrative work or supervision of ancillary

personnel. The amount of supervision can easily be limited by making

x i** an upper bounded variable which would not make the model any more
i*j*
difficult to solve. Thus, if SU. is defined as the maximum fraction of
1
time type i personnel will engage in indirect supervision of ancillary

personnel, the upper bound is given by

xi*j, < SUi'N. V i*cI* (3.13)
ij* -- i 1


Thus far the model is specified by (3.1), (3.4), and (3.11) (3.13)

and a further tightening up on the definitions of resources and require-

ments is desirable.

The resource considered thus far in the model is the available

health manpower. Since an HMO has as a principle objective the delivery

of effective health care in a cost-conscious manner, the resource should

in many cases be evaluated in monetary terms. Also, the resources used

here represent health care employers; thus in many cases the employees

will be full time employees only. This constraint is usually beneficial

to both the employee and the employer. Full time employees can be

represented by integer variables in the model. Thus, let Ni be defined

as an integer variable and define

x! fractional part of personnel group i which are slack or

idle (man-years),

c.. labor cost for type i personnel or team to perform one type

j service (dollars per medical service).









The result is


c.. = s./b.. V
i1j i ij


cij = I/bijnCls S n inj
neI


iIs ,


ti
9 iCI


Also let


b = units of time worked by team leader/year
ij units of team leader time/medical service


An example will help to clarify the meaning of these terms and

their relation to qkij. Suppose for service 1 the time and personnel

requirements are as listed in Table 1.


Table 1 Example of Personnel and Time Requirements


personnel


M.D.

R.N.

M.D. and R.N.


time to perform service 1 (min.)


10 (M.D.) and 5 (R.N.)


Also suppose an M.D. works 1440 hours per year in office visits and the

R.N. works 2000 hours per year. Then if the M.D. is designated the team

leader:

b3 = 1440/10/60 = 8640 services/year, and


q311 = 1, and for the RN,


q321 = 5/60 8640/2000 = .360


If the MD's salary is $30,000 and the RN's salary is $10,000 then the

direct labor cost per unit of service is given by


(3.14)










c31 = (1/8640) ((30,000) (1) + (10,000) (.360)) = 3.89


Returning to the development of the model, recall the objective is

to minimize the labor cost for all services provided which is given by


min s S (b. ic. ) x. (3.15)
j i 1( 1J 13

Incorporating the integer manpower constraint for N., constraint (3.11)

becomes

E x.. + E r qkij + x! N. = 0 V ieI (3.16)
Sj kj 1

and the objective becomes

min ES (b.i.c.) x.i + S s.x! (3.17)
j i ij 13 i I I

Note that the objective can be written as

min E s.N. (3.18)
icis L I

but for clarity it will be written as the two terms in (3.17).

It is also possible to generalize and refine the requirements con-

straint which is given by constraint (3.1). Physically, it is impossible

for an HMO to deliver more services than are requested by the subscribers.

It is however possible to deliver fewer services than are demanded but

this would not be consistent with the concept of prepaid practice. The

remaining possibility is that some health services be provided by

extraordinary means. Thus a new variable n. can be defined as

n. number of type j services demanded per year and not
provided by ordinary means.
provided by ordinary means.









This can be incorporated in constraint (3.1) to give


E b..x.. + n. = d. V jeJ, j#j* (3.19)
i i


The n. variable has several possible interpretations within an HMO

structure. In a multiclinic HMO it may be desirable to schedule some

patients into a more heavily staffed clinic during peak periods.

Another interpretation is that the HMO may contract out to other health

care providers for their overload patients. A third possibility is that

the n. represents those services performed on an overtime basis due to

understaffing. A fourth possibility is that the n. can be used as a

planning variable to determine if the HMO should provide the service or

if it can be provided cheaper to the subscribers outside the HMO. This

alternative will be developed later in the chapter.

Several restrictions must be placed on the n. variable for reason-

able solutions to arise from the model. To develop these restrictions

define the coefficients:

u. per unit cost for provision of type j services by

extraordinary means, and

MX. maximum fraction of services provided by extraordinary

means.

Constraint (3.19) shows the requirements can be provided by n. which has

no cost in the objective function. To rectify this, (3.17) can be modi-

fied to give


(3.20)


min E (b..c..) x.. + E s.xx + E u.nn .
i ij i j









In addition from a standpoint of convenience to the patient and paper-

work problems for the 4MO it is desirable to limit the services to be

provided by extraordinary means. This can easily be included in the

model using an upper bound constraint


n. < MX. d. V jeJ (3.21)


MX. can be set to zero if all patients are to be seen under normal care

for service j or set to non-zero if it is feasible to use one of the

extraordinary means listed above. Typically MX. would range from 0.0-0.1.

The modified model, to be denoted M2, is summarized below:


min S S (b..c..) x, + s.x! + E u.n. (3.22)
i i i j

subject to

S s fij..b.i.ij b i*eI* (3.23)
jeJi. iC* J


E xij + S Z q kijkj + x! N. = 0 I ieI (3.24)
j kj k


E b.jx + nj = d. j j j* (3.25)
i 13 iJ 3 3


x.j.j < SU N. i*el* (3.26)


n. < MX.- d. f jeJ (3.27)



This model allows for a much fuller and more general representation of

the system represented by Figure 7 than model Ml. If Ni is not

restricted to integer levels, M1 and M2 are approximately of the same

order of difficulty for solution purposes. If N. is restricted to









integer levels the result is a mixed integer program which is more diffi-

cult to solve than the linear program required for model Ml.


Further Development of Financial Aspects of the Model

Thus far the financial aspects of the HMO have not been fully

investigated. Health manpower costs have been considered, but they

represent less than half of the total cost in an HMO. This fact in

itself provides some motivation to include the remaining costs in the

HO0 model. In addition, an objective of the model is to determine the

cost of medical service. This determination will involve the cost of

particular medical services, the costs by specialty or department, and

the cost for the entire clinic or HMO. To further develop the model

along the concepts expressed in Figure 6 it is necessary to examine

manpower overhead costs, facility overhead costs, ancillary costs, the

fee structure and the technology cost.

An HMO will in most cases be organized in departments along medical

specialty lines. Thus it may have an adult medicine, pediatrics, OB/GYN

and other specialty departments. This departmentalization and ready

access for patients to any department leads to little overlap in the

functions carried out in the various departments. Model M2 did not

reflect any departmental structure, but this will now be corrected.

Define:

V zero-one decision variable; if V = 1 department m is offered
m m
and if V = 0 department m is not offered;

mm
M set of all medical departments under consideration;

Im set of personnel in department m;









J set of services considered for provision;

let J = (1,2,...j1* l,jl*'. mJ* ...j*) where j* is the
1 1 r-i m m
supervisory service provided by set I* personnel to supervise

set I* personnel in department m;

J' subset of J for which V = 1;
m
Jm set of services considered for provision or to be provided in

department m.

Thus
J = (U Jm)U( V j*)
m m


The V variable can thus be used as a decision variable to decide whether
m
it is economically desirable to include a department in a clinic or in

an entire HMO or whether these services can best be obtained elsewhere.

If the decision is to not include the department in one clinic this would

be provided at the central YZ0 facility. If an entire HMO decided not

to maintain a given department, they could contract out to another health

care provider or remove that service from their list of benefits. If the

departments are fixed, then the V can be set to zero or one, which in

turn makes the model easier to solve. The V variable must be introduced
m

in (3.22), (3.25), and (3.27) which respectively become


min E Z (b.ijci) xij + S s.x!
J3ij i 1

+ E (1 V ) S d.u. + u.n (3.28)
m m J j J


E bi x. + n. d.V = 0 V jeJ, j#j* (3.29)
jij i m


. < MX. d.
3-- 1 J


V jeJm, meM (3.30)









Standard accounting practices lead to the dichotomy between revenue

producing cost centers and non-revenue producing cost centers. Since

services are offered on a prepaid basis no medical department is strictly

a revenue producing cost center. However, there is still a clear dis-

tinction between the direct services performed by the medical departments

and the indirect services performed by the administrative, clerical and

managerial personnel. The position of ancillary services such as labora-

tory, x-ray, physical therapyetc.,is not as clear. In the development

of the cost model there will be three main overhead cost categories:

manpower overhead costs, facility overhead costs, and ancillary costs.

The costs for these functions will be reflected in the model but an

optimization of these functions will not be carried out.

There are three basic variables used to allocate overhead costs to

the revenue cost centers: departmental services performed, departmental

budget, or number of departmental employees. For the purpose of defining

the model the manpower overhead costs are broken down and allocated in

three basic parts:

(a) medical records, membership, appointments, etc. (allocated

on basis of patient visits to department);

(b) management, planning, legal, etc. (allocated on basis

of FTE professionals in a department); and

(c) personnel, administrators of employee benefits, etc.

(allocated on the basis of FTE employees in a department).

With the above guidelines, define:

AD manpower overhead or administrative cost for department m

(dollars per year),









PV manpower overhead cost per patient visit (dollars per

patient visit),

MAN management and planning cost per FTE professional (dollars

per man-year),

PER personnel cost per FTE employee (dollars per man-year),

b* number of type j services type iCI* personnel can perform

per year for a given level of technology.

The FTE professionals needed to provide medical services for a depart-

ment is given by

FTE = (V n )/bt (3.31)
m jem m J j

which can then be used to define the manpower overhead costs for the m

department

AD = PV E Z b..x..
m jeJm ieIm 1


+MAN E (d.V n.)/b* + PER N. (3.32)
jeJ m ilm

This cost can now be included in the objective function to give


min E (bijci.) x.i + E s.x! + E ujn.
ij 113 13 i 11 3j

+ E (1 Vm) m d.u. + AD (3.33)
m jeJ m

For this study, general office equipment and fixtures are included under

plant operations and maintenance or under construction or rental cost and

the equipment cost category has been reserved for medical equipment.

Since facility and equipment are long lived assets, they should not be

treated as an operating cost, but rather should be treated as a









capitalization cost and be amortized. To continue with the model

development define the following terms:

g initial cost per unit area for construction (dollars per

unit area),

g' amortized cost per unit area for construction (dollars per

unit area per year),

oc maintenance and utility costs (dollars per unit area per year),

P amortization rate for initial capitalization,
c

t cost of equipment in department m per FTE professional
m

(dollars per man-year),

t' amortized cost of equipment in department m per FTE profes-
m
sional (dollars per man-year per year),

w. space required per type i person (units of area per
1

man-year),

Y total floor space available,

Y floor space to be constructed for department m
m

(Y = E wiNi),
m icIm i i
Y* maximum initial capitalization (dollars).

If an HMO is in a planning stage, there may be an upper limit on

capital available for constructing an HMO or if it is already in opera-

tion there may be a limit on floor space available. In the latter case

this would imply


E Y < Y (3.34)
m --
m

while in the former case


(3.35)


E Y =Y .
m
m










A constraint similar to (3.35) will be used; recognizing that (3.34)

could easily be incorporated at a later point. For an IMO in the plan-

ning stage with a maximum amount of capital available the following

constraint arises:


g E w.N. + E t FTE < Y* (3.36)
i. ii m a -
i m

The capitalization costs must also be amortized and appear in the objec-

tive function which will be discussed shortly. However, the plant opera-

tions and maintenance cost have not yet been developed. This cost is


o 2 w.l. .
c. 1 1


Now all three of the facility overhead costs can be included in (3.33)

to give


min 2E (b.c..) xi + E s x' + Z u.n.
i j 13 3 1J i J J

+ E (1 V ) E d.u. + E AD + o E w.N.
m mjem J J m m i I


+ g' i w.N. + Z t' FTE (3.37)
Sii m m
i m


The overhead costs have all been included except the ancillary

costs. In this model this cost category will be used for the laboratory

and x-ray departments. These departments could be included in the regu-

lar medical department formulation with no change in model M2 or sub-

sequent models. However, to examine these two departments in the same

detail as the primary care departments was outside the scope of the study.

Thus they have been included as a separate category. If enough informa-

tion and data were available, this part of the formulation could be









dropped and laboratory and x-ray manpower utilization and costs could be

examined in the same manner as the primary care departments. To proceed,

define the following coefficients:

CLT average cost per laboratory test (dollars per test),

CXR average cost per x-ray service (dollars per service),

NLT number of laboratory tests ordered in department m per service

provided (tests per medical services),

NXRm number of x-ray services ordered in department m per service

provided (x-ray services per medical service).

The units between CLT and NLT and CXR and NXR should be consistent.
m- m
For example, if NXRm is given in series per medical service, then CXR

should be in dollars per series. From the above definition, the labora-

tory and x-ray costs are thus:


E (CLT NLT + CXR NXR ) Z E b..x.. (3.38)
m m m .6m is6m ij j (
m jej iel

Now (3.38) can be included in (3.37):


min E (b..c. ) x.. + s.x' + u.n.
i j i j

+ S (1 V ) S d.u. + E AD + o E w.N
m mjm m m c i

+ g' E w.N. + Z t'FTE
1 1 m m
i m

+ (CLT NLT + CXR NXR ) SE b x, (3.39)
mm jeJ islm 1


At this point, the objective function (3.39) is much more detailed

and versatile than the objective function for model M2 which is given by

(3.22). The function given by (3.39) is certainly more complex than that









expressed previously but the difficulty of solution has remained on the

same level. In fact if the V decision variables are set to either 0 or
m
1 (in (3.22) they are implied to be 1) then the present model and M2

are almost equal in difficulty of solution. The real change has occurred

in the data requirements. Information that was left out of model M2 is

needed in the present model. If the full cost for an HMO is not desired,

but rather, only the medical manpower costs are sought, then the extra

coefficients in the present model can be set to zero. It is felt,

however, that the extra effort required to find the additional coeffi-

cients results in a more meaningful and richer solution.


Additional Model Refinements

The model development could stop at this point but there are several

additional features which can easily be added and will further refine

the model without sacrificing solution capability. The first feature

presented below involves further refinement of the medical care structure

and the other three further refine the cost structure. In the previous

discussion involving indirect supervision of physician extenders and

nurses, several constraints arose and are given by (3.12) and (3.13).

These constraints arise mainly from the MD's viewpoint of the time

requirements for him to supervise lower level personnel. However,

another viewpoint can arise from the patient care aspect of medical care.

The physician extender is not qualified to diagnose and treat every

patient that comes to the HMO for medical care under the indirect super-

vision mode. In fact, for many health services, the physician extender

will only be used in a team role under the direct supervision of a physi-

cian. The details of this limitation will be fully explored in the next









chapter. For the moment it suffices to note that the above limitation

results in upper bounded variables. Let MAX.. be the maximum percent of

service j that can be carried out by personnel i in the indirect super-

vision role. This coefficient will be used for those indices ieI' which

refer to physician extenders. The upper bound is thus:


xij. MAXij dj V jeJ, icP (3.40)


Note that it is not necessary to include the V variable here since if
m

V = 0 constraint (3.29) and the objective function will force x.i = 0
m ij
in an optimal solution. This point is important since it means that

(3.40) is an upper bounded variable which adds very little to the solu-

tion difficulty.

The other three model refinements involve the cost structure and

the first to be discussed is the fee structure. Even though HMO's will

operate on a capitation basis a small fee for service may be collected.

This fee should be small so that sick patients are not discouraged from

seeking health care thereby subverting one of the prime reasons for pre-

paid medical care. This fee is sometimes charged to discourage the use

of a physician's time by patients who are basically not ill. The co-

payment is also used as a marketing device to decrease the fixed capita-

tion rate and thus make the plan more attractive when compared to other

insurance plans which may have a lower fixed cost but less comprehensive

coverage. The fee is frequently $1 or $2 per office visit and if the

fee for service j is denoted r., then the income from fees is
J


(3.41)


Sj CJ bijxij
j -









A further refinement can be made to the cost of equipment. There

are certain pieces of equipment that change the fundamental nature of

the delivery of a health care service. Examples of this are multiphasic

testing units for use in comprehensive physical exams and SMA-12 blood

chemical analyzers for use in laboratories. Both of these examples also

have the property of being extremely expensive. Since both large cost

and alternative health care delivery patterns could have a major effect

on the solution, this type of equipment will be separated from the

remainder of the medical equipment used. Technology cost was used by

Shuman (76) by introducing a fourth subscript onto all the problem

variables. This is not only cumbersome but also adds considerably to

the number of variables. In addition several levels of technology for

an entire O10 cannot be analyzed in a practical sense. The data not

only do not exist; it would be difficult and very costly to design an

experiment under which the data could be collected. Instead it is pos-

sible to evaluate the effect of specific technological advances on the

productivity of specific personnel providing specific services. Define

the terms:

e. initial cost for a type i person due to technology cost

(dollars),

e! amortized value for e (dollars per year),
1 i
I' set of personnel whose productivity is enhanced by additional

technology,

T. one if Ni > 0 and 0 if N. = 0 for iTe'

Then the technology cost is given by


S e.T.
iel' 1 1









and should be added to the capitalization constraint to give


g E w.N. + t FTE + S e.T < Y* (3.42)
Si m m m i-
i m iel'


In addition, to ensure the zero-one variable T. takes on its proper

value, the following constraint is necessary


N. K T. < 0, where K >> N. (3.43)
1 1 --


Several points should be made before proceeding. First note that the

set I' can include those personnel who do not need the additional tech-

nology cost to be effective but rather technology just revises their pro-

ductivity coefficient. It can also include those who would not be hired

if the technology is not employed such as technicians hired to run a

multiphasic testing unit. The second point is that the above term is

not central to the solution of the model and can be dropped if tech-

nology changes are not being considered in the decision process.

The last addition to the model involves an operating constraint for

HMO's. HMO's provide medical care on a capitation basis and must operate

within a budget defined by the capitation income plus any external

sources of revenue. Thus the yearly operating expenditures must be less

than the budgeted amount to cover cost of operation. The relation

between the budgeted amount and the capitation is developed first and

then the budgetary constraint is developed. The budget is developed for

a non-profit institution. For a profit making institution appropriate

changes can easily be made. Define the coefficients:

B* -upper limit on yearly budget for operating and salary expenses

for medical departments included in the optimization (dollars









per year),

OM other medical costs; this would include the costs of operating

departments which are not included in the optimization,

inpatient care, out of area professional services, additional

cost of premium plans, etc. (dollars),

P rate at which capital fund accumulates as a fraction of gross

income from subscriber capitation fees,

R capitation rate (dollars per subscriber per year),

XT external sources of revenue such as planning grants or

endowments (dollars per year).

ince the initial capitalization, Y* is being amortized at the rate


P the result is
c


E


Now s


B* = (1 P) S R P Y* OM + EXT
c


(3.44)


Now. a budgetary constraint can be written for which B* is fixed which

implies the capitation rate is fixed, or B* can be defined as a variable

which in turn will define the capitation rate. The former alternative

will be used here recognizing it is trivial to study a variable capita-

tion rate if it is later desired. The terms given in (3.41), (3.44) and

the yearly expenses from the objective function (3.39) can be combined to

give the budget constraint:

S E (b..c..) x + sx + o E w.N. E r (S b x.)
j i 1 c i j I ij ij

+ S (CLT NLT + CXR NXR ) ES b..x..
Sm m jeJ ielm 13 1

+ (PV S S b x.i + MAN (d. V n )/b
m jejm iclI jeJm j m j

+ PER E N.) < B* (3.45)
im
itI









The entire model will be called M3 and can now be summarized here. The

objective was given by (3.39) and must be revised to reflect the income

fee and amortized technology cost. In addition AD and FTE will be
m m
replaced by their definitions given by (3.32) and (3.31) respectively.

The result is the model M3:

min g' w.N. + SE (b..c ) xi. + S s.x' + E (1 V ) S d.u.
i1 j 1i i m m jeJm j

+ S u.n. + S t' ( E (dVm n.)/bt) + o Z w.N. E r. (E b. x..)
j J m jcJ c i J i

+ e eT T. + E (CLT NLT + CXR NXR ) S E S b .x..
iel' m m jem m 13 13

+ S (PV E m b..x. + MAN S (d.V n.)/b + PER Z N.)
m jem iIm 13 jem jm n ieI

(3.46)


subject to

Sxij + Z E qkijkj + x' N. = 0
j1 kj


V iC ,


V jeJ, j#j* ,


Z b..x.. + n. d.V = 0
i13 3 m


S E f ib x b x <0 V i*dl* ,
J iJi* iCl* ij j

SE (b..c ) x + s + o S w.N. E r. ( b..x..)
j iJ i 1 1 ci j 1 i i 1 11

+ S (CLT NLT + CXR NXR ) 5 Z b ix.
m m m jeJm islm 13 13
m jejm icim

+ (PV S b..x.. +MAN S (d.V n.)/b*
m jeJm icm 13 jej m J j

+ PER E Ni) < B*
iel

g E w.N + E t E (d.V n.)/bt + e.T. < Y*
i1 m jcJm m i i < Y*


(3.47)


(3.48)


(3.49)


(3.50)


(3.51)









Ti K N. 0 ieI' (3.52)



xi*j* SUi Ni V i*e* (3.53)


n. < MX. d. V jeJ, (3.54)


x..

Thus the problem is to find the xij, N., T. and V to minimize (3.46)

subject to (3.47) (3.55). Note chat the optimal basis will always be

such that constraint (3.49) is tight. This is because the xi*j. in

(3.49) will always have a positive cost; thus if a slack variable from

(3.49) appeared in the final basis, the objective function could

obviously be reduced by reducing the slack variable to zero, thereby

reducing the x ,.* and thus its contribution to the objective function.

This means that (3.493) could be used to limit xij, from the fcrmula-

tion and consequently eliminate (3.49). However, this would change

(3.53) to a constraint rather than an upper bound and thus would accom-

plish little in addition to the notational problems which would arise.

Thus (3.49) will be retained in the formulation.


A Comparison of Models Ml, M2,and M3

The formulation has been developed in three stages through models

M1, M2 and M3. It is instructive at this point to compare the features

and sizes of the three models. The features of the three models are:

M1 very simple model of the basic resource and requirements

relations;

M2 generalized and detailed refinement of the medical care

structure presented in Ml; and









M3 generalized and detailed description of the medical cost

structure in addition to the medical care refinements of

model M2.

Let the cardinality of the sets I, Is, I', and J and M be demoted by 0(I),

0(IS), 0(I'), 0(J), and 0(M). Also assume that the matrix of xij is

about 20 percent dense; about 50 percent of the personnel classes are

required to be integer; and that O(I') is about a fourth the 0(IS).

Then, if for example, there were 10 personnel classes, 15 teams, 60

services and 3 departments the size of the models would be as follows

(strictly speaking Ml would have to be developed slightly to allow

teams)


Table 2 Relative Sizes of Models Ml, M2 and M3


model Continuous Integer Zero-One Cntraints Upper
Variables Variables Variables Bounds

Ml 300 0 0 70 0
M2 370 5 0 73 63
M3 370 5 5 75 123



In solving linear programs, the number of constraints is Lhe major

factor in the time and difficulty of the solution. Upper bounds can be

added to a model with very little extra solution time and they do not re-

quire the addition of constraints. Also, the number of problem variables

only slightly affects the solution speed. Thus in going from a very

simplistic model to a much more detailed model the refinements were prin-

cipally made in such a way that the difficulty of the model changed very

slightly. Note also that in interpreting solutions to linear programs









the principal quantities of interest are the number of variables and

number of constraints. Here again very little additional difficulty is

encountered in the interpretation of the results.

The exception to the above paragraph is the integer and zero-one

variables. Solving a mixed integer linear program is more difficult

than solving a linear program. However, in this case the problem is

well within the solution range of mixed integer programming techniques.

Additionally, the zero-one variables could be set at an assumed value

as was implicit in Ml and M2 and the integer restriction on all Ni could

be dropped which would convert M3 into a linear program of about the

same difficulty of Ml or M2, but M3 would remain a much more fertile

model for decision making. The major caveat would then be the addi-

tional data requirements, but for an HMO with an adequate accounting

system the extra data would essentially be available. Thus model M3 will

be used for further development and analysis in the remainder of the

study.


Development of Planning Models


Development of the Overall Planning Model

The M3 model will be algebraically simplified to define the Overall

Planning Model (OPM). OPM can be used in a preliminary planning stage

of an IMO or with some simplifications it can be used to refine operation

of an MO0. The model is formulated to solve the following basic problem:

given a fixed capitation rate and a projected subscriber

base find

(1) manpower to be hired,









(2) delegation of services,

(3) facilities required,

(4) particular technological innovations to be

utilized (if any).

The M3 model has many terms and coefficients that can be combined. Thus

the model can be simplified by defining:


a i = (c, rj + CLT NLT + CXR NXR + V) b.. (3.56)
ijm i J m m 1

OT = (MAN + t') d./b4 d.u. (3.57)
Sm j j

P =MAN d./b (3.58)


0* = t d/b (3.59)
jm m j 3

h! = w1 (g' + Oc) + PER (3.60)


h. = o w. + PER (3.61)


h = gw (3.62)


ym = j (t' + MAN)/b4 (3.63)


y. = MAN/bt (3.64)


m = t /b (3.65)


ADD = E d.u.. (3.66)
J J J

Substitute (3.56) (3.66) into (3.46) (3.55) and the resulting formu-

lation is the OPM (note the constant term, ADD, is being carried with

the formulation):









min S E E a.. x. + E S V + S h;N
m jjm iem ijm j1 m jeJm j m icI i

+ E E y. n. + E s.x' + S e!T. + ADD
m jejm jm J iI s i 1 iEI' 1 i

subject to

x + + qkjx + x' Ni = 0 V iIs
j kj


S f ib ijxi bi x = 0 V i*Il* ,
jxJi* ie i v *l*

xij < SU.N. V iI* ,
-~" 11


E bijxij+ n. d V = 0
i 1313 3

n. < MX. d.
3j 3 3


V jeJ meM ,


V jeJm, V meM ,


xij MAX.. d V jej, iIp ,


ZS Z a. x. + Z h.N. +S S V
m jcm ilm ijm ies 1 1 m ejJm 3mm

+ E s s + Yjj < B* ,
ici sixi j -


S hN. + E e.T. + Z E V + E E y n < Y*,
iel 1s iCI m j mm m jeJm m j -


N. K T. < 0
1 1 -


V il' .


(3.67)




(3.68)


(3.69)


(3.70)


(3.71)


(3.72)


(3.73)


(3.74)


(3.75)



(3.76)


Additionally N. is integer, V and T. are zero-one, and all x i, x' and
1 m I ij 1
n. > 0.
3-
The OPM will be used extensively in the remaining analysis. It is

the basic model from which other models will be derived and it will also

be used extensively to arrive at computational results. One of the prin-

cipal difficulties for solution of the ORI is the mixed integer feature









of the model. However, there are many instances where the model could

be linearized. There are many HMO's where the decision to utilize a

certain technology level and provide certain medical departments may be

made for political, legislative, or intangible reasons. In this case

the zero-one variables would be removed from the model. There are also

many HMO's that effectively do not reflect an integer manpower constraint

and it will be shown in later results that assuming continuous manpower

is a reasonable assumption in many cases. Thus often the integer restric-

tions can be removed entirely from the model. However, they are in the

formulation if needed and this in turn allows the effects of removing

these restrictions to be analyzed.


Minimum Cost Model for Fixed Services

It was noted that the OPM could be made computationally easier if

the zero-one variables V which determined which departments would be
m
provided are eliminated. In the OPM departments that are economically

infeasible to offer would be reflected by zero values for V and for the
m

corresponding slack variables, n., which would appear in the basis

(making it degenerate). The basis size could be made smaller and many

of the zero-one variables eliminated if it is decided a priori which

services are to be offered. Aside from making the model more amenable,

fixing the services to be provided is essentially the approach now being

proposed in the legislative programs. Thus another question which

arises is:

given a fixed set of medical departments and a fixed

subscriber base, find the optimal staffing, delegation,

and facility to minimize the subscriber fee.









For this formulation define the set:


M' = m : V = 11, (3.77)


J' = j : jeJ meM'} j* (3.78)
msM'

and also let

E= E
m meM'

2 = E
j jeJ'

Recall also from (3.44) that B* is a function of R and Y*. Note that in

this model and in the OPM one could treat Y* as a variable to find the

optimal initial capital outlay. From a best solution standpoint if con-

straint (3.75) is active then it implies that the limit on original

capital is actually acting to increase the yearly cost of operating an

M0O. This will never happen if Y* is treated as a decision variable.

Note also that if all demands are not met the Z u.n. appears in the
J
yearly budget constraint (3.86). These services are paid for by the HMO

and provided through another source. Thus the Minimum Cost (MC) model

is given by (3.79) (3.88) and involves finding the x., x, n, N. T.

and R (also possibly Y*) to

min R (3.79)

subject to

Sx.ij + E qkijxij + x! Ni = 0 V isl* (3.80)
S kj 3 1 1

S E f .bijxij b xij* = 0 V i*cI* (3.81)
jeJi* iel* ii ij* i









ij* SUi Ni ieI* (3.82)


E b.ix.j + n. = d. jcJ', j#j* (3.83)


n. MX. d. t jEJ', j j* (3.84)


x..< MAX. d. F jej, iel (3.85)


EZ Z Z a.. x.. + E s.x5 + Z hN. + S (y. + u.) n.
m jcJ ilm njm iI s i I ie s i i

(1 P) S R < P Y* OM S 0Z (3.86)
c nm jm
m jeJm

E htNi + E e.T. + 2 yZ n < Y* S m Z (3.87).
iIs 1 1 jeJm j m jej j

N. K T. < 0 V iel' (3.88)
1 1 -

Additionally, N. is integer, T. is zero-one and xi., x!, n. and R> 0.

Making the same assumptions as were previously made regarding the density

of the x.. matrix this problem has the following characteristics:

(a) .2 0(I) 0(J') + 0(I) + O(J' + +0(M') continuous variables,

(b) .5 0(Is) integer variables,

(c) .2 0(Is) zero-one variables,

(d) 1.5 0(Is) + 0(J') + 2 constraints, and

(e) 2 0(J') + 0(1*) upper bounds.

Thus with 10 personnel classes, 15 teams, 60 services to be provided,

and 3 departments this problem would have about 370 continuous variables,

5 integer variables, 2 zero-one variables, 75 constraints, and 123 upper

bounds. This is easier to solve than the OPM but the MC model is also a

mixed integer program.









In conclusion, this model is useful if the services to be provided

are dictated by political, local or legislative reasons. It can also

be used to formulate a reasonable set of services if the objective is to

minimize the capitation rate for a fixed set of services rather than

minimize the subscribers total medical bill as the OPM does, whereas

the MC will give the staffing, delegation and facilities required for

minimizing the cost to the subscribers for a given set of services.


A Special Case of the Minimum Cost Model

The MC model can be further simplified by using it in an operational

planning mode rather than the preliminary planning stage since it is

assumed the professional personnel and facility are already fixed. The

planning question at the operational stage can be stated as:

given a fixed set of services, professional staff and

facilities, what is the optimal subscriber size, delegation

and ancillary staff to minimize the subscriber fee.

For this case T. and some N. are fixed and the integer restrictions on
i 1
the remaining N. are dropped; thus the model is no longer a mixed integer
1
program. Constraint (3.80) becomes

E x + Z qkijxij = N. V iCI* (3.89)
j k j k

and the initial capital constraint (3.87) is replaced by a constraint on

the amount of floor space available for medical services,


S w.N. < Y (3.90)
i 1 1

and the T. definition constraint can be dropped from the formulation. A
problem arises with constraint (3.86) which now has a nonlinear term
problem arises with constraint (3.86) which now has a nonlinear term









S R since both S and R are now assumed variable. However, this non-

linearity can be eliminated by a double transformation. First define


Q = S R (3.91)

and then (3.79) becomes


min Q/S (3.92)

and (3.86) is again a linear constraint with Q replacing S R. The new

model thus consists of (3.80) (3.86), (3.90) and (3.92). This model

is a fractional linear program since for a physically reasonable solu-

tion to the model S > 0. A slight modification of the simplex is made

in the Charnes-Cooper Algorithm (82) to solve this problem. However,

the model can also be easily transformed to a linear program by the

transformation


r = 1/S (3.93)

and then define


S= rxii Q' = rQ ,

x' = rx S' = rS ,
1 i

n'. = rn N' = rN.. (3.94)
1 3 1 1

Now (3.93) and (3.94) are substituted into the linear fractional model

to give

min Q' (3.95)

subject to


E x!. + E E q .jx + x"' N.r = 0 V ieI* (3.96)
13 kj 13 1 1


S x'. + ES q .x: + x'' N! = 0 V ie* (3.97)
j 1 k j k 1 1









Z f b x' b x = 0 V i*cl* (3.98)
Ji* icI* ij i ij i*j* 1*j*

x,, SU'. N.r < 0 V ile* (3.99)
i*j I 1 -

S b.jx j + ni = 0 V jcJ', j#j* (3.100)
i j


n' MX. d S' < 0 V jeJ', jIj* (3.101)


x MAX.. d' S' < 0 V jej, iei (3.102)


C S S a,. x. + E s.x' + E h.N!
m jejm iclm ijm + iI s is i i

+ E h.N.r + E (y. + u.) n'. (1 P) Q'
iei* j

+ r (P Y* + OM + jm) < 0 (3.103)
m jeJ

E w.N: rY < 0 (3.104)
*1 1

S' = 1 (3.105)

Thus (3.95) (3.105) is a linear program and can be solved in the usual

manner. In practice it may be preferable to use the Charnes-Cooper

Algorithm on the linear fractional program rather than redefining all

the variables and requirements vector as was done above. Whichever model

is used, the result is a useful operational planning tool which is

especially useful if an HMO wants to change from the traditional MD-nurse

medical practice to the three level MD-PE-nurse medical practice. The

model defined by (3.95) (3.105) is a little lengthier to solve since

the upper bounded variables were replaced by generalized upper bounding

constraints. Although generalized upper bounding algorithms have been









formulated (e.g. Geoffrian (83)) they are not as fast as upper bounding

nor as available in packaged linear programming routines. However, the

generalized upper bounding constraints can be treated as standard con-

straints with the resulting larger basis.


Subscriber Maximization Model

One of the reasons HIO's are being proposed is because they poten-

tially will offer care to more subscribers per physician than the tradi-

tional form of practice thus providing better utilization of this scarce

manpower resource. Thus a valid objective would be to maximize the

number of subscribers an HMO can serve for a fixed professional staff

and subscriber fee. Again for this problem, the original capital Y*,

can be assumed to be an input or a variable. The problem can thus be

stated as:

given a fixed professional staff and subscriber fee,

find the optimal delegation, facility, and hiring

policy for allied personnel to maximize the number

of people who can be served.

This model is derived through modification of the OPM and involves find-

ing the x.., N., T. and S (possibly also Y*) to

max S (3.106)

subject to

Sx.ij + sE q kij + x! = N. V iel* (3.107)
j kj


E x.i + E qkijx + xt N. = 0
kj k j 1J 1 1


V iei* (3.108)









i i b x b x = 0 V i*1* (3.109)
Ji* j ij i i*j*


x ij* < SUi. Ni iel* (3.110)


S b..x. + n. d'S = 0 V jej', j#j* (3.111)
1J 1j 3 J


n. MX. d'S < 0 V jej', jij* (3.112)


xij MAX.i djS < 0 jeJ', j#j* (3.113)


E E S a. x. + s.x + E h.N. + Z (y + u.) n.
Sjjm im im ij 13 s i* 1 j 3

(1 P) S R+ SE B. S + P Y* < OM E h.N. (3.114)
m j6Jm jm c 1 1

Sh* N. + E e.T. + E S y n, + E S
ie 1 il' m jeJm n mj m jeJm jm

< Y* S hN.
i* 1 i (3.115)


N. K T. < 0 V iel' (3.116)
1 1 -

Note, for this model and 0* must be redefined in terms of d' rather

than d.. Constraint (3.107) refers to the professional level personnel

which are at a fixed level, whereas (3.108) refers to the ancillary per-

sonnel and N. is an integer variable. Note the term S u.n. in (3.114)
1 j J 3
and the use of n. as a slack variable in (3.111). This is somewhat of a

paradox since the purpose of the model is to maximize the number of sub-

scribers served by the HMO, but the above use of n. allows services to

be bought outside of the HMO. However, the n. should not be used as a

surplus variable in (3.111) and have the corresponding term in (3.114)

eliminated. To do this might unreasonably restrict the number of









subscribers. An example will clarify this point. Suppose only one

general surgeon is available and he can provide services for 10,000

people. However, the remainder of the staff can provide services for

their specialties for 30,000 people. The use of n. as a surplus vari-

able would lead to an answer of 10,000 subscribers, but using it as a

slack variable would lead to a solution of 30,000 subscribers with

two-thirds of the members being referred to a surgeon outside of the

HMO and paid for by the HMO. This latter solution is certainly more

reasonable.


Minimal Use of Professional Manpower

In an attempt to minimize the use of manpower for which a shortage

exists, an alternative approach to the SM model can be taken. It is

plausible that in some cases it will be known what subscriber base is

desired for geographical or political reasons. Thus the problem can

be summarized as:

given a fixed subscriber base, a fixed fee, and a fixed

set of services ,find the optimal staffing, delegation

and facility to minimize the professional level per-

sonnel used.

This minimization will naturally need to account for the quality of

service provided. In this case, it would be a major consideration and

the indirect supervision constraints will play an important part in

determining the plausibility of the final solution. This Minimal Pro-

fessional Manpower Model (MPIM) is given below and involves finding the

x..' x" n., N., Ti and Y* to









min Z Ni (3.117)
ilI*

subject to:

S x.. + q + x' N. = 0 V iel (3.118)
j1 kj k1iij 1 1


S E fi..b ix bi xi = 0 1i*I* (3.119)
j 1Ji* 13 ii ij i*j* i*j*
jSJi* ieI*

Xi*j, < SU.i N. V iel* (3.120)


Sb.x.ij + n. = d. V jeJ', j#j* (3.121)


n. < MX. d. V jeJ', j#j* (3.122)


x. < MAX.. d. V jeJ, ielp (3.123)


Z Sm a.. x.. + h.N. + s.xI
m jc i m 13 1 is 1

+ E y n. + P Y* < (1 P) S R OM E jm (3.124)
j j c -m jeJm


Sh* N. + E e.T. + E S Y* n. Y* < S E (3.125)
ieis i 1 ieI' m jeim 3m m jem jm

N. K T. < 0 V iel'. (3.126)
1 i -

Additionally N. is integer, T. is zero-one and x.., x!, n., and
1 1 13 1 J
Y* > 0. The size of this problem, using the assumptions as for OPM, is:

(a) .2 0(I) 0(J') continuous variables,

(b) .5 0(I) integer variables,

(c) .2 0(I) zero-one variables,

(d) 1.5 0(I) + 0(J) + 2 constraints,

(e) 2 O(J') + 0(1*) upper bounds.









This formulation can also be used if the facility is fixed by making the

following changes:

(a) assureY* doesn't include paramedical equipment costs, Ti;

(b) in (3.124) add P E e!T. to the left hand side; and
c. 1 1i
(c) replace constraint (s.125) with E w.. < Y .
i -


Concluding Remarks

This chapter has presented a wide array of problem formulations

ranging in complexity from 1L to M3 and ranging in purpose from OPM to

MPMT. The internal validity of these models was partially developed

along with the development of the model in going from 1M to M3. Further

validation and solutions to the models will be covered in the remaining

chapters. The development of the complex model was carried out in such

a manner that, excluding the integer restrictions, 13 is of the same

order of difficulty to solve as the simplest model. The major difficulty

is the additional data requirements imposed by model M3; however, the

data needed to solve the mode are presented in the next chapter.

In summary, the models presented are mixed integer programs. One

of the models exhibited a quadratiz term but this was removed by a trans-

formation that resulted in a linear program. The models presented are

general and flexible enough to answer many HMO planning questions. A

partial list would include:

(a) assignment of personnel to medical services;

(b) selection of medical departments to offer;

(c) selection of needed facilities;

(d) optimal subscriber levels;









(e) optimal hiring policy;

(f) maximize subscribers per health professional;

(g) minimize the number of health professionals utilized;

(h) find the minimum cost structures for different base

populations;

(i) examine cost and manpower effects of P.E. utilization;

(j) examine P.E. utilization as.a function of subscriber

levels, P.E. salary, and supervisory levels;

(k) examine effect of integer manpower restrictions;

(1) examine imputed cost for medical services;

(m) examine different levels of responsibility for P.E.'s;

(n) examine which services are best delegated;

(o) examine usage of P.E.'s under a scarcity of P.E.'s; and

(p) examine which P.E. activities save MD's the most time.

These questions and others will be analyzed and at least partially

answered in the remaining chapters,




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PAGE 1

A SYSTEMS ANALYSIS OF OPTIMAL MANPOWER UTILIZATION IN HEALTH MAINTENANCE ORGANIZATIONS By Donald Paul Schneider A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1973

PAGE 2

Lf TO ESTER (X IV.

PAGE 3

ACKNOWLEDGMENTS I wish to acknowledge the considerable contribution to this work by Dr. Kerry E. Kilpatrick who acted as the Chairman of my Supervisory Committee. His direction and insight contributed to both the form and content of this dissertation. I also thank the remainder of my committee, Dr. H. Donald Ratliff, Dr. Thorn J. Hodgson, Dr. Frank R. Sloan and Richard C. Reynolds, M.D. , for their efforts which contributed to the completion of this work. I would also like to thank Dr. Stephen D. Roberts for his guidance and support in several stages of this research; Dr. Barney L. Capehart for his guidance in the early stages of my graduate studies; Dr. Donald R. Miller for his aid and helpful suggestions, and Dr. M. E. Thomas for his support throughout my stay at the University of Florida. I would also like to thank the members of the health care community who provided valuable advice, criticism, and the facilities so that the research could be developed, tested and validated. These include Dr. Douglas Fenderson, Director of the Office of Special Programs, Bureau of Health Manpower Education, National Institutes of Health; Mr. John Braun, Chief, Physician's Assistant Staff, Office of Special Programs, Bureau of Health Manpower Education, National Institutes of Health; Dr. L. F. Krystynak of the University of Florida, Mr. Richard Bohn, President of the Metropolitan Health Council of Indianapolis, Indiana; Dale R. Benson, M.D. , director of the Southeast Health Center of Indianapolis; Mr. Tim Payne, administrator of the Southeast Health Center;

PAGE 4

Mr. Dave Norton, consultant to the Florida Health Care Plan, Inc.; Mr. Richard Freeman, Special Assistant to the Deputy Secretary of Health, Education and Welfare; Mr. Dave Whelan, President of Health Management Group, Inc.; and Dr. Judith Liebman of the University of Illinois. Finally, I thank my wife Ester for her encouragement and patience throughout the course of this work. This dissertation was supported in part by the Health Systems Research Division of the University of Florida.

PAGE 5

TABLE OF CONTENTS Page ACKNOWLEDGMENTS iii LIST OF TABLES ix LIST OF FIGURES xiii KEY TO SYMBOLS xiv ABSTRACT xviii CHAPTER 1 INTRODUCTION 1 Background 1 Scope and Purpose 3 Research Objectives 5 Organization of Dissertation 7 2 BACKGROUND AND LITERATURE REVIEW 10 Health Maintenance Organizations 10 General Terminology 10 Legislative Background 12 Research Viewpoint 13 Allied Health Manpower 15 Physician Extenders 15 Physician Extenders in Primary Care 16 Physician Extender Utilization: The Team Concept . 19 Delegation of Medical Services 21 Motivation for Mathematical Modeling 23 Previous Studies 23 Systems Analysis as an Aid to the HMO Design Process 27 Planning the Benefits To Be Provided by an HMO . . 28 Proposed HMO Design Process 30 v

PAGE 6

Page DEVELOPMENT OF ANALYTICAL MODELS 35 Preliminary Models 35 Introduction 35 System Schematic for Model Development 36 Tradeoff Decisions To Be Incorporated in the Models 38 Preliminary Model Development 41 Development of the Medical Care Aspects of the Model 44 Further Development of Financial Aspects of the Model 51 Additional Model Refinements 58 A Comparison of Models Ml, M2, and M3 64 Development of Planning Models 66 Development of the Overall Planning Model 66 Minimum Cost Model for Fixed Services 69 A Special Case of the Minimum Cost Model 72 Subscriber Maximization Model 75 Minimal Use of Professional Manpower 77 Concluding Remarks • 79 DATA COLLECTION AND ANALYSIS 81 Introduction . ^1 An Overview of Health Care Data Collection .... 81 Purpose of the Chapter 81 Medical Classification Systems 83 The Criteria for a Medical Classification System . 83 A Review of Existing MCS 84 A Formulation of a New MCS 90 Time Requirements, Delegation and Utilization Data ... 93 Time Requirements 93 Delegation Guidelines 99 Utilization of Services 108 Medical Cost Data 113 Introduction 113 Cost Calculations 115 Concluding Remarks 120

PAGE 7

Page NOMINAL SOLUTIONS AND VALIDATION OF THE MODELS 122 Introduction 122 Solution Process for Linear Programming and Mixed Integer Programming 122 Validation Process 124 Problems Involved in the Validation Process 124 Formulation of a Validation Process 125 Steps Taken To Validate the Models 126 Implications of the Model Assumptions 131 Nominal Solutions 134 Comparison to the Prepaid Group Practice 134 Presentation of Nominal Solutions 136 Comparison of Nominal Solutions to an Existing Prepaid Plan 145 Case Examples 147 Use of the Models in the Design of an HMO in Indianapolis , Indiana 147 Evaluation of the Indianapolis HMO Case Study .... 163 Case Study of the Design of an HMO in Daytona Beach, Florida 166 Evaluation of Daytona Beach HMO Study 173 Concluding Remarks 175 PARAMETRIC AND SENSITIVITY ANALYSIS OF POLICY QUESTIONS 176 Introduction 176 Sensitivity Analysis 177 Facility Costs 177 Physician Extender Salary 179 Indirect Supervision Guidelines 182 Parametric Analysis 190 PE Utilization As a Function of Subscriber Levels and the Integer Restrictions 190 Optimal Delegation With a Scarcity of PE's 195 Maximum Subscribers Per Physician Under a Scarcity of PE's 201 VII

PAGE 8

Page Remarks 202 7 SUMMARY OF RESULTS AND CONCLUSIONS 206 Introduction 206 Results and Conclusions 206 Development of the Models and Data Base 206 Results From the Models 209 Results of the Validation Process 213 An Overview of the Results and Conclusions .... 215 Areas fcr Further Research 216 APPENDICES A MEDICAL CLASSIFICATION SYSTEMS 222 B PHYSICIAN EXTENDER DELEGATION DATA 235 C PRINCIPAL MODEL INPUTS AND NOMENCLATURE FOR PROBLEM VARIABLES 254 D DATA COLLECTION FOR THE INDIANAPOLIS, INDIANA HMO ... 261 REFERENCES 266 BIOGRAPHICAL SKETCH 275

PAGE 9

LIST OF TABLES Page TABLE 1 Example of Personnel and Time Requirements 47 2 Relative Sizes of Models Ml, M2 and M3 65 3 Sample Output for Analysis of Utilization, Time Requirements and Delegation 95 4 MD and RN Time Requirements for Medical Services .... 100 5 MD, PE and RN Time Requirements for Medical Services . . 102 6 Maximum Percent of Visits Under Indirect Supervision for Four Delegation Assumptions 109 7 Comparison of Demographic Characteristics for the Kaiser Sample and the PGP Ill 8 Percent Utilization for Adult Medicine, Pediatrics and OB/GYN in the KCBDCS 112 9 1972 PGP Budget 115 10 Nonoffice Visit Expenses for PGP 117 11 Nonhospital Departmental Costs for Three Primary Care Departments in PGP 120 12 Cost and Manpower Comparison of PGP and the Overall Planning Model 135 13 Comparison of 0PM Nominal Solutions to PGP 139 14 Delegation Analysis for Nominal Continuous Variable Solution 141 15 Nominal Solutions for MC Model 143 16 Nominal Solutions for the SM Model 144 17 Parametric Results for Indianapolis HMO Design 151

PAGE 10

Page TABLE 18 Variable Expenditures at Indianapolis HMO 156 19 Maximum Subscriber Levels for Indianapolis HMO As a Function of Staffing Pattern 161 20 Projected Demographic Characteristics for FHCP 168 21 Projected Utilization Rates Per Thousand Members for FHCP 168 22 Continuous Optimal Solution for FHCP 170 23 Integer Staffing Levels for FHCP 170 24 Parametric Results for Various Integer Staffing Levels for FHCP 172 25 Suggested Dynamic Hiring Plan for Adult Medicine at FHCP 173 26 Manpower Utilization Response to Increases in Facility Cost 178 27 PE Use As a Function of Salary Increment From the Nominal 180 28 An Analysis of Six Different Indirect Supervision Guidelines 184 29 Maximum Shifts From the Nominal in MD and PE Utilization Caused By Changes in the Indirect Supervision Guidelines 186 30 PE Utilization As a Function of Basic MD Supervision Time 189 31 Results of Integer Manpower Restrictions For 8000-30000 Subscriber Levels 193 32 Optimal Delegation and MD Requirements Under a Scarcity of PE's 197 33 Marginal MD and Cost Savings As Additional PE's Are Used 199 34 Maximum Subscriber Sizes Per MD Under a Scarcity of PE's 203

PAGE 11

Page TABLE A-l Principle Sections of the International Classification 999 of Diseases ''' A-2 California Relative Value Classification for Office and Home Visits 223 A-3 Major Categories of a Medical Service Classification System for General Practice 22 ^ A-4 Patterns of Medical Care for the Primary Care Specialties 225 A-5 Diagnostic Categories for which GEOMET Specifications of Care Were Prepared 22 ° A-6 Sample Listing of Elements of Care for Pediatrics ... 22 8 A-7 Sample Specifications of Care 229 A-8 Assignment of Proxy Specifications of Care 231 A-9 Clinical Subgroups in the Kaiser Clinical Behavior Disease Classification System 2 33 A-10 Ancillary Task Listing for General Medical Practice 234 B-l Physicians' Willingness To Delegate Activities to a Trained OB/GYN Assistant 235 B-2 Summary of Tasks for a Physician Assistant 236 B-3 Survey by Physicians Specialty for Possible Duties of Physician's Assistant 238 B-4 Physician Response for Delegation of Tasks to Physician Assistants ^ B-5 Feasible Delegation of Elements of Care 2 51 C-l Names Assigned to Personnel Classes 2 54 C-2 Names Assigned to the Medical Classification System . . 255 C-3 Principal Input Data Coefficients for the Mathematical Models 258 D_i Age-Sex Breakdown for Potential Enrollees in SHC . 261

PAGE 12

Page TABLE D-2 Projected Visits Per Year for SHC as a Function of Subscriber Level 263 D-3 Fixed Expenditures at SHC 265

PAGE 13

LIST OF FIGURES Page FIGURE 1 Present Decision Process for Determining Benefits ... 29 2 Proposed Decision Process for Determining Benefits ... 29 3 Three-Stage Hierarchy in the Planning of HMO's 31 4 Present HMO Design Dynamics 32 5 Proposed HMO Design Dynamics 33 6 A Schematic Representation of an HMO Structure 36 7 Medical Care Structure Showing Relation Between Resources and Requirements 37 8 Tri-Level Classification System 91 9 Flow Diagram of the TLCS Computer Program 94 10 Subscribers Per MD As a Function of PE/MD Ratio .... 204

PAGE 14

KEY TO SYMBOLS Subscripts : i refers to type i personnel (including teams) j refers to service j k refers to health care teams m refers to department m a composite coefficient (see equation (3.56)) ijm AD administrative costs (dollars per year) AD administrative costs allocated to department m (dollars per year) m ADD composite coefficient (see equation (3.66)) B* upper limit on yearly budget for operating and salary expenses for medical departments included in the optimization (dollars per year) b. . number of type j services a type i personnel can perform per year ij for a given level of technology (medical services per man-year) b* number of type j services a type ielpersonnel can perform per j year for a given level of technology (medical services per man-year) c. . labor cost for one type i to perform one service j (dollars per 1 1 medical service) CLT average cost per laboratory test (dollars per test) CXR average cost per x-ray service (dollars per service) d demand for service J (d. = Sd 1 .) (medical services per year) j J J d 1 . demand for type j service per subscriber per year (medical services * per subscriber per year) e'. . amortized cost for a type i personnel due to technological cost 1 (dollars per year) e. initial cost for a type i personnel due to technological cost 1 (dollars) EXT external sources of revenue (dollars per year)

PAGE 15

f . . level of independence for type i personnel to perform service j FTE full time equivalent professionals in department m (man-years) m g' amortized construction cost (dollars per unit area per year) g initial construction cost (dollars per unit area) h. composite coefficient (see equation (3.61)) hi composite coefficient (see equation (3.60)) hv composite coefficient (see equation (3.62)) I set of all medical personnel including teams I* set of professional manpower I* ancillary manpower i" set of physician extender personnel including teams led by physician extenders s I set of personnel excluding teams I set of health care teams I set of all personnel in department m i I set of personnel whose productivity is enhanced by additional technology J set of services considered for provision o_r to be provided i J subset of J for which V = 1 m J set of services considered for provision or to be provided in department m J set of services class i*el* personnel supervise l* j* supervisory services m K arbitrary, large constant M set of all medical departments under consideration MAN management and planning cost per FTE professional (dollars per manyear per year)

PAGE 16

MAX. . maximum percent of service j that can be carried out by personnel i in the indirect supervision mode MX. maximum fraction of type j services provided by nontypical means N. number of type i personnel employed (man-year) NLT number of lab tests ordered in department m per service provided (tests per medical service) NXR number of x-rays ordered in department m per service provided (x-rays per medical service) n. number of type j services demanded and not provided by ordinary means (medical services per year) o maintenance and utility costs per unit of area (dollars per unit area per year) OM other medical costs not included in the optimization (dollars per year) P yearly profit rate ojc_ rate at which capital fund accumulates P amortization rate for initial capitalization c P. maximum number of type i personnel available (man-years) PER personnel cost per FTE employee (dollars per man-year) PV administrative cost per patient visit (dollars per patient visit) q, .. man-years of personnel type i per man-year of team k providing service j (o, . . is defined to be one for the team leader) J kij R average yearly fee paid by subscribers for nonhospital services (dollars per year) r. patient fee for service j (dollars per medical service) S number of subscribers s. yearly salary of type i personnel (includes overhead salary such as retirement, vacation, insurance, etc.) (dollars per year) SU. maximum fraction of time type i personnel will engage in supervision of ancillary personnel fl if N.>0 i (0 if N. = iel'

PAGE 17

amortized cost of equipment in department m per FTE professional (dollars per man-year per year) initial cost of equipment in department m per FTE professional (dollars per man-year) per unit cost of providing type j service by extraordinary means 1 (dollars per medical service) {1 department m provided department m not provided w. space required per type i person (units of area per one manyear) x number of type i personnel assigned to service j (man-years) ij x..,. * number of supervisory level personnel assigned to the supervisory ^ service j* (nan-years) x'. fractional part of personnel i group which are idle (man-years) Y* maximum initial capitalization (dollars) Y total floor space available (units of area) Y floor space to be constructed for department m (Y = ieI m w i N i^ m (units of area per department) jm '3* composite coefficient (see equation (3.58)) composite coefficient (see equation (3.57)) • composite coefficient (see equation (3.59)) Y. composite coefficient (see equation (3.64)) Y 1 composite coefficient (see equation (3.63)) Y* composite coefficient (see equation (3.65)) J m

PAGE 18

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A SYSTEMS ANALYSIS OF OPTIMAL MANPOWER UTILIZATION IN HEALTH MAINTENANCE ORGANIZATIONS By Donald Paul Schneider August, 1973 Chairman: Dr. Kerry E. Kilpatrick Major Department: Industrial and Systems Engineering Mixed integer programming and linear programming models are proposed as aids to decision makers in the design and evaluation of health manpower requirements in the office care setting of Health Maintenance Organizations (HMO). Although special emphasis is given to the potential role of physician's assistants, nurse practitioners and nui.se midwives in HMO's, the staffing requirements for physicians, registered nurses and licensed practical nurses are also investigated. Four basic mathematical models are developed to analyze in detail the design relationships between resources and requirements in HMO's. The models are used to examine the interaction between effective manpower utilization, technology utilization, facility requirements and local inputs such as available capital and existing health care facilities. Another principal feature of the models is that they reflect the total cost for outpatient medical care services delivered at the HMO. The objectives used in the models pertain to either minimum cost or the minimum feasible use of physicians through the substitution of allied health personnel.

PAGE 19

A new three -level hierarchial medical classification system is developed which relates to the following manpower planning considerations: training and delegation, morbidity statistics, and manpower utilization. The new medical classification system was used to define and collect data regarding time requirements, delegation possibilities and patient utilization. In addition medical cost data were collected at a major prepaid group practice. Data relating to both direct and indirect costs are presented to fulfill the data requirements of the models. The models are validated through a seven-step process that includes: comparisons to two existing prepaid group practices; use of the models in the design of two HMO's; face validity; sensitivity analysis; parametric analysis; examination of internal validity; and an examination of data validity. Two detailed case studies are presented which demonstrate the flexibility and usefulness of the models in actual HMO planning. One case study was principally concerned with staffing requirements, benefits to be offered and the capitation rate while the other was chiefly concerned with the possible use of physician s assistants and a dynamic hiring plan as the HMO subscriber size increased. An extensive variety of results are presented relating to the use of allied health personnel in the primary care specialties in HMO's. An analysis of the potential cost and manpower effect extensive use of allied health personnel would have on large HMO's shows a 4 to 10 percent cost reduction and a 25 to 50 percent reduction in physician requirements depending on the medical specialty. An optimal delegation analysis shows that routine examinations, well child care, chronic illnesses, and diseases with a high emotional content are most economically and medically suited for delegation to physician's assistant level personnel

PAGE 20

sonnel. Results are also presented to show that one physician's assistant level person can replace about .6 of a physician in an HMO and that the optimal ratio of physician's assistant level personnel to physicians is 1.55, 2.10, and .47 in adult medicine, pediatrics, and obstetrics /gynecology , respectively. In addition, sensitivity analyses of physician's assistant utilization as a function of facility cost, salary, and delegation guidelines are presented. Parametric analyses of physician's assistant utilization as a function of the integer manpower restrictions and the size of the HMO are also presented.

PAGE 21

CHAPTER 1 INTRODUCTION Background The last decade has witnessed a growing national recognition that the U.S. health care system has failed to meet the expectations of the general populace (l). The plight of the rural poor and inner city poor has been especially noticeable. The overall national shortage of physicians and trained health personnel plus the disinclination of the professionals to settle in rural and impacted urban areas is creating a doubly critical problem (1). In addition an increasing proportion of physicians are not engaged in patient care at all but are engaged in research, administration, teaching, government service or consultation activities (l). Of those involved in patient care, the ratio of family practitioners (general practitioners, internists, and pediatricians) to the population fell by 33 percent from 1950 to 1965 (2). The demand for health care is being stimulated by two additional factors: a changed attitude toward health and health care and greater financial support for health care. It has only been in the last two decades when health insurance, Medicare, Medicaid, and many other public and private financing programs became available and translated medical needs into medical demand (1). Health care expectations have risen to the point where many people believe health care is a right

PAGE 22

2 rather than a privilege. In 1966 the American government in P.L. 89-749 assumed a commitment "to assure comprehensive health services of high quality for every person." Compounding these problems is the fact that too much of the physician's time is ineffectively utilized in routine and semi-clerical tasks. Much of the work physicians and nurses do can be characterized by routine tasks such as reading electrocardiograms, following a patient's vital signs manually, and administering and interpreting chemical, biochemical and physical tests (3). In addition, large portions of time and attention are devoted to the well or the so called "worried well" (4). Finally, costs of health care are rising rapidly. From 1965 to 1970 physician fees rose by an annual rate of from 5.4 percent to 9.2 percent (1). The average daily service charge for hospitals rose 279 percent from 1960 to 1970 (5). These cost increases are caused by specific factors such as rising labor costs; the increasing employment of more highly skilled personnel; the changing status and higher pay of the house staff of hospitals; the rise in the cost of construction and supplies; the increase in number and sophistication of diagnostic tests and therapeutic procedures; the changing mix of the patient population with a trend toward more serious illness; the persistence of too many economically inefficient small units; and the rising costs of administrative overhead (1). Out of consideration for these signs and symptoms of failure of the current health care system is the growing recognition that new health care systems must be encouraged and developed. Thus in January, 1971 President Nixon called for a new health care system in America (6).

PAGE 23

3 The central feature of his plan is the Health Maintenance Organization (HMO) which is similar in concept to neighborhood health centers but fundamentally embodies the principals of prepaid group practice (PPGP). Scope and Purpose This dissertation reviews the existing descriptive and conceptual literature on HMO's and PPGP's and utilizes this information to model mathematically HMO's. A systems analysis approach utilizing mixed integer programming and linear programming models is proposed which provides an aid to decision makers in the design and evaluation of health manpower requirements in the outpatient segment of the HMO. To model the manpower needs a medical classification system was developed to facilitate the development of the relationship between the system requirements in terms of typical patient visits and system resources in terms of trained health manpower. The models and medical classification system are used to evaluate the potential role of a physician extender (PE) in the HMO setting. There is a large number of different types of PE's involved in health care and a few examples include physician assistants, pediatric nurse practitioners, and nurse midwives. The models are developed to examine the interaction between effective manpower utilization, technology utilization, facility requirements and local inputs such as available capital and existing health care facilities. Another principle feature of the models is that they reflect the total cost for outpatient medical care services delivered at the HMO. The analytical models introduced in this dissertation can be used to evaluate staffing requirements for any type of medical service pro-

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4 vided in the outpatient setting by an HMO. However, due to data limitations the scope of the solutions presented are narrowed to the primary specialties; adult medicine, pediatrics and obstetrics/gynecology (OB/GYN) . The manpower types considered are thus the physicians and physician extenders commonly used in the above specialties as well as registered nurses (RN) and licensed practical nurses (LPN) . A principal byproduct of a systems analysis and mathematical model is a systematic framework in which data can be collected and analyzed. In the health care setting such a framework is particularly needed (7). Thus within the systems viewpoint developed in the models an extensive amount of data is presented relating to the above specialties, manpower, and the cost of medical care. The overall result of this research is the presentation of a systems methodology which will aid in the evaluation and design of HMO's. In addition, through use of the models and the data collected, definite design guidelines for the utilization of medical manpower in HMO's are established. Since the analytical models presented are very flexible, they allow the comparison of an existing HMO to an optimal design which incorporates many of the local inputs such as utilization rates, patterns of medical care, salary structure and other items that are relevant to the particular HMO being evaluated. The study compares two existing prepaid group practices to the design given by the analytical models and the models also are used to aid in the design of two HMO's. One of the HMO's was in the process of converting from a neighborhood health center to an HMO and the other HMO was in its preoperational planning stage. Through the comparison of results to existing HMO's and through the use of the models in the design of emerging HMO's, the viability

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5 and validity of the design approach was determined. Overall, the goal is to carry out a research effort in which systems analysis and operations research techniques are used and discussed, but end with results and conclusions which can be utilized by persons not necessarily acquainted with these techniques. Research Objectives This section briefly summarizes the specific research objectives that are carried out in this dissertation. The objectives can be divided into three principal areas: development of mathematical models to aid in the design of HMO's; collecting the data required to solve the models; and using the models to examine various policy questions and to aid in the design of two emerging HMO's. Four mathematical models are developed to analyze in detail the design relationships between resources and requirements in HMO's. These four models solve the following basic types of problems: (a) preoperational planning for which minimum cost solutions are sought for the services to be provided, manpower needed, delegation policy, facilities needed and particular technology innovations; (b) preoperational planning for which the optimal staffing, delegation policy and facility is sought to minimize the capitation rate; (c) manpower planning for which the optimal allied personnel policy is sought to

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6 maximize the HMO subscribers per physician; and (d) manpower planning for which the optimal allied personnel policy is sought to minimize the number of physicians required. These four models are mixed integer programs (or linear programs if the integer restrictions are dropped) and are developed in such a manner that solutions are obtained at a relatively low cost. The mathematical models were used to provide a framework in which data were collected. As a first step in the data collection effort, a new medical classification system is presented which relates to the following manpower planning considerations: training and delegation, morbidity statistics, and manpower utilization. In addition to previously published data, an extensive amount of original data collected at a major prepaid group practice is presented. In summary, data are presented for the following areas: (a) manpower time requirements; (b) delegation possibilities to PE's; (c) medical utilization by diagnosis; (d) direct medical costs; and (e) indirect medical costs. The third major research objective involves the use of the models and the data to derive solutions. As a first step in the validation process the results of the models are compared to two major prepaid group practices. In addition the models are used to derive solutions for the following problems:

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(a) an analysis of the potential cost and manpower effect extensive PE utilization would have on a major prepaid practice; (b) an analysis of optimal delegation guidelines for PE's; (c) a case study for the optimal manpower requirements and resulting cost for a neighborhood health center planning to convert to an HMO in Indianapolis, Indiana; (d) a case study for the possible utilization of PE's in an emerging HMO in Daytona Beach, Florida; (e) a sensitivity analysis of PE utilization as a function of facility cost, PE salary, and PE delegation guidelines; (f) a parametric analysis of PE utilization as a function of the integer manpower restrictions and size of the HMO; and (g) a parametric analysis of the maximum subscribers per physician in an HMO as a function of PE utilization and HMO size. Organization of the Dissertation In Chapter 2 the two main components of the medical system under study are presented. The concepts and properties of HMO's are discussed and a more detailed look at health manpower is provided. Special emphasis is given to a discussion of PE's. In addition a motivation for using

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8 mathematical models to aid in the design of the HMO is presented. This motivation includes the framework for HMO design that is carried out by the models. In Chapter 3 a system schematic and tradeoffs to be incorporated are presented. Preliminary models are developed to show the basic structural relationships in the HMO system. The preliminary models are then enriched in a step-by-step fashion to the point where a detailed model is presented. The detailed model provides the basis for the development of four additional models which are aimed at specific HMO and manpower planning questions. In Chapter 4 a new medical classification system is presented. This systam is then used to present data relating to manpower time requirements, delegation possibilities and patient utilization. In addition, both direct and indirect costs for prepaid medical care are presented. In Chapter 5 the solution method for the models is briefly discussed and a detailed examination of the validation process is presented. This includes a suggested sequence of steps which can be used to validate a prescriptive mathematical model. Solutions from the models are presented and compared to two major prepaid group practices and an analysis of the potential effect of PE utilization is explored. In addition two case studies are presented which give additional data and demonstrate some of the types of HMO analysis that can be carried out with the models, In Chapter 6 sensitivity analyses and parametric analyses are presented. The sensitivity analyses include an examination of facility costs, PE salary, and delegation and supervision guidelines. The parametric analyses include an examination of the integer manpower restrictions, HMO size, a scarcity of PE's and the maximum subscribers per

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9 physician. In addition the potential national manpower implications are briefly discussed. A summary of the results and conclusions of this research and suggestions for further research are presented in Chapter 7.

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CHAPTER 2 BACKGROUND AND LITERATURE REVIEW Health Maintenance Organizations General Terminology In many ways the Neighborhood Health Center (NHC) is a forerunner of the HMO without the HMO financing system. NHC's employ nurses and paramedical aids in expanded involvements, provide local employment for neighborhoods, invite consumer participation in the decision processes, affiliate with a hospital for referral and inpatient care, and provide outreach services to the community for health education and family health counseling (8) . The NHC has been a very viable concept and is widely accepted and used by the residents in its vicinity. However, although the NHC's serve their communities well, they are in reality a separate health care system and may be supplanted by HMO's in the near future. Another concept central to HMO's is the relation between and definition of group practice and prepaid group practice. Group practice has been described as "the application of medical services by three or more full-time physicians formally organized to provide medical care, consultation, diagnosis, and/or treatment through the joint use of equipment and personnel, and with the income from medical practice distributed in accordance with methods previously determined by the group." (9, p. 598) Groups may be single disciplinary or multi-disciplinary in nature and 10

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11 exist in the form of partnerships or as corporations. Prepaid group practice (PPGP) is a version of group practice in which the patient population prepays for health care at a specified yearly or monthly rate. PPGP attempts to mutualize through capitation the cost of comprehensive medical care for the population at risk and removes the fee-for-service barrier to care. The large PPGP's include teams of full-time physicians representing all of primary care and most of the minor specialties so that comprehensive services can be provided through an integrated single system (9) . Services are not only available at a hospital, but in neighborhood ambulatory care units which provide primary care. Generally PPGP's have a scale of operation which permits the extensive use of ancillary personnel, and the capitation method of payment, it has been suggested, tends to provide an incentive for integration of physician extender health teams and to maintain the health of the patient in an effort to deliver health care economically. The claimed advantages of prepaid group practice are numerous and include: provision of a comprehensive range of outpatient services; continuity of health care in one setting; pooling of resources to make possible the most efficient use of manpower, money, medical technology and equipment; quick and efficient use of consultants; and an emphasis on preventive medicine (10) . Other authors point out additional advantages such as increased productivity and a better division of labor (11) and peer review and better doctor-patient relationships (12) . In addition, capitation has been shown to be effective in decreasing surgical rates for such procedures as tonsillectomies, adenoidectomies and hysterectomies (13). Many of the above advantages have been observed in

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12 the Kaiser-Permanente system which is the largest prepaid group practice in the United States. As an example, the subscribers of Kaiser-Permanente reported savings of 30-40 percent per family for medical care (14). Also with the low surgical rates and the emphasis on ambulatory care, the number of short term general hospital beds in the Kaiser system is about 1.6 per thousand members compared to the national rate of 4.1 per thousand population (13) . Legislative Background As a result of a continuing dialog concerning the alternatives to the present health care system, health care has again entered the national political arena. In August, 1970, Senator Kennedy (D-Mass.) introduced the Health Security Act (15) . This bill called for sweeping changes in the national health system revolving about a National Health Insurance which would virtually replace private health insurance. This bill also emphasized moving the medical care system toward organized programs of health services, with special emphasis on teams of professional, technical and support personnel, and sought to move the health system toward PPGP. Partially because of Senator Kennedy's bill, health care came to the forefront of national politics and in President Nixon's 1971 State of the Union address (6), he set forth broad proposals for improving America's health care. These proposals included: a national health insurance program; increasing the number of doctors and other health personnel; making greater use of medical assistants to slow the rise in costs; and new programs to encourage better preventive medicine. He later followed this up with a paper to Congress detailing his health care

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13 proposals (16). In this report, the President was highly complimentary with regard to PPGP and made it a cornerstone of his health care program under the name Health Maintenance Organization. The main objective of his HMO would be to foster cost consciousness in the group practice setting. The cost savings would arise due to economics of scale and the use of ancillary medical personnel where possible. His plan called for a national commitment to help HMO's get started, along with a restructuring of private health insurance to make HMO coverage optional. It should be noted that the Administration's HMO plans are broad enough to include individually practicing physicians and community health facilities, bound together by contractual and professional agreements and serving the enrolled population side by side with the feefor service practice (17). This type of plan is exemplified by the San Joaquin Medical Care Foundation. The President also asked for the repeal of laws in 22 states which either limit group practice of medicine or the use of physician's assistants. He also called for a greater number of people in the allied health areas to help use existing medical manpower more effectively and the Secretary of Health, Education, and Welfare was directed to focus research in the field of health care services on new techniques for improving the productivity of our medical system. In addition to the health care legislation summarized above, there have been several other major health care bills under consideration by Congress (18-22) and further background material is given in reference (23) . Research Viewpoint The HMO concept has been proposed as a potential cure for a number of problems present in the American health care system. Among the most

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14 frequently cited of these problems are rising costs, the episodic rather than preventive nature of health care delivery, and maldistribution of services which has resulted in inadequate access to care in inner city and rural areas. Numerous viewpoints on the most desirable structure of an HMO have baen expressed by spokesmen of the Nixon Administration (17, 24, 25), the American Public Health Association (26), the American Medical Association (27) and others. These structures differ in many important details but are sufficiently similar to generalize for the purposes of this research. It is assumed that the precise concept of an HMO (or whatever term may subsequently replace it) will be in continual flux. For present purposes the following structural elements are taken as a minimum. An HMO is an entity which (a) serves an enrolled population who contract with the delivery system for provision of a range of health services; (b) is managed in a manner to insure legal, fiscal and professional accountability; and (c) provides prenegotiated comprehensive health services to all subscribers directly through its own staff and supporting resources or through other health delivery entities for a fixed payment paid on a periodic basis without regard to the frequency, extent } or kind of service actually provided during the period.

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15 The basic argument for the workability of HMOs is that with a fixed annual capitation fee it is in the best interests of both the HMO and the subscribers to maintain each subscriber in a high degree of health to minimize the utilization of costly services such as inpatient hospitalization. Other advantages offered by HMO's are expected to be: (a) a continuity of care through a variety of specialists in one location; (b) lower cost to the patient (28-30) ; (c) less physician involvement in clerical and managerial details (31) ; (d) regular working hours for physicians (31); and (e) continuing education and peer review of physicians (31) , Allied Health Manpower Physician Extenders Although there are hundreds of kinds of manpower utilized in the delivery of health services, the patient receiving medical care is in most frequent contact with either a physician or a nurse. Recently a new role has emerged which is intended to supplement the physician by relieving him of routine duties not requiring his extended training. Although these persons act under the supervision of a physician, they are not usually involved in the type of direct patient nursing care associated with the traditional nurses' role. As of March, 1971, at least 125 programs were in operation or in

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16 advanced planning to train persons fcr this new role (32) . The personnel trained in these programs are known by a plethora of names; a partial list follows: (a) physician associate, (b) physician assistant, (c) family health practitioner, (d) pediatric nurse associate, (e) public health nurse practitioner, (f) family nurse practitioner, (g) opthalmic nurse, (h) nurse midwife, (i) nurse anaesthetist, and (j) family nurse clinician. Although some of these programs are relatively well-established, most are quite new. To avoid the multitude of names, in this research the above personnel categories will generally be referred to as physician extenders (PE). Physician Extenders in Primary Care This dissertation deals principally with the delivery of primary care in adult medicine, OB/GYN and pediatrics. Physician extender types of importance to these areas are discussed in this section. There are two general types of physician extender programs evolving in the United States. One type is typically called a physician assistant (PA) program and is principally aimed at persons with at least a high school education and perhaps some college education and also with prior

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17 health care experience such as a medical corpsman. The other type seeks to expand the role of the nurse and is usually denoted by the term nurse plus other modifiers such as practitioner, clinician, or midwife. These programs generally accept RN's and give them further specialized training. There are many different types of physician assistant programs in existence. However a general definition of a TYPE A assistant was proposed by the American Association of Medical Colleges' Task Force on Physician's Assistants Programs . Type A, within this definition of an assistant to the physician, is capable of approaching the patient, collecting historical and physical data, organizing the data, and presenting it in such a way that the physician can visualize the medical problem and determine the next appropriate diagnostic or therapeutic step. He is also capable of assisting the physician by performing diagnostic and therapeutic procedures and coordinating the role of other more technical assistants. It is recognized that he functions under the general supervision and responsibility of the physician, though he might, under special circumstances and under defined rules, operate away from the immediate surveillance of the physician. To properly perform at this level, the assistant must possess enough knowledge of medicine to permit a degree of interpretation of findings and a degree of independent action within these defined rules and circumstances. (33, p. 102) The first PA training program was at Duke University (34) and Estes (35) pointed out that the tasks physicians perform can be divided into those requiring the complex judgement their education prepared them for and those that require technical skills that can be learned by repitition. It is these technical skills that Duke trained the PA's to perform with the additional goal to prepare the PA to "do anything which the doctor can program him to do." (36, p. 33) The use of TYPE A or generalist PA's has also been defined and analyzed in the University of

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18 Washington's MEDEX program (37). Ex-corpsmen in this program follow a three-month academic program followed by a twelve-month preceptorship that includes three days of formal education per month. The Washington MEDEX program has been used as a model to set up MEDEX programs in many other universities (34). The use of ex-corpsmen as input to the PA programs has to be considered as temporary due to the reduced future supply of corpsmen; thus if PA's are to become a standard part of the health care system, people without previous medical experience will have to be trained or an increased number of nurses could be admitted to PA programs (34). An important example of the nurse expander type program is the pediatric nurse practitioner (PNP) . The first formal training program was established by Silver and Ford (38) in Denver and since then the American Nurses Association and the American Academy of Pediatrics have issued a joint statement defining this concept and established guidelines for programs of continuing education (39). Twentyfour training programs for PNP's were listed in July 1971 (40). At the University of Colorado, the PNP is a graduate nurse with a baccalaureate degree who has received four months of intensive theory and practice in pediatrics at the University of Colorado Medical Center (41). During their training, emphasis is placed on patient interviewing techniques, performing a complete physical, various aspects of parent-child relationships, child development and counseling techniques (41) . They also learn to assist in both the management of healthy children and those with a variety of acute and chronic disorders (42) . Another major category of the expanded role of the nurse is the

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19 nurse midwife (NMW) . According to the American College of Nurse Midwifery definition, the NMW is "a registered nurse who, by virtue of her added skill gained through an organized program of study and clinical experience, recognized by the American College of Nurse-Midwifery, has extended the limits of her practice into the area of management of care of mothers and babies through the maternity cycle so long as progress meets criteria accepted as normal." (43, p. 354) Although there are many other types of training programs for many medical specialties, the PA, PNP and NMW programs were specifically mentioned due to their involvement in the primary care areas: PA's are usually trained to assist general practitioners or physicians in internal medicine; PNP's are trained to assist pediatricians; and NMW's are trained to assist physicians in OB/GYN. These are the three primary care areas focused on in this paper. Since m=my of the programs produce health care providers with different titles but very similar capabilities, this will be simplified by referring to all as PE's and recalling the three primary care prototypes described above. Physician Extender Utilization: The Team Concept Utilization of auxiliary personnel in primary medical care delivery is usually done in the context of a "health care team." At present, tradition, licensing, registration, and practice act restrictions dictate that the auxiliary personnel be supervised by an MD (44-51) . Although it is likely that this configuration will continue for some time to come, some research (52) has been directed toward family health teams for HMO's that are totally comprised of allied health personnel. Granting more

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20 autonomy to allied health professionals raises questions of professional acceptance, legal accountability, and patient acceptance. In recognition of these issues the AMA (27) has called for more research into the questions of which type of assistant to develop, the tasks they can assume, their acceptance by patients and physicians, and their impact on costs and productivity. This dissertation will explicitly consider three health care team configurations: (a) a team comprised of a physician, an RN, and possibly an LPN; (b) a team comprised of a physician extender, an RN, and possibly an LPN; ?nd, (c) a team comprised of a physician, a physician extender, and an RN. A PE in the second type of team noted above would be acting under indirect supervision by an MD. Under that configuration the MD would typically confer briefly with the PE regarding the patient and the PE's findings, or the MD may briefly see the patient and read over the PE's findings. In the third type of team, the PE would be acting unaer direct supervision. This would not necessarily imply that the MD is in the room at all times with the PE. However, it does imply that the MD has direct control over the particular patient visit. The PE would typically take the patient history and perform a preliminary workup or physical exam. This portion of the visit is time consuming and does not require the highly developed skills of the MD . The MD would then take these findings and carry on from that point with the patient. It's possible the PE would later be used to carry out tests, a treatment regimen, or to

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21 explain a home treatment regimen to the patient. Delegation of Medical Services The question of which functions can be carried out by a physician extender is at the core of the problem of PE utilization. For the purposes of this study, a broad definition of the PE types is not enough to fully analyze potential PE utilization. A more detailed answer of what allied health personnel are prepared to do end what professional personnel are prepared to delegate to them is required. Although the use of PE's is relatively new in the United States, there has been considerable use of similar level personnel in other countries. As far back as the 1700' s "feldshers" were functioning in Russia (44) . In urban areas the feldsher works as an assistant to the physician but in the rural areas the feldsher frequently performs in a primary care role (53). An even more striking example of the utilization of allied health personnel exists in China. China has several levels of assistants for the physicians. One level of assistant, with a limited formal training of about three months and on the job training, provides certain elements of primary care in rural areas and another level is typically comprised of housewives with ten or more days training who work on a neighborhood level (54). With regard to health care teams, a professor of orthopedics in China noted: In the countryside--and I am sure this will cause eyebrows to be raised--we made no distinction between nurses and doctors. .. .In fact, doctors and nurses were in essence doing the same job to the best of their abilities, and their abilities depended as much on their adaptability and sense of responsibility as on the type and duration of training which they had undergone. (55, p. 192)

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22 In Cuba, the nurses routinely give intravenous injections and make house calls (56) . In many other countries (most but not all are developing nations) paramedical aids are an integral part of the health care system (57-60). However, within the United States the organized use of personnel on the PE level is relatively new. As a consequence there has been some uncertainty as to their possible function and the specific training programs needed. Since PE's will perform in 3 subsidiary capacity, several surveys or studies to elicit the opinions of physicians have been performed (33, 61-71). In a survey of 3,425 internists the American Society of Internal Medicine found that internists believed many elements of their practice could be delegated to an allied health worker (61) . The American Academy of Pediatrics surveyed 5,799 pediatricians and found that over 70 percent favored delegation of recording the patient history and counseling on child care, feeding and development (62). About 25 percent favored delegation of well child and sick child examinations. It has also been reported that 50-65 percent of the physicians in Wisconsin indicate a need for a physician assistant (63). Patient acceptance has been good (64) and over 50 percent found the care provided by a pediatrician and a pediatric nurse practitioner better than that received from a physician alone (65) . The major problem involved in utilizing the studies noted above is their lack of a common medical classification system upon which delegation can be analyzed. The studies used tasks, functions, services, prucedures, typical patient visits and sometimes a combination of these. However, the modeling effort in this dissertation requires a single consistent classification system in which delegation can be analyzed.

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23 There are many classification systems for medical patients but unfortunately few are useful for analysis of manpower and delegation decisions. The most widely known is the International Classification of Diseases, Abstracted (ICDA) but it is of more use in hospital admissions where diagnosis is a feasible classification index. The California Relative Value Units (CRVU) are also used to some extent, but it is too vague in the area of patient office visits. There are several compilations of tasks performed in the health care system (71, 72), but tasks do not lend themselves well to viable patterns of delegation and analysis. Instead of the above methods of medical classification the concept of a medical service or typical patient visit will be used in this study. This concept allows the model to concentrate only on viable patterns of delegation, simplify the computational details and increases the intuitive appeal of the results (73) . Previous medical service listings have been reported for general practice (73) and for the primary care specialties (74). Since the former is limited to general practice and the latter is too general, a new medical classification is presented in Chapter 4 which enables the analysis of the relationship between training, delegation and manpower utilization to be fully explored. Motivation for Mathematical Modeling Previous Studies Formal PE programs were started in the United States only a few years ago. As a result there have been few studies which have analyzed the use of PE's. Likewise the HMO proposal was first introduced in 1970 and also suffers from a lack of analysis. In both areas, discussions

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24 regarding the concept behind paramedical personnel and HMO's are relatively plentiful and, while these studies have guided the overall goal of this paper, they do not provide a concrete basis on which to start an analysis. However, there have been several exploratory studies performed which are fairly directly related to the goals of this paper. The research most useful to review was performed by Shuman (75, 76), Golladay, Smith and Miller (73), Reinhardt (77), and Goldstein and Horowitz (78) . This collection of studies is of particular interest since they represent the spectrum of techniques which have been used to analyze health manpower usage. Shuman and Golladay et al. arrived at totally different normative mathematical models to analyze manpower utilization, while Reinhardt used a descriptive model in the form of production functions to analyze the increased efficiency resulting from the use of paramedical aides. On the other hand, Goldstein and Horowitz took a personnel management approach to increasing manpower efficiency in a hospital. Each of these will be discussed in greater detail in the following paragraphs. Shuman' s work dealt mainly with regional health manpower planning and the substitution between various personnel classes. Both papers by Shuman are of interest but since the aspects essential to this study are contained in (76) only the latter work will be reviewed. Shuman considers three ways by which productivity may be increased: introduction of technology, transfer of tasks to less skilled personnel, and organizational changes. A key point he makes is that the manpower problem is part of a larger problem: the determination of an efficient means for the delivery of health services. Only then can it be determined whether

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25 shortages actually exist for MD's, nurses or allied health personnel. This rather straight forward point has been largely neglected in most manpower studies and casts doubt on many of their conclusions. In other words the emphasis should be on the shortages of health services not on a manpower shortage. Starting with this insight into the problems in the health care system, Shuman then formulated an analytic model to attempt to determine the proper mix of manpower to provide the services. Shuman's work was one of the first attempts to model analytically the problem and consequently there are many problems left unanswered. The principle shortcomings revolve around the size of the model as it is structured and the lack of data and manpower analysis contained in the study. Several aspects of Shuman' s models are discussed in Chapter 3. Golladay, Smith and Miller (73) investigated the optimal role for parap->-ofessionals in the health care system and their potential impact on the productivity of the physician. The study developed an analytical model of primary care practice which enabled them to explore the implications of delegation for physician productivity, per patient costs, and demands for all categories of medical workers. The most unique feature of the study involved the data collection for task analysis in medical practice. The analytic model was derived to answer these questions: 1) what is the optimal staffing pattern for a practice and how is it related to the size of the patient population; 2) how many hours of patient contact time would be required to satisfy the medical demands of a specified patient population; and,

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26 3) which activities would be delegated in an efficiently run practice? Their model is described in Chapter 3. Golladay, Smith and Miller concluded that 1) use of one PA may increase the productivity of a physician by 74 percent; and 2) from a monetary standpoint, MD's would profit from using PA's. In contrast to the normative models proposed by Shuman and Golladay et al., Reinhardt derived a descriptive model utilizing a production function approach. This type of approach is the most common quantitative technique used to analyze manpower utilization and is frequently used by economists. Reinhardt set out to answer two questions: 1) to what extent is it possible to raise the output per physician hour through use of paramedical personnel; and 2) can physicians in group practice use auxiliary personnel more efficiently than physicians in solo practice? His conclusion was that MD's should employ 3-4 aides rather than the 1-2 aides they now employ and that this would increase medical production by 20 percent. He also concluded group practice resulted in 11 percent to 16 percent higher production per MD than solo practice. Note these figures are conservative since they represent the use of allied personnel in 1965 and 1967 and not an optimal or even near-optimal task delegation. His work does however firmly lead to the conclusion that allied personnel will lead in practice to increased medical care production.

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27 Goldstein and Horowitz used personnel management techniques in an attempt at better utilization of medical manpower. Their study involved establishing what tasks were performed in the hospital, what training level was required to perform each of the tasks and what level personnel were presently performing the task. The two major goals of the study involved: (1) study and analyze the hiring-in requirements and the duties and functions of paramedical personnel in a single hospital; and, (2) to recommend changes to restructure occupations and to improve the utilization of manpower in that hospital. Their study did not attempt any optimization but it did result in concrete recommendations for better utilization of manpower. It is also an approach that is intuitively appealing to many people including those who have an inherent distrust of mathematics and model building. Its principal drawback is that it relies upon studying a well established institution such as a hospital in order to arrive at results. It also limited itself to reshuffling tasks paramedical personnel perform, and not substituting paramedical personnel forMD's. Systems Analysis as an Aid to the HMO Design Process The approach taken by Shuman, Golladay et al., and Reinhardt and the approach taken in this dissertation can be termed systems analysis. Systems analysis has been described by Kershaw and McKean as the "comparison of alternative means of carrying out some function, when those means are rather complicated and comprise a number of interrelated elements."

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28 (79, p. 1) The essential feature cf a systems analysis is thus the recognition of the interrelatedness of parts. The system should be defined so as to encompass all parts that are related in a significant fashion (79)An HMO is a system that consists of staff, facilities and materials and is organized to deliver medical care. However, the output of the HMO is difficult to quantify. It can be argued, for example, that the output of a medical system should be measured in terms of the improvement or stabilization of the health of the patients. In practice however, this concept is extremely difficult to apply and in this dissertation the output is measured in terms cf medical services provided. The mathematical models will allow an analysis of the interrelated factors to be performed and will allow the examination of the substitution of various alternative resource combinations. In addition to manpower, the models should also permit the analysis of the effects of automation and technology upon output. An approach to incorporating technology into the models is discussed in the next chapter. Although extremely important, questions on the quality of care provided and the effects of alternative system configurations on the general health of the population covered are considered to be beyond the scope of this dissertation. Planning the Benefits To Be Provided by an HMO There are two basic approaches to examining the choice of services. The first approach (see Figure 1) is the traditional method which is most commonly proposed. This technique assumes that legislative groups in consultation with various health personnel will decide what services an HMO should provide. The principal weakness is that it is a decision made

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29 without regard to the other variables in the planning process. Note that Figure 1 denotes a system with no feedback loops. Begin Planning

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30 The models are designed such that they can be useful in the proposed decision process depicted by Figure 2. The individual medical services used in the models are detailed enough to distinguish between time requirements and training requirements. Sets of these services can be considered for the various medical specialties and the models are designed so that the specialties can be included or excluded from the HMO depending on economic factors. The models also allow the decision maker to fix some or all sets of services as necessary for provision in the HMO due to political or other conditions. Proposed HMO Design Process This research assumes a three-level hierarchy in the design of an HMO f see Figure 3) . The first level describes the financing, social characteristic, incentives, generalities and overall objectives of HMO's. This is the level that is most frequently discussed in the literature. The second level deals with HMO's on a more specific basis. This level of decision making would be concerned with the size of subscriber group, levels of technology, general personnel guidelines, capitation rate, relations with hospitals, etc. The third level examines HMO's on a microscopic level. The decision on this level would be concerned with the type and number of various personnel classes, specific technology utilization, task allocation, patient flow, etc. This three-level hierarchy completely specifies the design of an HMO. Because the models developed in this dissertation can best be used to analyze levels two and three they are presented as a systematic technique to decision making on these levels.

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31 Level 1 Legislation Financing Social Characteristics Overall Objectives Level 2 Size of HMO's Sen/ices Personnel Guidelines Capitation Rate Relations with Hospitals Level 3 Specific type of Personnel Number of each type of Personnel Needed Specific Technology Utilization Assignment of Services Figure 3 Three-Stage Hierarchy in the Planning of HMO's Figure 3 showed the relationship which exists between the levels of decision making for planning an HMO. Figures 4 and 5 present the dynamics of the decision process. Figure 4 presents an approximation of the dynamics involved in the present HMO design concept while Figure 5 presents the dynamic relationships which are modeled in this paper. Note that Figure 5 portrays the strong interaction which exists between subsystems of the HMO while Figure 4 shows a weaker interaction which occurs in the present design process. As was noted previously, the research effort is primarily aimed at effective manpower utilization. However, as Figure 5 shows, the manpower utilization is strongly interactive with the other subsystems of the HMO.

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32 u

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33

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34 These other subsystems will be examined only as far as is needed to perceive their input to the mathematical models. The optimal design, or even design, of these other subsystems is beyond the scope of this research. In the next chapter, models are developed which will permit the evaluation of alternative designs of HMO's. To examine the design of HMO's, three measures of effectiveness are utilized and developed by the mathematical models: 1) minimizing cost to the subscriber; 2) using the least number of professional manpower to serve a given set of subscribers (and maintain quality) ; and, 3) using a given set of professionals such that the number of services they provide are maximized. Using these objectives, the models can help optimally design certain aspects of the HMO. Thus, they can be used to present design guidelines and enable one to perform sensitivity analysis on the inputs.

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CHAPTER 3 DEVELOPMENT OF ANALYTICAL MODELS Preliminary Models Introduction In this chapter several models are proposed to answer some of the questions which arise in the overall design process for HMO's. These models are designed to represent a useful formulation for part of the HMO system and to be solvable in a practical sense. Each of the models involves the assignment of personnel to services and the staffing levels required. Beyond this, the models can be dichotomized as: (a) maximize subscribers by optimal allocation and mix of professional manpower and facility resources, and ancillary manpower, or (b) minimize resources used to provide a fixed set of services or requirements. Initially, a very simple model is derived. A step by step motivation and refinement is then carried out; culminating in a more complex, but more flexible and refined model. The complex model is then used to derive four other principle models. Throughout the development new notation will be introduced in the text; additionally, a complete listing is given in the Key To Symbols . 35

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36 System Schematic for Model Development A recurring HMO theme, as expressed in the literature noted in the first two chapters, is the cost-effectiveness through utilization of group practice and the capitation incentives. To examine the costeffectiveness of HMO's one must examine the costs in the HMO structure. A schematic of the structure of an HMO is given in Figure 6. MEDICAL CLERICAL ADMIN. LAB X-RAY OTHER ANCILLARY REFLECTED BUT NOT EXAMINED Figure 6 A Schematic Representation of the HMO Structure The inpatient care and dental care portions of an HMO are major problems in themselves and can be effectively isolated from the analysis of office based medical care. This does not imply there are no relationships between inpatient and ambulatory care, but only that the relationships can be handled external to this analysis. For example, an increased use of ambulatory care usually occurs in prepaid practice due to the decreased use of inpatient facilities. However since utilization of ambulatory care is an input to the models, this increase can be noted

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37 and used to determine the input to the models which would then reflect the ambulatory care manpower and costs resulting from the increased use of ambulatory care facilities. Also, within the HMO structure there are additional functions other than the medical care function. There are support personnel, such as clerical, administrative, laboratory, x-ray, and other ancillary aides, and management personnel for planning and direction and these functions are reflected in the models. The models focus on medical manpower, but to look at overall cost-effectiveness the models should reflect the costs of non-medical care functions for two principal reasons: (a) to examine the effect the costs of these non-medical functions have on the medical manpower; and (b) to examine the full costs for medical services and HMO's as a whole (excluding inpatient and dental). Within the medical care structure there are two main factions— those who subscribe to the plan for medical services and those who work for the plan and provide medical services. This is shown in Figure 7. REQUIREMENTS: RESOURCES: Subscribers Medical Personnel Demand for services Capability to provide services Services Provided Figure 7 Medical Care Structure Showing Relation Between Resources and Requirements

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38 The upper loop must be expressed in some taxonomy of health care delivery while the lower loop must be expressed in manpower types and capabilities. In addition, to be combined in the last block, the manpower capabilities must be expressable in terms of the taxonomy of health care delivery. This is an extremely difficult concept to put into practice. In previous related studies Golladay, Smith and Miller (73) approached this empirically for a small sample, Pondy (81) took a related but more superficial approach and Shuman (76) did not attempt to put the concept into practice. Tradeoff Decisions To Be Incorporated in the Models Chapter 2 presented a detailed view of HMO's and health manpower and resulted in a systems viewpoint of the interactions between the two. Figures 6 and 7 further helped to sharpen the focus to the point where mathematical models could be developed. At this point the particular decision making areas to be considered in the models will be explicitly stated. When normative mathematical models make decisions, they make them by trading off resources and requirements against each other in such a way that the objective function reaches its extremum. The constraints act to complicate the decision making to the point where mathematical programming techniques must usually be used to solve the problem. As a result of the systems development it has been determined that several factors are important and should be considered by the mathematical models in their decision making. The major tradeoffs that are incorporated in the minimum cost models are summarized below. 1. The models tradeoff delegating a service to the lowest cost person (who can perform the service) versus the additional cost of supervision by the MD.

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39 2. The models tradeoff delegating a service to the lowest cost person (who can perform the service) versus the supervision time required from the MD. Since supervision time is usually a scarce resource this implies also selecting those services to be delegated as well as to whom to delegate the service, 3. The models tradeoff the cost of providing a service by an MD and nurse versus the cost of providing the service by an MD, PE and nurse versus providing the service by a PE and nurse. In the second case, MD time decreases but MD plus PE time is greater than in the first case. In the third case, MD time for the service becomes zero, but additional MD time is required for the indirect supervision of the PE. 4. The models tradeoff the cost of higher cost personnel versus the integer restrictions on manpower levels. Thus for example, if delegating a service that requires .2 man years would require that one more PE would be hired with the subsequent .8 man years of idleness; it may be better to delegate the service to another, perhaps higher salaried person. 5. The models tradeoff the total cost of a service in the HMO versus what it can be purchased for outside the HMO. Note that the total cost for a service in an HMO is interrelated with all other services offered. This tradeoff can be

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40 done on a service by service level or on a medical specialty level. 6. The models tradeoff the cost for additional technology versus the higher productivity or lower salary levels required. Only the major factors have been included in the tradeoffs summarized above. There are other subsidiary factors such as capital requirements, capability limitations, and scarcity of manpower that are potentially involved in most of the above tradeoffs. This chapter also includes models concerned with the minimal use of MD's or for maximizing subscribers per MD for which the six tradeoffs listed above are still relevant, but the key is minimal use of MD time. In some cases the two give the same result, but there are many exceptions. In addition this latter type of model includes two additional factors: (a) as subscriber levels increase this means that more patient visits are eligible for PE's to handle; and (b) a budgetary limit is imposed, thus there may be ways to add additional subscribers but they would be too costly (in the models this is taken as the revenue = expenses point not the marginal revenue = marginal expenses point). The above tradeoffs are explicitly designed into the models. There may be other types of tradeoffs made depending on the exact use of the models or the data used for solving the models, but these additional tradeoffs are expressable in terms of the above tradeoffs.

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41 Preliminary Model Development Figures 6 and 7 represent two different but related structures in the HMO. Figure 6 diagrams what could be viewed as a cost structure while Figure 7 diagrams a medical care structure. On the most elemental level Figure 7 could be modeled by viewing the subscriber demands as the requirements vector and the medical personnel as the resources. Two objectives present themselves for this model: (a) minimize the medical manpower needs for a given number of subscribers; or (b) maximize the subscribers for a given number of medical personnel. The first objective takes the requirements as fixed and the resources to be variable while the second objective is the converse of the first. Use the definitions: I set of medical personnel of type i, I* set of MD's, I* set of non-MD's, J set of medical services of type j, x . manpower type i performing service j (man-years) , d. demand for service j (medical services per year), b rate at which manpower type i produce service j (medical ij • . services per man-year) , N. number of manpower type i employed (man-years), s. salary for type i personnel (dollars per year), E S , i iel S 2 .

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42 With these definitions we can meet the medical care requirements with the constraint Z b. .x. . > d. • jeJ. (3.1) We can also define the number of manpower type i employed as Z x. .-N. < • iel <3.2) and the first objective becomes min 2 N. , (3.3) i i or if constraint (3.2) is not used we have min S S x. . . (3.4) . . n JJ The model given by (3.1) (3.4) will be called Ml and is a linear programming model which essentially characterizes the models used by Golladay, Smith and Miller (73) and by Pondy (81). To arrive at the Golladay, Smith and Miller model the converse of the b. . coefficient is used. The b . coefficient in (3.1) converts resources to activities ij while Golladay, Smith and Miller use a coefficient in constraint (3.2) to convert activities to resources. This allows them to define health care teams or technologies in a straight forward manner but has the undesirable property of forcing the inputs from each member of the team to occur in fixed ratios — to change the ratios a new team must be defined. In addition Golladay, Smith and Miller take the MD input as fixed and seek to minimize the salary of ancillary personnel as their objective.

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43 This places weighting factors in equation (3.4) and the summation is taken over those i for non-MD's and constraint (3.2) is eliminated for non-MD's. The resultant model (where k is the team or technology) is: min E E s.a., x, (3.5) iel* k X lk k subject to E ax <_ N. V iel* , (3.6) k E jc = n. V jeJ . (3.7) keK. k J J The Pondy model is very similar. Both can be efficiently solved as a minimum cost network flow problem with nonnegative gains (80) . Thus both the Golladay, Smith and Miller model and the Pondy model follow directly from the elementary constraints on resources and requirements. This structure does not allow a full exploration of the relationship expressed in Figure 7. It also ignores the cost structure in which the medical system operates. It can be noted that both models were primarily focused on the fee-for-service setting. The model resulting from the second objective easily follows if the following definitions are made. Let S number of subscribers , d' services of type j demanded per subscriber. J Here the resources are fixed and the requirements are variable. Thus the model is : max S (3.8)

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44 subject to Ex < N • id , (3.9) J S b ij X ij " d j S ° • J€J . (3.10) This model arises from the implication that the present shortage of medical manpower is an overriding concern in the health care setting and thus seeks to provide medical care to the most people given the manpower available. No corresponding model appears in the literature. The weaknesses are the same as were noted above and in addition this model ignores the economics of medical care entirely. Development of the Medical Care Aspects of the Model Several general weaknesses of the Ml model have been pointed out. At this point the model will be developed further along the sco^e of Figure 7. This further development will lead to a model which exhibits greater flexibility and depth in its portrayal of prepaid group practice. The concept of minimizing medical manpower cost will be used. Medical care is provided either by individuals or by teams. Within a health care team the leader would typically be an MDj however yearns of PE's and nurses are also possible. In the former case, direct supervision by MD's is implicit within the team. However, in the latter case indirect supervision by physicians would normally be required. The Golladay, Smith and Miller model (73) and Pondy model (81) explicitly consider teams but do not consider the latter problem. On the other hand a model proposed by Shuman (76) considers indirect supervision but not teams. With the following definitions, model Ml can be revised to provide the needed generality.

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45 Let g I set of individual health care personnel, I set of health care teams, 1 set of manpower including teams, q . man-years of manpower type i per man-year of team k providing service j, 2 = E k kel ' * _* t I « I U I \J I . The particular introduction and definition of q, . . is the key to the generalization of the model. Using that definition (3.1) and (3.4) are unaffected. The only change occurs in (3.2) which becomes S x. . + S Z q. . .x. . j J k j N. < • iel . (3.11) l — In addition, a method to view indirect supervision must be introduced, not only for PE-nurse teams but also for PE's or nurses in an individual capacity. This concept, as used by Shuman (76), provided for fixed supervision levels regardless of the service being performed or the health care personnel involved. The constraint can be modified to reflect these considerations by defining: f . . level of independence for type i personnel to perform service i; f . . = implies no indirect supervision required J ' ij while f . . = 1 implies full indirect supervision, * J set of services class i el personnel supervise, * x j* is the supervisory service provided by personnel i i*j* The supervisory constraint involves the quality of health care in that it constrains the number of personnel a professional staff member may supervise and the level of independence exercised by the paramedical assistants. The general supervisory constraint is given by

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46 S 2 f. .b. .x. . < b...,x. u ., • i*el* . (3.12) je j. A iel* 1J 1J 1J l *J* ** J * It is generally accepted that MD's do not want to be burdened by an excessive amount of administrative work or supervision of ancillary personnel. The amount of supervision can easily be limited by making x '*-* an u Pper bounded variable which would not make the model any more difficult to solve. Thus, if SU. is defined as the maximum fraction of 1 time type i personnel will engage in indirect supervision of ancillary personnel, the upper bound is given by x.j..^. < SU.'N. • i*«I* . (3.13) Thus far the model is specified by (3.1), (3.4), and (3.11) (3.13) and a further tightening up on the definitions of resources and requirements is desirable. The resource considered thus far in the model is the available health manpower. Since an HMO has as a principle objective the delivery of effective health care in a cost-conscious manner, the resource should in many cases be evaluated in monetary terms. Also, the resources used here represent healch care employers; thus in many cases the employees will be full time employees only. This constraint is usually beneficial to both the employee and the employer. Full time employees can be represented by integer variables in the model. Thus, let N. be defined as an integer variable and define x! fractional part of personnel group i which are slack or idle (man-years), c. . labor cost for type i personnel or team to perform one type j service (dollars per medical service).

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The result is 47 c. . = s. /b . . ij i Ij • iel , c. . = 1/b. . T, s q. . ij ij _s n\ni J J nel J • iel (3.14) Also let units of time worked by team leader/year ij units of team leader time/medical service An example will help to clarify the meaning of these terms and their relation to q, . . Suppose for service 1 the time and personnel kij . requirements are as listed in Table 1. Table 1 Example of Personnel and Time Requirements i

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48 c (1/8640) ((30,000) (1) + (10,000) (.360)) = 3.89 Returning to the development of the model, recall the objective is to minimize the labor cost for all services provided which is given by min E E (b. .c. .) x. . . (3.15) Incorporating the integer manpower constraint for N. , constraint (3.11) becomes S x. . + E S q. . .x, . + x! N. = • iel (3.16) . ij , . ^kij Tcj l i ] k j and the objective becomes min 2 E (b. .c. .) x. . + E s.x! (3.17) . . ij ij ij .11. j l J l Note that the objective can be written as min E s.N. (3.18) . ,-S 11 iel but for clarity it will be written as the two terms in (3.17). It is also possible to generalize and refine the requirements constraint which is given by constraint (3.1). Physically, it is impossible for an HMO to deliver more services than are requested by the subscribers. It is however possible to deliver fewer services than are demanded but this would not be consistent with the concept of prepaid practice. The remaining possibility is that some health services be provided by extraordinary means. Thus a new variable n. can be defined as n. number of type j services demanded per year and not provided by ordinary means.

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49 This can be incorporated in constraint (3.1) to give 2 b ij x ij + n j = d j • J eJ > J^J* • ( 3 19 > The n. variable has several possible interpretations within an HMO J structure. In a multiclinic HMO it may be desirable to schedule some patients into a more heavily staffed clinic during peak periods. Another interpretation is that the HMO may contract out to other health care providers for their overload patients. A third possibility is that the n. represents those services performed on an overtime basis due to understaffing. A fourth possibility is that the n. can be used as a planning variable to determine if the HMO should provide the service or if it can be provided cheaper to the subscribers outside the HMO. This alternative will be developed later in the chapter. Several restrictions must be placed on the n. variable for reasonJ able solutions to arise from the model. To develop these restrictions define the coefficients: u. per unit cost for provision of type j services by extraordinary means, and MX. maximum fraction of services provided by extraordinary means. Constraint (3.19) shows the requirements can be provided by n. which has no cost in the objective function. To rectify this, (3.17) can be modified to give min E S (b. .c. .) x. . + 2 s.x! + 2 u.n. . (3.20) . . li ii ii .11 j 1 i J J J J i J

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50 In addition from a standpoint of convenience to the patient and paperwork problems for the HMO it is desirable to limit the services to be provided by extraordinary means. This can easily be included in the model using an upper bound constraint n. < MX. • d. • jej • (3.21) J J J MX. can be set to zero if all patients are to be seen under normal care for service j or set to non-zero if it is feasible to use one of the extraordinary means listed above. Typically MX. would range from 0.0-0.1, The modified model, to be denoted M2, is summarized below: min E E (b . .c. .) x. . + E s.x! + E u.n. (3.22) . . lj li li .11 J J ij JJ J i 3 subject to E E f. .b. .x. . < b. ...x. , ., • i*el* , (3.23) . . , ii 11 li — 1*1* i*1* jeJ iei* J J J j j J i* E x. . + E E q, . .x, . + x! N. = • iei (3.24) . ij . . ^kij kj i l j k j Ebx+n=d. • jej, j#j* , (3.25) t ij ij J J x..,.., < SU • N. • i*el* , (3.26) i*j* l n < MX.d. • jej . (3.27) J J J This model allows for a much fuller and more general representation of the system represented by Figure 7 than model Ml. If N is not restricted to integer levels, Ml and M2 are approximately of the same order of difficulty for solution purposes. If N. is restricted to

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51 integer levels the result is a mixed integer program which is more difficult to solve than the linear program required for model Ml. Further Development of Financial Aspects of the Model Thus far the financial aspects of the HMO have not been fullyinvestigated. Health manpower costs have been considered, but they represent less than half of the total cost in an HMO. This fact in itself provides some motivation to include the remaining costs in the HMO model. In addition, an objective of the model is to determine the cost of medical service. This determination will involve the cost of particular medical services, the costs by specialty or department, and the cost for the entire clinic or HMO. To further develop the model along the concepts expressed in Figure 6 it is necessary to examine manpower overhead costs, facility overhead costs, ancillary costs, the fee structure and the technology cost. An HMO will in most cases be organized in departments along medical specialty lines. Thus it may have an adult medicine, pediatrics, OB/GYN and other specialty departments. This departmentalization and ready access for patients to any department leads to little overlap in the functions carried out in the various departments. Model M2 did not reflect any departmental structure, but this will now be corrected. Define: V zero-one decision variable: if V =1 department m is offered m m and if V =0 department m is not offered; m M set of all medical departments under consideration; I set of personnel in department m;

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52 J set of services considered for provision; let J = (1,2, ...j* l,j * ...j* T-O*) where J* is the 1 1 m-i m m supervisory service provided by set I* personnel to supervise set I* personnel in department m; J' subset of J for which V = 1; m J set of services considered for provision or to be provided in department m. Thus J = ( V J m ) u ( U j*) • m m The V variable can thus be used as a decision variable to decide whether m it is economically desirable to include a department in a clinic or in an entire HMO or whether these services can best be obtained elsewhere. If the decision is to not include the department in one clinic this would be provided at the central HMO facility. If an entire HMO decided not to maintain a given department, they could contract out to another health care provider or remove that service from their list of benefits. If the departments are fixed, then the V can be set to zero or one, which in r m turn makes the model easier to solve. The V variable must be introduced m in (3.22), (3.25), and (3.27) which respectively become min 2 E (b. .c. .) x. . + 2 s.x'. . . 11 ij li .11 l j J i + E (1 V ) E d.u. + E u.n » (3.28) _ m . _m j j .ii m jej J J j E b x + n. d.V = • jeJ, ;tfj* , (3.29) , ij ij J J m n < MX • d VjeJ m , meM . (3.30) j ~ j J

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53 Standard accounting practices lead to the dichotomy between revenue producing cost centers and non-revenue producing cost centers. Since services are offered on a prepaid basis no medical department is strictly a revenue producing cost center. However, there is still a clear distinction between the direct services performed by the medical departments and the indirect services performed by the administrative, clerical and' managerial personnel. The position of ancillary services such as laboratory, x-ray, physical therapy ,,etc. , is not as clear. In the development of the cost model there will be three main overhead cost categories: manpower overhead costs, facility overhead costs, and ancillary costs. The costs for these functions will be reflected in the model but an optimization of these functions will not be carried out. There are three basic variables used to allocate overhead costs to the revenue cost centers: departmental services performed, departmental budget, or number of departmental employees. For the purpose of defining the model the manpower overhead costs are broken down and allocated in three basic parts: (a) medical records, membership, appointments, etc. (allocated on basis of patient visits to department); (b) management, planning, legal, etc. (allocated on basis of FTE professionals in a department); and (c) personnel, administrators of employee benefits, etc. (allocated on the basis of FTE employees in a department). With the above guidelines, define: AD manpower overhead or administrative cost for department m (dollars per year) ,

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54 PV manpower overhead cost per patient visit (dollars per patient visit) , MAN management and planning cost per FTE professional (dollars per man-year) , PER personnel cost per FTE employee (dollars per man-year) , b* number of type j services type iel* personnel can perform per year for a given level of technology. The FTE professionals needed to provide medical services for a department is given by FTE = E (d.V n.)/b* . (3.31) m jeJ m j m j j which can then be used to define the manpower overhead costs for the m department AD = PV Z E b. .x. . m . _m .„_m lj ij jej iel J J + MAN E (d.V n.)/b* + PER E N. . (3.32) . m j m j j . _m i jeJ j j ie i This cost can now be included in the objective function to give min E E (b. .c. .) x. . + E s.x! + E u.n. . . ij it ij .11 j j i j J J i J + E (1 V ) E d.u. + E AD . (3.33) m . m j j m m jeJ m For this study, general office equipment and fixtures are included under plant operations and maintenance or under construction or rental cost and the equipment cost category has been reserved for medical equipment. Since facility and equipment are long lived assets, they should not be treated as an operating cost, but rather should be treated as a

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55 capitalization cost and be amortized. To continue with the model development define the following terms: g initial cost per unit area for construction (dollars per unit area) , g' amortized cost per unit area for construction (dollars per unit area per year) , o maintenance and utility costs (dollars per unit area per year) . P amortization rate for initial capitalization, c c ' t cost of equipment in department m per FTE professional (dollars per man-year) , t' amortized cost of equipment in department m per FTE professional (dollars per man-year per year) , w. space required per type i person (units of area per man-year) , Y total floor space available, Y floor space to be constructed for department m (Y = S w.N.), m . „ T m i x lCl Y* maximum initial capitalization (dollars). If an HMO is in a planning stage, there may be an upper limit on capital available for constructing an HMO or if it is already in operation there may be a limit on floor space available. In the latter case this would imply EY
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56 A constraint similar to (3.35) will be used; recognizing that (3.34) could easily be incorporated at a later point. For an IIMO in the planning stage with a maximum amount of capital available the following constraint arises: g E w.N. + E t FTE < Y* . (3.36) & . l l m m — l m The capitalization costs must also be amortized and appear in the objective function which will be discussed shortly. However, the plcnt operations and maintenance cost have not yet been developed. This cost is o E w.N. . c. 11 l Now all three of the facility overhead costs can be included in (3.33) to give min I E (b..c.) x.. +E s x! +1 u.n. ± j ij U U iH . j j + E (1 V ) E d.u. + E AD + o E w.N, m , j i m c.ii m J£J m i + g T E w.N. + E t' FTE . (3.37) .11 m m l in The overhead costs have all been included except the ancillary costs. In this model this cost category will be used for the laboratory and x-ray departments. These departments could be included in the regular medical department formulation with no change in model M2 or subsequent models. However, to examine these two departments in the same detail as the primary care departments was outside the scope of the study. Thus they have been included as a separate category. If enough information and data were available, this part of the formulation could be

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57 dropped and laboratory and x-ray manpower utilization and costs could be examined in the same manner as the primary care departments. To proceed, define the following coefficients: CLT average cost per laboratory test (dollars per test) , CXR average cost per x-ray service (dollars per service) , NLT number of laboratory tests ordered in department m per service m provided (tests per medical services) , NXR number of x-ray services ordered in department m per service m provided (x-ray services per medical service) . The units between CLT and NLT . and CXR and NXR should be consistent. m m For example, if NXR is given in series per medical service, then CXR m should be in dollars per series. From the above definition, the laboratory and x-ray costs are thus: £ (CLT NLT + CXR • NXR ) £ £ „ b ,X. . . (3.38) m m . T m . m ij ij m jeJ iel Now (3.38) can be included in (3.37): min EE (b. .c. .) x. . + £ s.x'. + E u.n. 1 j 1J 1J 1J i ±X j J J + E < X " V E m Vj +SAD m + °c E Vi m jeJ J J m l + g' S w.N. + S t'FTE & 11 mm l m + £ (CLT -NLT + CXR • NXR ) L S b t 4 X ,M ' (3 ' 39) m m . jn, . _m ij ij m jeJ iel At this point, the objective function (3.39) is much more detailed and versatile than the objective function for model M2 which is given by (3.22). The function given by (3.39) is certainly more complex than that

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58 expressed previously but the difficulty of solution has remained on the same level. In fact if the V decision variables are set to either or m 1 (in (3.22) they are implied to be 1) then the present model and M2 are almost equal in difficulty of solution. The real change has occurred in the data requirements. Information that was left out of model M2 is needed in the present model. If the full cost for an HMO is not desired, but rather, only the medical manpower costs are sought, then the extra coefficients in the present model can be set to zero. It is felt, however, that the extra effort required to find the additional coefficients results in a more meaningful and richer solution. Additional Model Refinements The model development could stop at this point but there are several additional features which can easily be added and will further refine the model without sacrificing solution capability. The first feature presented below involves further refinement of the medical care structure and the other three further refine the cost structure. In the previous discussion involving indirect supervision of physician extenders and nurses, several constraints arose and are given by (3.12) and (3.13). These constraints arise mainly from the MD's viewpoint of the time requirements for him to supervise lower level personnel. However, another viewpoint can arise from the patient care aspect of medical care. The physician extender is not qualified to diagnose and treat every patient that comes to the HMO for medical care under the indirect supervision mode. In fact, for many health services, the physician extender will only be used in a team role under the direct supervision of a physician. The details of this limitation will be fully explored in the next

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59 chapter. For the moment it suffices to note that the above limitation results in upper bounded variables. Let MAX. . be the maximum percent of service j that can be carried out by personnel i in the indirect supervision role. This coefficient will be used for those indices iel which refer to physician extenders. The upper bound is thus: x j J i 1J 1J

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60 A further refinement can be made to the cost of equipment. There are certain pieces of equipment that change the fundamental nature of the delivery of a health care service. Examples of this are multiphasic testing units for use in comprehensive physical exams and SMA-12 blood chemical analyzers for use in laboratories. Both of these examples also have the property of being extremely expensive. Since both large cost and alternative health care delivery patterns could have a major effect on the solution, this type of equipment will be separated from the remainder of the medical equipment used. Technology cost was used by Shuman (76) by introducing a fourth subscript onto all the problem variables. This is not only cumbersome but also adds considerably to the number of variables. In addition several levels of technology for an entire HMO cannot be analyzed in a practical sense. The data not only do not exist; it would be difficult and very costly to design an experiment under which the data could be collected. Instead it is possible to evaluate the effect of specific technological advances on the productivity of specific personnel providing specific services. Define the terms: e. initial cost for a type i person due to technology cost (dollars) , e! amortized value for e (dollars per year) , i i I* set of personnel whose productivity is enhanced by additional technology, T one if N. > and if N. =0 for iel' . i x i Then the technology cost is given by E e.T. • Tf 1 L iei'

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61 and should be added to the capitalization constraint to give g E w N. + S t FTE + 2 e.T. < Y* . (3.42) . i i m m . _, i i l m iel In addition, to ensure the zero-one variable T. takes on its proper value, the following constraint is necessary N. K • T. < 0, where K » N. . (3.43) l l — i Several points should be made before proceeding. First note that the set I' can include those personnel who do not need the additional technology cost to be effective but rather technology just revises their productivity coefficient. It can also include those who would not be hired if the technology is not employed such as technicians hired to run a multiphasic testing unit. The second point is that the above term is not central to the solution of the model and can be dropped if technology changes are not being considered in the decision process. The last addition to the model involves an operating constraint for HMO's. HMO's provide medical care on a capitation basis and must operate within a budget defined by the capitation income plus any external sources of revenue. Thus the yearly operating expenditures must be less than the budgeted amount to cover cost of operation. The relation between the budgeted amount and the capitation is developed first and then the budgetary constraint is developed. The budget is developed for a non-profit institution. For a profit making institution appropriate changes can easily be made. Define the coefficients: B* -upper limit on yearly budget for operating and salary expenses for medical departments included in the optimization (dollars

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62 per year), OM other medical costs; this would include the costs of operating departments which are not included in the optimization, inpatient care, out of area professional services, additional cost of premium plans, etc. (dollars), P rate at which capital fund accumulates as a fraction of gross income from subscriber capitation fees, R capitation rate (dollars per subscriber per year) , EXT external sources of revenue such as planning grants or endowments (dollars per year) . Now since the initial capitalization, Y* is being amortized at the rate P the result is c B* = (1 P) S • R P Y* OM + EXT (3.44) Now a budgetary constraint can be written for which B* is fixed which implies the capitation rate is fixed, or B* can be defined as a variable which in turn will define the capitation rate. The former alternative will be used here recognizing it is trivial to study a variable capitation rate if it is later desired. The terms given in (3.41), (3.44) and the yearly expenses from the objective function (3.39) can be combined to give the budget constraint: E E (b..c. .) x. . + E s.x| + o E w.N. E r (E b x ) J i ij iJ U i i i c t 1 1 j J ± U U + E (CLT • NLT m + CXR • NXR m ) E ffl E b x m jeJ iel + E (PV E E b. .x. . + MAN E m (d . V n )/b* m jeJ iel J J jej + PER E N.) < B* . (3.45) . _m i — iel

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63 The entire model will be called M3 and can now be summarized here. The objective was given by (3.39) and must be revised to reflect the income fee and amortized technology cost. In addition AD and FTE will be mm replaced by their definitions given by (3.32) and (3.31) respectively. The result is the model M3: min g' 2 w.N. + 2 2 (b. ,c. .) x + 2 s.x* + 2 (1 V ) 2 d u i i * j i U ^ ^ i i * m m jej m J J + 2 u.n. tit 1 ( 2 „ (d.V n,)/b*) + o 2 w N 2 r (2 b x ) j J J m m je/ J m J J ° i X X j J i 1J 1J + 2 e» T + 2 (CLT • NLT m + CXR • NXRJ • 2 ffl 2 b x iel' m J £ J i £ I + 2 (PV 2 2 b..x..+MAN 2 (d.V -n.)/b*+PER 2 N.) m jcJ m iel m 1J 1J jeJ m J m J J iel m x (3.46) subject to 2 x. . + 2 2 q, . .x. . + x! N. = • iel , (3.47) 2 b..x.. + n. d.V = • jeJ, j^j* , (3.48) t ij ij J J m 2 2 f b x h ..x., ., < • i*el* , (3.49) ,,,-r* ij ij ij **J* i*j* ~ 2 2 (b c. .) x. . + 2 s.x! + o 2 w.N. 2 r (2 b x ) J ± ij ij ij .ii c . i i . j . ij ij + 2 (CLT • NLT + CXR • NXR ) 2 2b x m jej m iel m 1J 1J + ^ W E m E m b ij X ij + *** . E m < d j V m " V^l m jeJ iel J jeJ + PER 2 N.) < B* , . m i — iel g 2 w.N. + 2 t 2 m (d.V m n )/b* + 2 e T < Y* , i mjeJ i*i (3.50) (3.51)

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64 T i K • N. < • iel' , (3.52) X i*j* < SU i • N. • i*el* , (3.53) n. : MX. • d. • jeJ, (3.54) x.. Thus the problem is to find the x... N., T. and V to minimize (3.46) ij l l m J subject to (3.47) (3.55). Note chat the optimal basis will always be such that constraint (3.49) is tight. This is because the x.,., in (3.49) will always have a positive cost; thus if a slack variable from (3.49) appeared in the final basis, the objective function could obviously be reduced by reducing the slack variable to zero, thereby reducing the x. , and thus its contribution to the obiective function. This means that (3.49) could be used to limit x. , . , from the fcrmulation and consequently eliminate (3.49). However, this would change (3.53) to a constraint rather than an upper bound and thus would accomplish little in addition to the notational problems which would arise. Thus (3.49) will be retained in the formulation. A Comparison of Models Ml , M2, and M3 The formulation has been developed in three stages through models Ml, M2 and M3. It is instructive at this point to compare the features and sizes of the three models. The features of the three models are: Ml very simple model of the basic resource and requirements relations; M2 generalized and detailed refinement of the medical care structure presented in Ml; and

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65 M3 generalized and detailed description of the medical cost structure in addition to the medical care refinements of model M2 . Let the cardinality of the sets I, I , I 1 , and J and M be demoted by 0(1), 0(I S ), O(I'), 0(J), and 0(M). Also assume that the matrix of x.. is about 20 percent dense; about 50 percent of the personnel classes are required to be integer; and that O(I') is about a fourth the (I ) . Then, if for example, there were 10 personnel classes, 15 teams, 60 services and 3 departments the size of the models would be as follows (strictly speaking Ml would have to be developed slightly to allow teams) Table 2 Relative Sizes of Models Ml, M2 and M3 ., , , Continuous Integer Zero-One n...,..^-.. Upper uoaex Variables Variables Variables Bounds Ml 300 70 M2 370 5 73 63 M3 370 5 5 75 123 In solving linear programs, the number of constraints is i.he major factor in the time and difficulty of the solution. Upper bounds can be added to a model with very little extra solution time and they do not require the addition of constraints. Also, the number of problem variables only slightly affects the solution speed. Thus in going from a very simplistic model to a much more detailed model the refinements were principally made in such a way that the difficulty of the model changed very slightly. Note also that in interpreting solutions to linear programs

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.66 the principal quantities of interest are the number of variables and number of constraints. Here again very little additional difficulty is encountered in the interpretation of the results. The exception to the above paragraph is the integer and zero-one variables. Solving a mixed integer linear program is more difficult than solving a linear program. However, in this case the problem is well within the solution range of mixed integer programming techniques. Additionally, the zero-one variables could be set at an assumed value as was implicit in Ml and M2 and the integer restriction on all N. could be dropped which would convert M3 into a linear program of about the same difficulty of Ml or M2, but M3 would remain a much more fertile model for decision making. The major caveat would then be the additional data requirements, but for an HMO with an adequate accounting system the extra data would essentially be available. Thus model M3 will be used for further development and analysis in the remainder of the study. Development of Planning Models Development of the Overall Planning Model The M3 model will be algebraically simplified to define the Overall Planning Model (OPM) . 0PM can be used in a preliminary planning stage of an HMO or with some simplifications it can be used to refine operation of an HMO. The model is formulated to solve the following basic problem: given a fixed capitation rate and a projected subscriber base find (1) manpower to be hired,

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67 (2) delegation of services, (3) facilities required, (4) particular technological innovations to be utilized (if any) . The M3 model has many terms and coefficients that can be combined. Thus the model can be simplified by defining: a. . = (c. . r. + CLT • NLT + CXR • NXR + PV) b. . . (3.56) ljm lj j m m lj • p! = (MAN + t') d,/b* d.u. , (3.57) B. = MAN • d./b* , (3.58) a* . t • d./b* , (3.59) jm m j j h! = w. (g 1 + o ) + PER , (3.60) xi c h. = o w. + PER , (3.61) 1 c 1 h* = gw. , (3.62) v* u (t 1 + MAN)/b* , (3.63) jm j m j v = MAN/b* , (3.64) J J v* = t /b* , (3.65) 'jm m j ADD = E d.u. . (3.66) j J J Substitute (3.56) (3.66) into (3.46) (3.55) and the resulting formulation is the 0PM (note the constant term, ADD, is being carried with the formulation):

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68 rain Z Z E a..x..+E E B '. V + E h'.N. . T m . m ljm lj . m ' jm m . _s 1 1 m jej iei J J m jcj J iei + E E y' n. + E s.x'. + E e'.T. + ADD (3.67) m jcj J J iei iei' subject to Ex + E E q, . .x, . + x'. N. = • iei . (3.68) . ij , . kij kj l l j J k j E E f b .x. . b. , .,x. , ., = • i*el* , (3.69) jej.* iei* 1J 1J 1J **J* 4 *J* J i* X>J ., < SU.N. • iei* , (3.70) i*j* 11 E b. .x. . + n. d.V = • je/ 1 , • meM , (3.71) £ ij ij J J m n. < MX. d. • jej m , • meM , (3.72) J ~ J J x 0. J The 0PM will be used extensively in the remaining analysis. It is the basic model from which other models will be derived and it will also be used extensively to arrive at computational results. One of the principal difficulties for solution of the 0PM is the mixed integer feature

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69 of the model. However, there are many instances where the model could be linearized. There are many HMO's where the decision to utilize a certain technology level and provide certain medical departments may be made for political, legislative, or intangible reasons. In this case the zero-one variables would be removed from the model. There are also many HMO's that effectively do not reflect an integer manpower constraint and it will be shown in later results that assuming continuous manpower is a reasonable assumption in many cases. Thus often the integer restrictions can be removed entirely from the model. However, they are in the formulation if needed and this in turn allows the effects of removing these restrictions to be analyzed. Minimum Cost Model for Fixed Services It was noted that the OFM could be made computationally easier if the zero-one variables V which determined which departments would be m provided are eliminated. In the OR-1 departments that are economically infeasible to offer would be reflected by zero values for V and for the J m corresponding slack variables, n., which would appear in the basis (making it degenerate) . The basis size could be made smaller and many of the zero-one variables eliminated if it is decided a priori which services are to be offered. Aside from making the model more amenable, fixing the services to be provided is essentially the approach now being proposed in the legislative programs. Thus another question which arises is: given a fixed set of medical departments and a fixed subscriber base, find the optimal staffing, delegation, and facility to minimize the subscriber fee.

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70 For this formulation define the set: M ' = { m:V m =1 } , (3.77) J* -{j : JSJ m , meM'} [) j* , (3.78) J meM' and also let E = E m mSM f E = E j jej' Recall also from (3.44) that B* is a function of R and Y*. Note that in this model and in the 0PM one could treat Y* as a variable to find the optimal initial capital outlay. From a best solution standpoint if constraint (3.75) is active then it implies that the limit on original capital is actually acting to increase the yearly cost of operating an HMO. This will never happen if Y* is treated as a decision variable. Note also that if all demands are not met the E u.n. appears in the j J 2 yearly budget constraint (3.86). These services are paid for by the HMO and provided through another source. Thus the Minimum Cost (MC) model is given by (3.79) (3.88) and involves finding the x.., x' n , N , T. and R (also possibly Y*) to min R (3.79) subject to E x. . + E E q, . .x. . + x! N. = • iel* , (3.80) j k j E E f. .b. .x . b. n.x.. ,. = • i*el* , (3.81) ii ii ii i*i* i*i* jej.. iel* J J lj J J

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71 x. , ., < SU. • N. V iel* , (3.82) E b iJ X iJ + "j = d j *J«J f . J*J* » (3.83) n j " MX J ' d j * J£J '' j ^ j * ' (3 ' 84) x.. 0. Making the same assumptions as were previously made regarding the density of the x matrix this problem has the following characteristics: ij (a) .2 0(1) O(J') + 0(1) + O(J') + O(M') continuous variables, s (b) .5 0(1 ) integer variables, (c) .2 0(1 ) zero-one variables, (d) 1.5 0(I S ) + O(J') + 2 constraints, and (e) 2 O(J') + 0(1*) upper bounds. Thus with 10 personnel classes, 15 teams, 60 services to be provided, and 3 departments this problem would have about 370 continuous variables, 5 integer variables, 2 zero-one variables, 75 constraints, and 123 upper bounds. This is easier to solve than the OPM but the MC model is also a mixed integer program.

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72 In conclusion, this model is useful if the services to be provided are dictated by political, local or legislative reasons. It can also be used to formulate a reasonable set of services if the objective is to minimize the capitation rate for a fixed set of services rather than minimize the subscribers total medical bill as the OPM does, whereas the MC will give the staffing, delegation and facilities required for minimizing the cost to the subscribers for a given set of services. A Special Case of the Minimum Cost Model The MC model can be further simplified by using it in an operational planning mode rather than the preliminary planning stage since it is assumed the professional personnel and facility are already fixed. The planning question at the operational stage can be stated as: given a fixed set of services, professional staff and facilities, what is the optimal subscriber size, delegation and ancillary staff to minimize the subscriber fee. For this case T and some N. are fixed and the integer restrictions on i i the remaining N. are dropped; thus the model is no longer a mixed integer program. Constraint (3.80) becomes Ex..+EEq,..x..=N. • iel* (3.89) j J k j and the initial capital constraint (3.87) is replaced by a constraint on the amount of floor space available for medical services, E w.N. < Y , (3.90) i 1l and the T. definition constraint can be dropped from the formulation. A problem arises with constraint (3.86) which now has a nonlinear term

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73 S • R since both S and R are now assumed variable. However, this nonlinearity can be eliminated by a double transformation. First define Q = S • R (3.91) and then (3.79) becomes min Q/S (3.92). and (3.86) is again a linear constraint with Q replacing S • R. The new model thus consists of (3.80) (3.86), (3.90) and (3.92). This model is a fractional linear program since for a physically reasonable solution to the model S > 0. A slight modification of the simplex is made in the Charnes-Cooper Algorithm (82) to solve this problem. However, the model can also be easily transformed to a linear program by the transformation r = 1/S (3.93) and then define x! . = rx. . , Q' rQ , x!' = rx! , S' = rS , n 1 . = rn. , N! = rN. . (3.94) J J i i Now (3.93) and (3.94) are substituted into the linear fractional model to give min Q 1 (3.95) subject to Ex' + E E q, . .x| . + x'. ' N.r = • iel* , (3.96) ij . . n kij ij l l j k j Ex' + E E q, . .x'. . + x| ' N! = V iel* , (3.97) j ij k . kij ij i

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74 E E £, .b. .x| . b.^.x! , = • i*el* , (3.98) • t . :, 11 11 LJ 1*1* 1*1* x]j ,* SU. N.r < • iei* , (3.99) i*j* i l — ' E b. jX ^. + n^ =0 • jej', j^j* , (3.100) n'. MX. • d'. s' < • jej*, j^j* , (3.101) x|. MAX.. • d'. S 1 < • jej, i€l P , (3.102) ij ij J E E E a., x*. . + s s.x] 1 + E h-.NI m jeJ iei J J lei isl-> + E h.N.r + S (v. + u.) n! (1 P) Q* iei* j J J J + r (P Y* + OM + £ E B, ) < (3.103) c . m jm m jeJ J E w N'. rY < (3.104) ii — l S' = 1 (3.105) Thus (3.95) (3.105) is a linear program and can be solved in the usual manner. In practice it may be preferable to use the Charnes-Cooper Algorithm on the linear fractional program rather than redefining all the variables and requirements vector as was done above. Whichever model is used, the result is a useful operational planning tool which is especially useful if an HMO wants to change from the traditional MD-nurse medical practice to the three level MD-PE-nurse medical practice. The model defined by (3.95) (3.105) is a little lengthier to solve since the upper bounded variables were replaced by generalized upper bounding constraints. Although generalized upper bounding algorithms have been

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75 formulated (e.g. Geoffrian (83)) they are not as fast as upper bounding nor as available in packaged linear programming routines. However, the generalized upper bounding constraints can be treated as standard constraints with the resulting larger basis. Subscriber Maximization Model One of the reasons HMO's are being proposed is because they potentially will offer care to more subscribers per physician than the traditional form of practice thus providing better utilization of this scarce manpower resource. Thus a valid objective would be to maximize the number of subscribers an HMO can serve for a fixed professional staff and subscriber fee. Again for this problem, the original capital Y*, can be assumed to be an input or a variable. The problem can thus be stated as: given a fixed professional staff and subscriber fee , find the optimal delegation, facility, and hiring policy for allied personnel to maximize the number of people who can be served. This model is derived through modification of the OPM and involves finding the x.., N., T. and S (possibly also Y*) to ij i i max S (3.106) subject to Zx..+nq,..x.. + x! = N. • iel* , (3.107) . ij , . n kij ij l l j k j Z x. . + E E q, . .x. . + x! N. = V iel* , (3.108) j xj k . *kij ij X i

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76 E E f-.b-x. b.. ..X.. • i*el* , (3.109) jej 4 iel* 1J 1J 1J **** l * j * i* x.,., < SU. • N. • iel* , (3.110) i*j* -Li E b..x.. + n. d'.S = • jej', j^j* , (3.111) n. MX. d'S < • jej', Wj* , (3.112) J J J x. . MAX. . • d'.S < • Id', j^j* , (3.113) ij ij j — E E E a..x..+ E s.x! + E h N + E (v. + u.) n. . m . m ijm ij . „s i i . -.,. i l . i j j m jej iel J J iel iel* j J j j (1 P) S • R + E E g . S + P Y* < OM E h.N. , (3.114) . T m J m c — , _ . 1 i ' m jeJ J iel* E h* N. + E e.T. + E E V* n, + 2 E a* s iel iel 1 m jeJ J J m jej J < Y* E h*N, .11q . ie i* * * • (3.115) N. K • T. < • iel 1 . (3.116) Note, for this model 6. and R"V must be redefined in terms of d'. rather ' 'jm H jm j than d.. Constraint (3.107) refers to the professional level personnel which are at a fixed level, whereas (3.108) refers to the ancillary personnel and N. is an integer variable. Note the term E u.n. in (3.114) i j J J and the use of n. as a slack variable in (3.111). This is somewhat of a paradox since the purpose of the model is to maximize the number of subscribers served by the HMO, but the above use of n. allows services to J be bought outside of the HMO. However, the n. should not be used as a surplus variable in (3.111) and have the corresponding term in (3.114) eliminated. To do this might unreasonably restrict the number of

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77 subscribers. An example will clarify this point. Suppose only one general surgeon is available and he can provide services for 10,000 people. However, the remainder of the staff can provide services for their specialties for 30,000 people. The use of n. as a surplus variable would lead to an answer of 10,000 subscribers, but using it as a slack variable would lead to a solution of 30,000 subscribers with two-thirds of the members being referred to a surgeon outside of the HMO and paid for by the HMO. Thi.° latter solution is certainly more reasonable. Minimal Use of Professional Manpower In an attempt to minimize the use cf manpower for which a shortage exists, an alternative approach to the SM model can be taken. It is plausible that in some cases it will be known what subscriber base is desired for geographical or political reasons. Thus the problem can be summarized as: given a fixed subscriber base, a fixed fee, and a fixed set of services ,find the optimal staffing, delegation and facility to minimize the professional level personnel used. This minimization will naturally need to account for the quality of service provided. In this case, it would be a major consideration and the indirect supervision constraints will play an important part in determining the plausibility of the final solution. This Minimal Professional Manpower Model (MPMM) is given below and involves finding the x , x' , n , N. , T. and Y* to ij i j i i

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78 min S N ± (3.117) iel* subject to: E x. . + 2 S q, . .x. . + x N. = V iel , (3.118) E E f . .b .x.. b, J ...x.... =0 • i*el* , (3.119) , -j ij ii ij t*j* i*j* J i* x iJL1J < SU. • N. ' • iel* , (3.120) i*j* — i i E b..x.. + n = d. • jeJ', j^j* , (3.121) n. 0. The size of this problem, using the assumptions as for OPM, is: (a) .2 0(1) 0(J") continuous variables, (b) .5 0(1) integer variables, (c) .2 0(1) zero-one variables, (d) 1.5 0(1) + 0(J) + 2 constraints, (e) 2 O(J') + 0(1*) upper bounds.

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79 This formulation can also be used if the facility is fixed by making the following changes: (a) assuireY* doesn't include paramedical equipment costs, T.; (b) in (3.124) add P E e!T. to the left hand side; and c . 1 1 l (c) replace constraint (s.125) with I w.N. <_ Y . i Concluding Remarks This chapter has presented a wide array of problem formulations ranging in complexity from Ml to M3 and ranging in purpose from OPM to MPMM. The internal validity of these models was partially developed along with the development of the model in going from Ml to M3. Further validation and solutions to the models will be covered in the remaining chapters. The development of the complex model was carried out in such a manner that, excluding the integer restrictions, M3 is of the same order of difficulty to solve as the simplest model. The major difficulty is the additional data requirements imposed by model M3; however, the data needed to solve the mode are presented in the next chapter. In summary, the models presented are mixed integer programs. One of the models exhibited a quadratic term but this was removed by a transformation that resulted in a linear program. The models presented are general and flexible enough to answer many HMO planning questions. A partial list would include: (a) assignment of personnel to medical services; (b) selection of medical departments to offer; (c) selection of needed facilities; (d) optimal subscriber levels;

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80 (e) optimal hiring policy; (f) maximize subscribers per health professional; (g) minimize the number of health professionals utilized; (h) find the minimum cost structures for different base populations; (i) examine cost and manpower effects of P.E. utilization; (j) examine P.E. utilization as. a function of subscriber levels, P.E. salary, and supervisory levels; (k) examine effect of integer manpower restrictions; (1) examine imputed cost for medical services; (m) examine different levels of responsibility for P.E.'s; (n) examine which services are best delegated; (o) examine usage of P.E.'s under a scarcity of P.E.'s; and ~(p) examine which P.E. activities save MD's the most time. These questions and others will be analyzed and at least partially answered in the remaining chapters.

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CHAPTER 4 DATA COLLECTION AND ANALYSIS Introduction An O verview of Health Care Data Collection Data collection is always a difficult part of any research effort and in the health care field it is especially difficult. There are two principal reasons for this. First, the health care industry has been extremely fragmented and highly individualized with little research being performed on the actual process of providing health care. Secondly, the health care setting represents a system where people, medical science and organizations interact and this naturally leads to a very complex system. The result is that data requirements, which are easy to discuss conceptually, as in the last chapter, are extremely time consuming and difficult to meet. Nevertheless, data collection is necessary to achieve success in terms of using the models to derive solutions to the problems presented. Carefully collected data also allow a validation of the models through comparison and analysis of the solutions. Purpose of the Chapter One of the principal failings of many health care studies has been their lack of an adequate data collection process. Given this fact, the goal of this chapter is to set forth a quantitative data base of 81

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82 sufficient depth and validity such that the models can be validated and be used to generate solutions. The data collection effort was undertaken with the goal of finding and utilizing the best data available. This search included four aspects: (a) direct use of appropriate existing data; (b) direct collection of data in appropriate health settings; (c) synthesis of data from existing data; and (d) advice of experts in the field. Categories (a) and (b) are the most desirable from a data validity standpoint, thus most of the data collected fall under those two categories with exceptions only where they enhanced the total data base. Many of the data reported in this chapter were previously unavailable and the remaining data had noc been collected into a comprehensive, consistent data base. It might be noted that a useful by-product of the modeling effort has been the establishment of a basis for collecting a consistent data set. In general, data must be collected for all the nonzero or nonunity coefficients in the model. These data can be broken down into the following general categories : time requirements, utilization of services, delegation guidelines, direct labor costs, general administrative overhead costs, facility and equipment costs, ancillary costs, and

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83 (h) operating costs. Most of the original data collected are given in the chapter except for longer tables which are given in the Appendices. Supporting data from other sources are generally given in the Appendices. In addition to the data listed above, a new medical classification system for use in analyzing manpower requirements is presented along with its relation to the physician extender delegation problem. Medical Classification Systems The Criteria for a. Medical Classification System The question of a medical classification system (MCS) is germane to the data collection and the analysis using the models. As was noted previously, the output of the HMO system has been taken to be the medical services delivered. As a consequence, most of the variables included in the model are related to the delivery of medical services. Thus the data collection must in part be carried out within some MCS. Key items such as patient utilization, time requirements, and delegation possibilities must all be discussed in terms of an MCS. The many disease classification systems that have been used in medicine have largely been oriented toward etiology, prognosis, pathophysiology or procedures (84). These systems have been developed largely to suit the needs of medical practitioners and biomedical scientists. However for manpower analysis these systems are not adequate. The needs of health services utilization analysis vary with the purpose of the analysis and require the inclusion of the perspectives of both the population and the providers in the classification system (85).

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84 There are at least five criteria which an MCS should meet to be effective in manpower analysis. First, the MCS should focus on manpower utilization above all other factors. This would indicate that many patient visits which have different diagnoses or symptoms may be classified together if the manpower requirements are the same. Second, the MCS should be in some manner relatable to training programs. Since a principle feature of this analysis involves the use of physician extenders, the MCS should be able to represent their output capabilities in terms of the training they have received. It should also be able to distinguish the difference between the PE training and that of the MD or nurse. Third, the MCS should be broad enough to cover all medical office visits. Fourth, the MCS should consider the difficulties involved in data collection. If data are not available, or cannot be collected within the MCS, it is of very limited use. Last, the MCS should be useful in response to policy questions. An MCS that is very detailed will not lend itself to analysis and a very broad MCS may not show any response when fairly significant changes are made in the system. A Review of Existing MCS There have been a large number of MCS's formulated and some of these will be briefly discussed here. Among the more common systems used in manpower analysis are: (a) office visits, (b) International Classification of Diseases, Abstracted (ICDA) (86), (c) Current Procedural Terminology (CPT) (87) , (d) California Relative Value (CRV) (88),

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85 (e) Golladay, Smith and Miller (73), (f) 3raun, Howard, and Pondy (71), (g) GEOMET (74), (89), (90), (h) Kaiser Clinical-Behavior Disease Classification System (KCBDCS) (84), (i) Manpower Evaluation Protocol (7), and, (j) Freeman (72) . Each of these systems will be briefly discussed and their weaknesses with regard to this manpower analysis will be pointed out. By far the most common MCS used to analyze manpower needs is simply to classify patients by inpatient visit, outpatient visit or office visit. This MCS is used only for its simplicity. It cannot be related to manpower capabilities or respond to basic policy questions in manpowp*utilization since it is far too broad. The ICDA system is designed for the classification of morbidity and mortality information for statistical purposes and for the indexing of hospital records by diseases and operations (86). Since 1968 it has served as the basis for coding diagnostic data for official morbidity and mortality statistics in the United States (86) . In the ICDA system not every condition is classified in a separate rubric; however, there is a category to which every condition can be referred. The system is arranged in seventeen main sections and the detailed list consists of 671 categories of disease and morbid conditions, plus 182 categories for classification of the external cause of injury and 187 categories for characterization of injuries (86). See Table A-l in Appendix A for the major ICDA categories. The major strength of the ICDA is its statistical base for collection of morbidity data. It has

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86 several weaknesses: (a) it is not focused on manpower utilization; (b) it is too detailed to respond to manpower policy questions; and (c) in its broad form it is not relatable to training programs and in its detailed form the 1040 listings are too extensive. Another system in common use is the CPT which is a dictionary of terms and codes for the naming and designation of diagnostic and therapeutic procedures in surgery, medicine, and the specialties (87) . In addition, it contains a special listing of procedures related to internal medicine. The CPT is indexed by a five-digit code and is extremely detailed in its listing of diagnostic and therapeutic procedures. Its weaknesses in the manpower area lie in three areas: (a) it does not focus on manpower utilization; (b) it contains only the provider perspective and ignores the patient perspective; and (c) in its entirety it is too lengthy to use in a manpower analysis. The CRV is a reflection of the practice of medicine in California. It is a coded listing of physician services with unit values to indicate the relativity within each individual section of median charges by physicians for these services (88). For the primary care specialties the listing is broken down into the following categories: (a) visits, (b) emergency room service,

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87 (c) consultations, (d) immunizations, (e) psychiatric services, (f) monitoring services, (g) specific diagnostic services, and (h) specific therapeutic services. As a sample of the CRV, a listing of all the categories included under visits is given in Appendix A in Table A-2. The principal weakness of the CRV is that it contains only the provider perspective and ignores the patient perspective which in turn makes it difficult to use in terms of patient utilization of medical services. This latter perspective could be included if the eight categories listed above were combined into another listing of typical patient visits. The GolUday, Smith and Miller listing of services was used in their study on manpower utilization (73). They used services, which they describe as a sequence of tasks, to recognize the importance of the sequencing of tasks in determining the feasibility of delegation and to increase the intuitive content of the results (73) . Their listing of services is given in Table A-3 in Appendix A. The principal weaknesses are: that it is aimed at general practice rather than the specialized services of an HMO, the classification excludes many visits even in general practice, and its combination of medical procedures, examinations and diagnoses are of questionable consistency. The MCS used by Braun, Howard and Pondy (71), to evaluate potential and existing utilization of physician assistants, consists of a listing of medical tasks and is based on the Manpower Evaluation Protocol (7) . There are 368 tasks which are divided into six major

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88 task categories: (a) history taking, (b) physical examination, (c) laboratory procedures, (d) medical tasks, (e) surgical tasks, and (f) other medical care tasks including administrative. This system will be discussed in more detail in the section Delegation Guidelines . Several MCS's have been developed by GEOMET, Inc.. One of them is based on a similar concept to that used in the Golladay, Smith and Miller MCS (74). It has been used in a previous manpower study (91), but it has similar weaknesses as the Golladay, Smith and Miller system. A listing of this MCS is given in Appendix A in Table A-4. The other GEOMET MCS is much more detailed in its scope and depth (89, 90). GEOMET essentially combined the ICDA, and CPT, and elements of the CRV systems into the GEOMET Specifications of Care (GSC) . In doing this they were able to come closer to a system which is more manpower utilization oriented. Initially, 160,000 patient encounters were recorded by ICDA number. The 74 most common ICDA numbers were then used to form the basis of the GSC and are listed in Appendix A in Table A-5. For each of the 74 ICDA numbers a specification of medical care was derived. This specification consists of one or more prototypes depending on the variety of cases classified under one ICDA number. Each of the prototypes has in turn a listing of elements of care which are based on the CPT. GEOMET also added about 50 elements of care to the CPT system (89) .

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89 A sample listing of some of the elements of care is given in Table A-6 of Appendix A and a sample of a specification of care is given in Table A-7 of Appendix A. For a complete listing see references (89) and (90). After the specifications of care were completed, other ICDA numbers with similar care requirements were assigned by proxy to previously derived specifications of care (89). These are contained in Table A-8 of Appendix A. The GCS was based on an extensive number of patient encounters and analysis but its principal weakness lies in its use of the ICDA system as its highest level system. Since it has a built-in transformation from the elements of care to the ICDA numbers through the use of the specifications of care, it is possible to relate manpower training to the outcomes. However, at the same time there are basically too many ICDA numbers needed to specify patient visits. Even after about 125 ICDA numbers, approximately 20 percent ef the patient visits are unaccounted for and additional numbers added to the list contribute less than half of a percent. The KCBDCS was specifically formulated to examine patient utilization of medical services and the subsequent manpower utilization and was designed to group those diseases likely to produce similar behavioral responses in persons with similar background characteristics (84). The system does not maintain the structure of the ICDA, but every condition classified in the ICDA is directly convertible to the new system (84). As a first step the ICDA numbers were grouped into four divisions: diseases; pregnancy and its complications; trauma and adverse effects of external causes; and nondisease, refractive error and miscellaneous. These four divisions were broken down into 46 clinical subgroups, which were then combined into 10 behavioral classes relevant

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90 to the analysis of medical care utilization behavior. The KCBDCS is given in Table A9 of Appendix A. A principal weakness of the KCBDCS is that its difficult to relate manpower capabilities to the classification system. However, it does have several strong features in that it is patient as well as provider oriented and a direct transformation from the ICDA to the KCBDCS has been formulated (84) . The last MCS to be discussed here was used in a manpower analysis by Freeman (72). This MCS is task and activity oriented. The tasks carried out by the physician were categorized into six activity groupings: (a) history taking, (b) physical exam, (c) charting, (d) patient instruction, (e) patient treatment, and (f) nonmedical. The tasks for ancillary personnel are listed in Table A-10 of Appendix A. This study was aimed at general and internal medicine and thus is not broad enough for use in other specialties, but it did include specifications of tasks required as a function of eleven diagnostic categories and the time requirements involved. A Formulation of £ New MCS The previous section introduced many MCS's and noted the weaknesses of each as they apply to the analysis of manpower utilization. However, many of the MCS's have extremely desirable features. This was recognized by GEOMET when they formulated the GSC based on the ICDA, CPT and

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91 CRV systems. They were able to combine the. best features of each to arrive at a better system for manpower analysis. Hurtado and Greenlick also recognized this when they formulated their system based on the ICDA system. The ICDA has become widely accepted as a system for reporting patient utilization and is a common point between the GSC and KCBDCS. However, both systems have a weakness: the GSC is not oriented enough from the patient perspective and has too many categories while the KCBDCS is too broad and does not lend itself to differentiating between manpower levels. However, it is clear that the two systems complement each other: one is strong where the other is weak and vice versa. Thus a new MCS will be proposed here and will be called the Tri-Level Classification System (TLCS) . The system can be represented by Figure 8. Kaiser Clinical Behavior Disease Classification System International Classification of Diseases, Abstracted T Elements of Care manpower utilization morbidity statistics training & delegation Figure 8 Tri-Level Classification System The TLCS is a hierarchial MCS with three levels formulated such that a transformation from one level to the next higher level is defined. It is designed such that the lowest or most detailed level responds to differences in manpower capabilities. Thus, delegation to PE's and nurses can be defined on the detailed level where many of the surveys and analyses of delegation have taken place. The middle level is

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92 given by the ICDA system for which extensive patient utilization figures have been collected. The highest or broadest level is used to reflect manpower utilization and to respond to policy considerations. All three levels previously existed, but their combination into one comprehensive MCS acts to eliminate or dilute their respective weaknesses and enhance their strengths. The TLCS was also defined to take advantage of the extensive time requirements data collected by GEOMET (74, 89, 90). For each of the elements of care a time requirement to perform that element was specified for the MD, RN, LPN and nurses aid. The time requirements for PE's are developed later in this Chapter. The specification was carried out for Adult Medicine, Pediatrics, OB/GYN and several ancillary departments. Thus using the system specified in Figure 8 it is possible to define time requirements for the highest level of the system. To perform this however is an extensive data processing problem. The prototypes of care (see Table A-7) represent about 325 pages of data which represent about 10,000 elements of care listings. On the next level, the transformation from ICDA to KCBDCS represents about 75 pages of data. In addition, about 25 pages of subsidiary utilization data is needed to perform the transformations. Tn manipulate these extensive data transformations a computer program was used and the flow of information into the program is diagrammed in Figure 9. It can be noted that demographic characteristics are input to the program and affect the frequency of the elements of care as well as the utilization under the KCBDCS. The output also differentiates between severity of cases and between initial or return visits. This information is used to aid in the delegation analysis.

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93 An example of the output is given in Table 3. The particular example is for prenatal and postnatal services. The first line of each of the four rows gives the element of care number which is based in most cases on the CPT number. The second line gives the percentage of visits for which that element of care is used and the third through fifth lines give the weighted time requirements for the MD, RN and LPN respectively. There are about eight rows of five lines for each Kaiser classification number. The total time requirements for the classification number are thus summed over all the weighted times under each of the elements of care. Thus it is possible to designate certain elements of care as delegatable to PE's and quickly examine the effect on MD time requirements. This in turn enables one to examine many delegation strategies in a manner other than the ad hoc approach usually resorted to cat of necessity. Time Requirements , Delegation and Utilization Data Time Requirements When the models were developed in Chapter 3, a productivity coefficient, b , was used to specify the number of cype j services a type i ij person could perform per year. Recall that type i personnel could refer to teams or persons. The medical personnel and teams to be considered were given in Chapter 2 and the services to be considered were introduced earlier in this chapter. This section will lead to the specification of the b.. coefficients in the TLCS. Several time studies have been performed on medical practice, but they typically cover only one medical specialty and are performed using

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94 Office Visits By Age and Sex Utilization By Age, Sex, and ICDA Utilization Model Total Utilization By ICDA Transformation From ICDA to Kaiser Initial and Return Visit Percentage by Kaiser Prototypes of Care Proxy List Specifications of Care Time Requirements By Element of Care Numbers Model To Determine: 1) Frequency of Elements, 2) Utilization By Kaiser Number, Severity and First or Return 3) Time Requirements. Final Analysis Report For Each Kaiser Number (See Table 3 for Sample) Figure 9: Flow Diagram of the TLCS Computer Program

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95 TABLE 3 Sample Output for Analysis of Utilization, Time Requirements and Delegation Kaiser Classification 81 Prenatal and Postnatal Services First Visits = 57.88 Return Visits = 259.16 Mild Visits = 317.04 Moderate Visits = 0.0 Severe Visits = 0.0 Elements of Care, Utilization and Time Requirements Element

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96 anMCS that is too broad for the purposes of this study. In addition all studies have been performed in small private practices with the exception of the GEOMET studies (74, 89, 90). The results of the other studies will be briefly summarized and the GEOMET data will be analyzed in detail. Several of the studies were concerned with the percentage of time that MD's and nurses actually spend in direct patient contact. One study examined six pediatrics offices and found that RN's xvere spending only 21 percent of their time with patients (92) while another showed that pediatricians were spending about 48 percent of their time in direct patient contact in their office and of that time the majority was with patients who were not ill (93) . Three studies on MD time per patient in private practice showed the following: (a) in a general practice with extensive use of nurses, mean MD time varied from approximately five to ten minutes depending on the diagnosis (72) ; (b) a study of general practice showed a mean MD time of 10.4 minutes per patient (94); and (c) a study of four pediatricians showed an average of 10.2 minutes for well patients and 8.1 minutes for ill patients (95). Another study showed that PNP's spent almost twice as much time in contact with patients (47 percent versus 24 percent) as did regular office nurses (96) .

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97 The results summarized above are interesting but cannot be used to formulate a comprehensive, consistent data set for this study. The major problems with using them are their broadness of categories and the fact that they were all collected in private practices. The method used to derive the time requirements for this study was briefly discussed in relation to the computer program diagrammed in Figure 9 and the resulting output in Table 3. For each element of care, GEOMET specified the time requirements for the MD, RN and LPN for each of the three departments: (a) adult medicine, (b) pediatrics, and (c) OB/GYN. These time requirements were then transformed into time requirements in the KCBDCS through the use of the TLCS. It was assumed that the LPN would be used for preparation of the patient to see the physician and to accompany the physician in those cases where the presence of a female in the examination room is generally required for ethical reasons only. Thus a separate service, patient preparation, was included and most of the LPN time was included under this service. Note, the formulation also allowed for the RN, PE or MD to provide this service but in most cases it would more efficiently be performed by the LPN. An additional service, MD supervision, was defined to account for the MD time in the indirect supervision mode. The time requirements for patient preparation were given by GEOMET to be four minutes and the supervisory time had a basic level of four minutes. Note that the supervisory time is also modified by the f . . coefficient for levels of independence. The time requirements

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98 for the MD and RN for the remaining services are listed in Table 4. Those Kaiser numbers with no time requirements given have an insignificant utilization reported for the department involved. Aside from the patient preparation, the LPN is used in two additional categories. The LPN time requirements for these two categories are: (a) preventive services (01) 3.9 minutes, and (b) prenatal and postnatal services (81) 5.3 minutes. In addition to the MB-RN teams there are also MD-PE-RN teams and PE-RN teams considered in this analysis. PE time was not collected by GEOMET, but two previous studies did involve collection of PE time requirements. The studies by Golladay, Smith and Miller (73) and by Pondy (81) both concluded that for the same service the time requirements for both the MD and PE are the same. This observation is used in this study with two additions: (a) for an MD-PE team two minutes are added to both persons for coordination and/or communication purposes; and (b) for a PE under indirect supervision the MD supervisory time is also added to the PE time since the supervision would typically be carried out through a conference between the MD and PE. Thus the PE-RN teams have the same time requirements as the MD-RN teams plus the additions listed above. The MD-PE-RN time requirements are a little more involved. To determine this type of team time requirements involves specifying which of

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99 the tasks normally carried out by the MD will instead be carried out by the PE. Only the time requirements will be given here and the reasons for the particular division of tasks will be discussed under Delegation Guidelines . In addition to adding up the separate times for each element of care the extra two minutes for coordination and communication problems is added to the total. This has the desirable side effect of discouraging MD-PE-KN teams in the optimal solution that have very little PE input and instead picking the equivalent MD-RN team. Table 5 lists the MD, PE, and RN time requirements for the MD-PE-RN team configurations. Note that the design of the program represented in Figure 9 allows for very straightforward variation on these times if other delegation guidelines are to be followed. The principal input coefficients are listed in Appendix C and the productivity coefficients are contained under the b.. column. More will be said about interpreting Appendix C later in this chapter. Delegation Guidelines An introduction to PE programs and delegation possibilities was contained in Chapter 2. This section delves more deeply into the delegation questions and results in some basic delegation guidelines within the TLCS. Most previous studies in this area are hampered by an ad hoc approach and the fact that a standardized MCS has not been used to facilitate comparison of results. However, many studies are quite useful for supporting evidence and will be discussed here and the lengthier results will be summarized in Appendix B. The study by Braun, Howard and Pondy (71) was particularly useful and will be presented in greater detail. Several studies have recently centered on the role of a pediatric

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104 nurse practitioner and have shown an extensive delegation of functions to the PNP is possible. The initiators of the first PNP training program have listed the following activities as those for which PNP's are trained (70): take a complete pediatric history; perform a comprehensive basic physical examination; immunizations; determine developmental status; evaluate hearing, speech and vision; perform urinalysis and hemoglobin determination; evaluate and manage common problems of the healthy child and minor illnesses; counsel parents; assist in management of emergencies; and care for newborn infants. Silver (70) also notes that 71 percent of the patients managed by a PNP in a neighborhood health station were handled without referral to an MD. Another study stated the PNP handled routine well-child checkups and then reviewed the findings with the physician who then evaluated the findings and saw the patient as necessary (41) The same study found that the PNP handled sick children with relatively mild illnesses (41). A survey of 73 PNP's showed that 70-100 percent were performing the following activities (40) : (a) medical and illness history; (b) interval history of well and sick children; (c) physical exams for well and sick children; and (d) case management. Another study involved the use of PNP's at Kaiser-Permanente Medical Center (97). This study indicated the PNP's were taking complete histories; making complete physical examinations; managing minor illnesses; and would refer the child to a physician as needed. The PE in the OB/GYN specialty is usually called either a nurse midwife (NMW) or a physician's assistant. A study of the use of an NMW

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105 in a prepaid group practice showed the following procedures were performed (43) : (a) takes obstetrical and gynecological history; (b) performs breast, abdominal and pelvic examination; (c) performs Papanicolaou smear; (d) may order urinalysis, blood count and x-rays; (e) performs wet smears for vaginal infections; (f) may treat, according to findings, vulvovaginitis and urinary tract infections; (g) may advise about and dispense all types of family planning techniques; and (h) refers patients with abnormal findings to the appropriate physician. Another study reported the use of a PA in all routine prenatal visits including pelvic assessment in some cases (67). A survey of North Carolina physicians showed that most were willing to delegate routine prenatal visits but were not willing to delegate most gynecology examinations (33) . The results are presented in Table B-l of Appendix B. An interesting aspect of the survey is that the physicians were much more willing to delegate to female PA's than male PA's. In addition to the specialized areas noted above, several studies have been performed for physician assistants and medical practice with a broader scope. One study reported 75-100 percent of the physicians approved delegating such items as laboratory and related functions, therapeutic duties, assisting physician in acute illness or injury, and health maintenance type care (98) . The same study showed 30-50 percent (depending on specialty) were willing to delegate general physical exams

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106 with another 10-20 percent undecided. On the other hand, fewer than 15 percent favored delegating special procedures such as proctoscopy or spinal taps except in emergencies. The study by Powers (33), cited previously, included an extensive analysis of potential duties for the PA. A summary of tasks the PA is trained to perform in the Bowman Gray program at Wake Forest is given in Appendix B in Table B-2. A survey of 637 physicians showed that physicians responded relatively favorably to delegation of many functions (66). The definitions used and some of the results of the survey are contained in Appendix B in Table B-3. The study concluded that the actual decision-making regarding medical diagnosis and the prescription of a therapeutic regimen were activities the physician would least readily delegate. The last study to be reviewed was performed by Braun, Howard and Pondy (71). This study is probably the most comprehensive study available and the most useful. A survey was taken of physicians who are actually using a PA and their response was sought for the delegation possibilities of 368 tasks. The raw data obtained in the study were used to compile Table B-4 in Appendix B. In part of the survey compiled by Braun, Howard, and Pondy the physicians were asked to check one of the following categories for each task: (a) I have no knowledge of his ability; (b) cannot perform at all; (c) can perform under close supervision; (d) can perform under limited supervision; (e) can perform with supervisor's initiative and approval but under his own direction;

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107 (f) can perform under his own initiative and direction; and (g) needs additional training. The results are graphed in Table B-4 with categories (a), (b) , (c), and (g) listed under "Other" which indicates a non-positive response. The solid line indicates the maximum value given by at least one-third of the respondents and the dashed line indicates the mean response. The results of the above studies were used to formulate guidelines for delegation of functions to PE's. These delegation guidelines were formulated on two levels as is generally indicated in the literature. One level delegates entire patient visits to the PE with indirect supervision by the physician. As the literature indicates, routine physical exams, well-child care, and mild illnesses fall in this category. On this level the nominal delegation guidelines were specified as follows: (a) patients are classified as mild, moderate or severe through the use of the GEOMET specifications of care; (b) the PE may see those patients classified as mild (or not ill) with indirect supervision; and (c) the PE may see return visit patients, who are designated as mild or moderate, with indirect supervision. Three additional modes of indirect supervision were analyzed: (a) PE may see only mild cases with indirect supervision;

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108 (b) PE may see only mild and moderate return cases with indirect supervision; and (c) PE may see only mild, return cases in indirect supervision. Note that in a return visit an initial diagnosis and treatment regimen would have already been specified by a physician for those patients classified as moderate cases. The percentage of patient visits falling under these four indirect supervision guidelines is given in Table 6 for each of the Kaiser classifications used in this study. The second type of delegation guidelines established were for the case of MD-PE-RN teams in which case the PE would be under the direct supervision of the MD on the case. In this case the elements of care are designated as possible for delegation. For this problem the detailed task list given in Table B-4 of Appendix B was particularly useful. Those elements that came under "approved direction" or "own direction" are listed as "yes" in Table B-5 in Appendix B. The word "initial" refers to an initial workup for the physician for the intermediate and comprehensive exams. Those functions which fall under interpretation or diagnosis were generally not considered for delegation. Utilization of Services A majority of the remaining data in this chapter were collected at an established prepaid group practice to be designated PGP. However, it was necessary to fill in certain areas with data from the Kaiser prepaid health care system. Utilization of medical services must be specified in the KCBDCS to be used in the TLCS and these data were not available in the PGP. However, they were collected by the Health Services Research Center

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109 c s u o 3 i-l 4-J 4-1 0) (X t^ g en < CO C r-l O CO 1-4. 3 4J 1-1 3. 6 g O 3 g 1 3 X O (0 -i-l S W w

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3 O Pi & 6 T3 3 s < 110 S 5 & s 60 co SZ g B to (3 QJ Sj )-i .,-1 Vj Sj 4_i o a u a) cu oi uj: a) -u j3 >, C -u -W C -u CO H O O h-l O a sa

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Ill of Kaiser Foundation Hospitals, thus their data were used to establish the percent of visits falling under each classification number by medical specialty and this in turn was used to allocate the utilization at PGP. The demographic characteristics of the Kaiser sample and that of the PGP are very similar as can be noted in Table 7 .* The percentage utilization in terms of the KCBDCS is given in Table 8.* TABLE 7 Comparison of Demographic Characteristics for the Kaiser Sample and the PGP Sex

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TABLE 8 Percent Utilization for Adult Medicine, Pediatrics, and OB/GYN in the KCBDCS Percent of Visits 112
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113 that would result from different utilization levels and/or from a different breakdown by classification numbers. Medical Cost Data Introduction This section will set forth the cost data necessary to utilize the models previously derived. The major portion of the data was collected at the PGP. The cost data were collected with the intention of including the total costs which arise in the three primary care departments and excluding the costs which arise in the remainder of the PGP. The relevant costs include indirect as well as direct costs. In cost accounting, a distinction is made between revenue producing centers and service centers which are also called non-revenue centers. This is not simply a distinction between overhead cost and direct cost since revenue centers also have overhead costs (99). The service center costs are costs which the HMO must incur to operate, but where there is no service given directly to the patient. Note that due to the prepaid nature of an HMO, the concept of a revenue center must be broadened. Since the output of the system is measured in terms of medical office visits, the revenue centers will be taken as those units that produce medical office visits. Thus such centers as x-ray, laboratory, physical therapy, etc. will be defined to be service centers. In the PGP analyzed, the cost accounting system had three main divisions: cost centers, expense accounts and expense account allocation to cost centers. Costs and revenues for several ancillary services such as pharmacy and optical were separated from the medical cost accounting system. The objective of a cost finding system is to spread the costs

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114 of maintenance, operations, administration, and ancillary services to the revenue centers. There are four basic methods used to perform this cost analysis; direct, step-down, double apportionment, and multiple apportionment. Direct allocation is the simplest. However it (a) ignores the exchanges of services between non-revenue producing centers; and (b) does not compensate for the different demands for services by revenue departments on non-revenue departments (100) . Also, direct allocation is generally not allowed by third party payers (100). The step-down method involves the distribution of the costs of nonrevenue producing departments to other non-revenue departments and in turn to revenue departments. The term step-down is used because of the format in which distribution of non-revenue department costs are made. The costs of the non-revenue department serving the most departments (both revenue and non-revenue) are distributed first; the nonrevenue department serving the second largest number of departments is distributed next, and so on (100). For further details see Berman and Weeks (100) . Given the cost accounting system in practice at PGP, the step-down method was perfectly suited to allocate costs using the following nonrevenue centers: (a) occupancy, (b) supporting overhead, (c) laboratory, and (d) x-ray.

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115 The costs were distributed in the above order in the step-down method since occupancy served the most departments. Ancillary services such as physical therapy, nutrition, social service, and podiatry were included in supporting overhead. In addition to cost data additional detailed data were collected relating to (a) utilization of medical services offered; (b) number and types of employees in the medical and administrative departments; and (c) space allocations for the various departments. This information was used as the basis for allocation of the non-revenue center costs to the revenue centers. It should be noted that the data used to allocate cost data are as important as the cost data. Although an extensive amount of data was collected only a summary will be provided here due to the sensitive nature of the raw data. Cost Calculations To give an introductory picture of the PGP, the 1972 budget is given in Table 9. This budget is listed in terms of per person per month (PPM) income and expense. TABLE 9 1972 PGP Budget PPM Income Total Medical Income $17.27 Direct Expenses Personal and Related Services Physician capitation: Payroll 2 -56

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116 TABLE 9 Continued PPM Outside prof, services in area .79 Other payroll 2.59 Payroll Contingency Reserve .03 Employee Benefits .67 Professional services out of area .04 Prof. Group Contract .32 Other purchased services .20 Maintenance and Repairs .01 Total Supplies Rentals Depreciation and Amortization Hospital and Related Premium Plan Drugs Other Program Services Other Total, Direct Less: Occupancy Less: Supporting Overhead Total expense $17.08 $7

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117 additional costs brought the hospital and related costs to $8.06 PPM. Several other budgeted areas were not relevant to the office visit costs and the results are given in Table 10. Note that all cost figures used are for 1972. TABLE 10 Nonoffice Visit Expenses for PGP Total Income 17.27 PPM Less: Hospital and related 8.06 Premium drug plans .08 Outside professional services out of area .04 Other program services .17 Outside professional services in area .79 Projected excess .19 Other purchased services .20 Contingency reserve .03 Net 7.71 PPM For each department the MD salary plus benefits was computed based on their office visit time per week. Nurses were assumed to spend one-half of their time directly involved in patient contact and one-half in other activities such as advice and instructions over the telephone, calls to pharmacies, record keeping, and filing. Thus half of their salary was charged to overhead rather than directly to patient visits. A full time equivalent (FTE) PE was assumed to spend all of his time in patient care in office visits. Thus the salaries plus benefits allocated to office visit costs per FTE employee wereas follows (salary plus benefits is about $39,000 per year for MD's): (a) MD in adult medicine, $24600; (b) MD in pediatrics, $28900; (c) MD in OB/GYN, $14700; (d) RN, $6250;

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118 (e) LPN, $4750; (f) PE, $16,500. The PE salary plus benefits was an assumed figure since PE's were not being used in the PGP. These figures are used to calculate the c_ and s coefficients in the models. l The medical equipment at cost was $783,100 thus for 76 FTE MD's and a straight line depreciation for an average five year life: (a) t = $10,304, and v ' m (b) t' = $2060. Monthly cost center reports from adult medicine, pediatrics and OB/GYN were used to find the direct costs for the three departments. These cost center reports contained the following cost items: (a) medical group payroll, (b) nurses and technicians payroll, (c) administrative and clerical payroll, (d) employee benefits, (e) laundry, (f) equipment maintenance and repairs, (g) operating supplies, (h) dues, fees and contributions, (i) professional education, (j) staff meetings and overtime, (k) subscriptions and pamphlets, (1) travel, (m) parking, and (n) miscellaneous.

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119 The results, adjusted for nonhospital costs only for the departments studied were: (a) adult medicine, $922,000 per year; (b) pediatrics, $680,000 per year; and (c) OB/GYN, $299,000 per year. The above costs do not include the indirect costs. The facility costs, which must be added on to the above figure, were: (a) g = $27.39 per square foot, and (b) o = $4.94 per square foot. In addition, supporting overhead charges must be added to the direct costs. These costs largely relate to salaries plus benefits for administration, other ancillary services (such as dietician, physical therapy, electrocardiograms), supplies, and other miscellaneous. These costs were split up into the three parts given in the model development. There is $2,818,000 allocated to these three functions plus $405,000 in nursing salary plus benefits not previously allocated. When allocated on the basis of the coefficients used in the model, the results are: (a) MAN = $7070/FTE MD, (b) PV = $9.25/D0V, and (c) PER = $490/FTE employee. Laboratory and x-ray are two ancillary services listed separately in the model. Monthly reports for these two departments were used, along with their allocated portion of occupancy and overhead costs to compute the costs. The yearly cost was $454,000 for 47,000 x-ray procedures (a procedure can be comprised of several individual shots). Thus CXR = $9.65 and NXR = .174. Laboratory costs were computed in the same manner

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120 to give CLT = $.92 for 725,000 laboratory tests. The utilization was m 3.15, 1.35 and 2.83 tests per DOV for adult medicine, pediatrics and OB/GYN, respectively. These costs can now be combined to give the nonhospital departmental costs and are listed in Table 11. TABLE 11 Nonhospital Departmental Costs for Three Primary Care Departments in PGP Adult Med. Ped. OB/GYN MD salary plus benefits 575,000 456,000 148,000 1/2 nurse and technician salary plus benefits 132,000 99,500 68,000 occupancy 230,000 120,000 59,000 equipment depreciation and replacement 49,000 30,000 15,500 x-ray 130,000 119,000 24,000 laboratory 224,000 89,000 47,000 management 182,000 112,000 58,000 patient visits 715,000 655,000 166,000 personnel 21,000 12,500 6,800 professional group contract 153,000 137,500 12,200 Total for 3 departments = $4,846,000 2,411,000 1,830,500 604,500 Concluding Remarks This chapter has set forth the MCS developed to provide a framework for the data collection. The MCS was also designed to handle the delegation possibilities the models are capable of analyzing and thus the MCS also provides a solution framework. The data presented in this Chapter are used in most of the solutions discussed in the remaining chapters. In addition to the form in which they were presented in this chapter, they are also presented in a form for use in the models in Appendix C. The data are presented using abbreviated names for the problem variables. The procedure used to derive

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121 the variable names is presented in Tables C-l and C-2 of Appendix C and the input for the principle problem variables is listed in Table C-3. In Table C-3 the columns, headed by q, list the q. i . used to distribute the total team back to the manpower categories used. Recall, for the head of a team q = 1, thus this is not listed in Table C-3. The column headed SUP refers to the coefficient in the indirect supervision constraint for the particular manpower and medical service involved.

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CHAPTER 5 NOMINAL SOLUTIONS AND VALIDATION OF THE MODELS Introduction This chapter presents solutions to the models derived in Chapter 3 using the medical classification system and data developed in Chapter 4. Before presenting actual solutions to the models, two topics are introduced. The first involves the actual process through which the models are solved. The second describes the process of validation of the model and of the results. This topic was implicit in the model development and data collection, but at this point the validation process will be examined more closely. In partial fulfillment of the validation process nominal solutions to the models are presented which are compared to the PGP and to the Kaiser-Permanente prepaid practice. In addition, the flexibility and validity of the models is further tested through the use of the models in the preoperational design of emerging HMO's in Indianapolis, Indiana , and Daytona Beach, Florida. These results when grouped with the parametric and sensitivity analysis performed in Chapter 6 establish, as far as is presently practical, the validity of the models. The results also display the variety of analyses and designs that may be performed through the use of the models. Solution Process for Linear Programming and Mixed Integ er Programming 122

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123 The models presented in Chapter 3 belong to a class of models known as mixed integer programs (MIP) or linear programs (LP) if the integer restrictions are removed. Discussion on the background and solution procedures for linear programs can be found in references (101-104). The linear programming versions of the models formulated in Chapter 3 were solved using the Mathematical Programming System-Extended (MPSX) (105). MPSX has a number of features especially desirable for the solution of the present models: (a) uses revised simplex with bounded variables; (b) uses an efficient inversion technique; (c) uses multiple pricing; and (d) uses dynamic storage allocation. Solution of the models typically took about 30 seconds of CPU time on an IEM 360/75. MPSX also has extensive post optimal and parametric analysis capabilities lending themselves well to the types of analysis performed in this study. In conclusion, MPSX was used because of its availability, flexibility, and efficiency, but it can be noted that most other LP languages for relatively large models could also be used to solve the models. Although a great deal of useful analysis can be performed with the linearized versions of the models, it is also desirable to solve them with the integer restrictions. The most widely known solution techniques are cutting plane algorithms (106, 107), branch and bound algorithms (101), and partitioning algorithms (108). Additional references for MIP's are given in (109-112). The solutions for the MIP's given in this chapter and Chapter 6

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124 were found through the use of a branch and bound technique proposed by Land and Doig (113) . This technique was programmed by Sareshian (114) at IBM and was primarily intended for use on smaller models. However, several modifications were made to the program and the models were run on an IBM 360/75. Performance was erratic but most problems took from one to three minutes of CPU time. The choice of the above program for solution of the MIP' s was dictated largely by availability, but although it is not the most efficient algorithm for solution of MIP's it did prove adequate for the task. Validation Process Problems Involved in the Validation Process Validation is one of the most elusive unresolved problems associated with the application of operations research models. In fact, Naylor et al . (115) develop an argument to show that it is an unsolvable problem. Among the various arguments presented concerning validation, the two extremes are those of Kant and Hutchinson. Kant held the view that any theory is no more than the logical consequence of a series of premises that were true and not open in themselves to empirical validation (116). The opposite extreme is represented by Hutchinson who holds that no postulate or assumption is admissable unless it can be independently verified (116). Friedman (117) avoids the argument by holding that tests for validation should only be applied to the forecasting behavior of the model. A further complication is the normative nature of the present models. A normative model provides a solution which is optimal with respect to some criterion on systems performance. Clearly, if the

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125 actual system is operated under different criterion or suboptimally with respect to the chosen criterion, the operational settings of the decision variables may differ significantly from the optimal values found by the model. Also, because the system being modeled in this dissertation is, in part, hypothetical, direct comparison between the model's solutions and the actual systems are possible only over a limited range. With regard to this latter problem Koopmans states: However, it may also happen that,... no opportunity remains for observing the effect of not taking the recommended action or of taking some alternative action. In such cases, the recommendation is as good as the postulates from which it was correctly derived, but the analysis need not be less worthwhile for that reason. (118, p. 134) In spite of these difficulties, procedures are available to strengthen the validity and credibility of the models. While no universality is claimed for the techniques employed here, an attempt was made to thoroughly apply all accepted validation methodology. The models' structure and input data were evaluated for internal validity and face validity; the performance of the models was evaluated through comparison of the nominal runs discussed in this hapter with actual operating systems; and the performance of the models was evaluated through sensitivity analyses discussed in Chapter 6. Finally, whether these models provide an aid to decision makers in the design and evaluation of manpower requirements of an HMO is evaluated through two case studies in which the models are applied to HMO's in different stages of development. The results of the models are compared to those obtained by the planners using traditional approaches. Formulation of a Validation Process

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126 Although validation has rarely been explicitly discussed in mathematical programming publications, some work done in the validation of computer simulation techniques is applicable to mathematical programming models. Hermann (119) suggests five steps for the validation of simulation models and these have been modified and extended for application to mathematical programming models. The eight points formulated for the validation process are: (a) internal or structural validity; (b) face validity of the tradeoffs and inputoutput relationships; (c) sensitivity testing of the parameters of the model; (d) parametric testing for trend analysis; (e) similarity testing lo previous models; (f) subsystem validity; (g) data validity; and (h) event or time-series validity. In practice, only a subset of the first seven points will usually be possible and the last point involves a lengthy analysis of the results of an implementation of the model. In addition to the above points Enshoff and Sisson (131) assert, "Credibility the only kind of validity we have for a first time model, requires a detailed examination of the internal structure of the model and of the data used for estimated parameters. It requires careful comparison with such historical data as is available." (120, p. 205) Steps Taken To Validate the Models

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127 Validation is a process that is intertwined with the entire research process and cannot be isolated from the remainder of the research without constantly referring to and restating other aspects of the research. However, it is possible to explicitly summarize the validation process. A summary presented in terms of the eight points listed in the previous section follows. !• Internal validity requires that the structure of the model incorporate the principle features of the system required for decision analysis in a way that accurately portrays the interactions between these features. The principle decision factors given in the model are motivated in Chapter 2. Chapter 2 presents a verbal description of HMO's as a financial and organizational entity. It was noted tbat two key decision factors involved in the HMO structure are the services or benefits to be offered and the cost of these services. In addition, Chapter 2 described the various personnel classes who could provide the medical services offered in the HMO. The chapter concluded by joining the manpower aspects and organizational aspects and noting that from a systems analysis viewpoint the two aspects are highly interrelated. In Chapter 3 the system description was used to develop mathematical models. All of the system resources and requirements described in Chapter 2 were incorporated in the model. From a medical provider or resources standpoint this included such features as the productivity analysis of the various manpower classes, the tradeoffs between manpower and capital, and the medical limitations of certain classes of the med~Tcal providers ."From an organizational standpoint it included features

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128 such as the total cost of medical care including indirect costs, ancillary services and the selection of services to be offered. In summary, the structure of the problem was developed in Chapter 2 and the structure of the model was developed in a stepwise fashion in Chapter 3 to incorporate all the features of the system needed to perform a decision analysis on the tradeoffs in the HMO-manpower system. 2. Face validit y requires the resource allocation tradeoffs and the relationships between inputs and outputs to be realistic when viewed by people familiar with the real system. To establish a realistic model one needs to become familiar with the real system so that important considerations are reflected in the model. Throughout the development of the models first hand observations of the actual system, such as PGP, second hand observations through published literature on HMO and manpower planning, and discussions with people in HMO and manpower planning led to an evolution of the models to their present state. The models were also used in the preliminary planning of two HMO's and thus were subjected to further testing by persons involved in HMO planning. In addition a panel of experts in various aspects of HMO and manpower planning examined and critiqued the models and the results. These inputs were used as a guide as the research progressed and to establish the face validity of the models and the solutions from the models. 3. Sensitivity testing shows if the decisions in the models are insensitive when subsidiary

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129 parameters are varied and whether the model reacts in a defensible manner when inputs or assumptions are changed. Two types of sensitivity analysis are presented in Chapter 6. The first type involves the facility costs. It is shown that the decision process is insensitive to the facility costs. The second type involves changing some of the inputs or assumptions such as the indirect supervision restrictions, indirect supervision time requirements and the integer restrictions. The results indicate that the model behaves in a manner that can retrospectively be explained and defended in terms of the tradeoffs made. 4. Parametric testing should reflect trends that are reasonable and retrospectively predictable in terms of the tradeoffs. Chapter 6 presents parametric analysis using the models. The inputs parameterized are the basic resources and requirements in the system; namely availability of PE's and subscriber levels. The trends and results are listed and explained in Chapter 6. 5. Similarity testing involves comparing the models to previous models and analyzing their similarities and differences. The development of the models in Chapter 3 started with several basic models previously proposed and showed in a stepwise fashion the further development that was necessary to completely describe the relationships between the resources and

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130 requirements. 6. Subsystem validity can be tested by using simplified versions of the model to generate results which can more directly be analyzed or compared to existing systems. Later in this chapter a comparison with PGP and KaiserPermanent e is presented. This comparison was achieved through use of a submodel that essentially eliminates most of the resource allocation tradaoffs. The result is that the optimal nature of the solutions is severely restricted to the point where a comparison with the present system can be made. This does not show the validity of the overall model, but the results presented show that the subsystem very closely matches operational results. 7. Data validity means that the data are representative of the system and are the result of careful analysis. Chapter 4 presented a very detailed and comprehensive analysis of the data used in the models. A new medical classification system was developed to use existing data rather than resort to hypothetical data. The remaining data were collected at PGP or were extracted from data collected at other sites. As far as was possible the data came from systems that are operationally very similar to HMO's and thus would be applicable to an HMO model. Although the data do not directly affect the validity of the models they do have two by-products. First, the data collection effort and the analysis of real data can lead to revisions in the model to more

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131 accurately reflect reality. Secondly, the data used directly affects the validity of the results of the model. Without valid data it becomes very difficult to assess the validity of the model itself. 8. Event or time series validity is established if the system reacts in a manner predicted by the models after recommendations of the models are implemented. Later in this chapter case histories of the use of the models in the design of two emerging HMO's is presented. The results show that the model was robust enough to reflect the particular policies and conditions of the HMO; was able to optimally answer the questions posed by the HMO developers; and resulted in solutions that were accepted by the HMO planners. The use of the models in the design effort and the results of that effort contribute to the face validity of the models . Later, when the HMO's open, if the recommendations are implemented it will be possible to examine the event or time-series validity of the models. Implications of the Model Assumptions In an attempt to further examine the internal validity of the models some of the assumptions which were used to derive the models will be examined in more detail. A normative mathematical model is used to prescribe an optimal course of action based on some system criterion. However, this does not imply that a model must include all aspects of a system and in most cases such a model would be unsolvable. Thus assumptions are made in an effort to isolate the key aspects of the system and simplify aspects that are not central to the questions for

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132 which solutions are sought. The models assume that the utilization of medical services takes place at the same level throughout the time period of the model. In reality, patient demand is a stochastic process which is possibly a function of the day of the week, time of the year or the incidence of epidemics. However, the process by which patient demand is converted to utilization is partially controllable through the appointment or scheduling of patient visit process. In this way seasonal and daily fluctuations are partially leveled off. Epidemics can be handled through increased provider time for a short period of time and through the delay of patient visits for well child visits, routine physical exams, etc. If it is believed that seasonal fluctuations are important and cannot be leveled off, then the models could be run on a seasonal basis to examine manpower requirements as a function of the time of the year. Another stochastic variation ignored by the models involves the time to provide a medical service by medical personnel. Variation occurs not only because different types of patient visits are classified under one medical service, but also because the time to perform the same task varies from one performance to the next. Instead of using stochastic variables for provider time, which would have led to a model not readily solvable by analytical methods, the mean task time was used. Although there are day to day fluctuations in the mean, the model is not directed at predicting day to day performance; thus this stochastic variance is not central to the models. The present medical system operates without notable effect from this daily variance and the fact

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133 that the models tend to include more medical providers, in the form of PE's, acts to decrease the daily output variance. Additionally, since providers are sensitive to the pressure of increased demand, the output rate increases in periods of peak demand further reducing the output variance. As was noted previously, linear programming precludes economies of scale. This factor is potentially important in the estimation of facility and equipment costs. Because the true cost function for facility and equipment cost is unknown the model should not be applied to HMO's much smaller or larger than PGP unless a new data base for facility and equipment cost is assembled. The model is working under the assumption that the facility and equipment costs are linear in some region about the optimal solution. However, the sensitivity analysis in Chapter 6 shows that these costs have only a minor effect on the optimal values of the decision variables. Thus, the range of application of the data may be cautiously extended. The basic conversion of resources to meet the requirements is handled through a linear production function. The production is assumed linear for a fixed technology level. This assumption implies that if x units of a medical service are produced in y minutes then b • x units are produced in b • y minutes for a fixed technology and the same personnel providing the service. However, the models allow for a change in technology level at a fixed charge and a corresponding change in the productivity coefficients. The allocation of indirect costs to the departments and medical services was discussed in the model development. The techniques of

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134 accounting give guidelines as to how indirect costs should be allocated, but frequently the allocation of indirect costs fall into a gray area of uncertainty. Fortunately, these costs have a minor effect on the primary decision variables that refer to manpower utilization. However, since they can have a direct effect on the n. decision variables, a careful allocation of indirect costs should be carried out. It should be noted that the uncertainties involved with this assumption are largely a function of accounting techniques and are not a fault of the model. Nominal Solutions Comparison to the Prepaid Group Practice The objective of this comparative analysis is to examine how closely the models will match a system presently in operation. At PGP the PE's presently have a very limited role. Former corpsmen are used in the urgent visit clinic and one nurse midwife is used very sparingly on a part-time basis. Since the corpsmen are not used in the departments being simulated and the nurse midwife saw very few patients, PE's were not included in the delegation possibilities. Later, the effect their inclusion would have on the system will be discussed. The result is that the major tradeoffs of the model are not included in the analysis. Thus the comparison can help to validate the submodel that remains. Note that the entire structure of the model still remains, but the manpower tradeoffs are reduced to a trivial state which essentially changes the model results from prescriptive to descriptive. Thus a special, simplified case of the use of the model can be investigated.

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135 The cost data described in Chapter 4 were used directly, but the time requirements and delegation data were changed to reflect the conditions at PGP. Nursing duties consist primarily of giving injections, telephone consultation, finding and completing patient records, filling out forms and preparing the exam room for the MD and the patient. The physician nominally sees three patients per hour in office practice at PGP but there are several exceptions to this norm. Complete physical exams and special diagnostic problems are scheduled for a forty minute block instead of twenty minutes. In addition, utilization and office time data showed the OB/GYN department to be effectively on a four patient per hour basis. Integer restrictions were relaxed since PGP has a large number of part-time employees. The Overall Planning Model (OFM) was used to perform the analysis and the results are given in Table 12. TABLE 12 Cost and Manpower Comparison of PGP and the Overall Planning Model Category

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136 In the primary area of interest, MD utilization, the predictions were quite close. While they were somewhat erratic in nursing, this can in part be attributed to the fact that the nursing role at PGP is not as well defined as the physician role. It would be expected that if significant changes were made in the system, the model would not be as accurate in predicting the changes, but a basic property of any model is that it should be able to closely duplicate a system it is intended to model. Presentation of Nominal Solutions The solutions presented in this section are nominal in the sense that they represent results based on the reference values given in Chapter 4 for the input data. For any given plan other data may be nominal and be quite different from the reference data included in solutions presented in this section. An indication of the effects other reference data would have on the response of the system is given in the parametric and sensitivity analysis in Chapter 6. Nominal solutions are presented for the OPM, MC, and SM models for a subscriber level of 82,000. This facilitates comparison with PGP and also enables an investigation of the relationship between the various manpower categories and delegation results without the nuances of subscriber levels to cloud the results. Several points to note with regard to the nominal data are: (a) time requirements data are given in Tables 4 and 5 of Chapter 4; (b) cost data are the same as were used in the PGP comparison analysis;

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137 (c) delegation guidelines imply that PE's may see mild cases or mild and moderate cases on return visits under indirect supervision; and (d) the utilization rates are the same as in the PGP comparison run. The first nominal solution was found using OPM with no PE's in the system. For this run, as in the PGP comparison, most of the tradeoffs are essentially eliminated from the model. The second nominal solution allowed PE's to be used to their fullest capacity with the integer restrictions removed. For this solution the model made decisions based on the following basic tradeoffs: (a) delegation of a service to the lowest cost person (who can perform the service) versus the additional cost of MD supervision; (b) delegation of a service to the lowest cost person (who can perform the service) versus the supervision time required from the MD; (c) delegation of services to MD-PE-RN or PE-RN teams which require more total personnel time versus delegation to MD-RN teams which require more MD time; and (d) the total cost of a service in the HMO

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138 versus what it can be purchased for outside the HMO. These are the nominal tradeoffs that are associated with virtually all of the solutions presented in the remainder of the dissertation. In the future, these four will be assumed and any additions or deletions will be noted. The third nominal solution involves the same assumptions and tradeoffs as noted for the second nominal solution and in addition the integer restrictions are enforced. Thus an additional tradeoff is made in the selection of integer manpower levels. It was previously noted that only the ambulatory care aspects of HMO's are examined in this study and that possible PE use in the inpatient setting is not analyzed here. Thus when PE's replace MD's in the ambulatory care facility this has an impact on MD's available for inpatient care. For the purposes of presenting the results, the MD time in the inpatient setting is assumed to be replaced by hospital based MD's. Thus, in comparison of the results, MD time in the inpatient facility is fixed regardless of whether or not PE's are utilized. The solutions can be easily converted to whatever other assumption is desired regarding inpatient care. The results for the first three nominal solutions are presented in Table 13 along with the present system at PGP. The plus numbers under the integer solution result from the additional hospital based MD's required as noted above. For the continuous solution with PE's the additional MD's are included in the totals. Several points can be noted with regard to these nominal solutions:

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139 TABLE 13 Comparison of Offl Nominal Solutions to PGP Manpower Category-

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140 play a major role in manpower utilization; (c) use of PE's in the system resulted in a monetary savings of $145,000 or about 4.1 percent; (d) the manpower savings was dramatic since the total number of MD's decreased from 33.21 in the no PE solution to 19.77 in the solution with PE's, or a decrease of 40 percent; and (e) PE's were used the most extensively in pediatrics largely due to the high number of well child visits which were delegated to the PE's. In addition to the conclusions noted above it is interesting to examine the continuous solution with PE's in terms of the tradeoffs involved in the models. For adult medicine the delegation results are listed in Table 14. Note that the figures are full FTE's of the team leader. In this particular solution, the upper limit on supervision time was not reached so it was not involved in the tradeoffs. Although there are exceptions caused by other tradeoffs, several general statements can be made regarding the solutions given by the models: (a) a service requiring very little indirect supervision is delegated to a PE and nurse team in keeping with nominal tradeoff (a); (b) for services requiring less MD time it usually is delegated to an MD and nurse due to the extra cost associated with MD-PE teams (nominal tradeoff (c)) or with

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TABLE 14 Delegation Analysis for Nominal Continuous Variable Solution 141 Classification*

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142 indirect supervision (nominal tradeoff (a)); (c) due to the fact that the supervisory constraint was not reached, PE and nurse teams are at either the zero level or their upper bound; (d) for services with high indirect supervision requirements anMD, PE, and nurse team is frequently delegated. It can also be noted that in many cases the interaction between the tradeoffs becomes too intertwined and the delegation cannot be examined with respect to one tradeoff at a time. The solutions resulting from the tradeoffs lead to the following general delegation guidelines; (a) preventive services have a low supervision requirement and are delegated to PE's; (b) chronic illnesses are primarily delegated to MD-PE teams; (c) acute illnesses are primarily delegated to MD and nurse teams or PE and nurse teams as permitted; (d) symptoms of undiagnosed diseases are delegated to MD-PE teams; and (e) diseases with high emotional content are delegated to MD-PE teams or to PE's. Thus although the model is a cost minimization model, it does contain enough in the way of medical tradeoffs and information to lead to a delegation policy that is desirable from a medical viewpoint. Nominal solutions were also derived using the minimum cost model (MC) . These solutions were derived in a parallel manner to the OPM

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143 results and are presented in Table 15. The conclusions are basically the same as those of the OM model, although there are many instances when the MC model is useful as is demonstrated in the case studies later in this chapter. TABLE 15 Nominal Solutions for MC Model Manpower

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144 TABLE 16 Nominal Solutions for the SM Model

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145 gation is PE and nurse first, MD, PE and nurse second, and MD and nurse third (there are exceptions since as constraining limits are reached an interaction between tradeoffs results) ; (g) MD requirements decrease dramatically; (h) the subscribers per MD plus PE clearly show the increase in total medical personnel which accompanies the use of PE's since the subscribers per MD with no PE's is about 5000, 7850, and 11,100 for adult medicine, pediatrics, and OB/GYN respectively; and (i) the PE/MD ratio is lower in OB/GYN principally because of the lower total time in the office setting for the OB/GYN specialist, thus this ratio would change if the PE were assigned extensive inpatient duties. Comparison of Nominal Solutions to an Existing Prepaid Plan In this section the 0PM results with no PE use are compared to the Kaiser-Permanente Southern California region. Only an overall comparison is possible since detailed figures for Kaiser-Permanente were not available, but the comparison is nonetheless interesting. Kaiser's system in 1972 had so few PE's that it can be compared to the no PE nominal solution presented in the last section. Their Southern

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146 California region has 744 FTE physicians and about 944,000 participants. For the three departments analyzed, Kaiser had 5280 office visits/MD* while the model shows 5050 office visits/MD which is about a 4 percent difference. When corrected for the same patient utilization rate (Kaiser's is higher than PGP) Kaiser has one primary physician per 2600 participants while the model predicts one per 2500 participants. The 0PM solutions were found without reference to the Kaiser system and yet the solutions show a very good correspondence to the Kaiser figures. Although costs are even more difficult to compare due to differences in benefits a rough comparison can be made. As was shown previously the PGP income for non-hospital services less the excess and contingency is about $9 per person per month (PPM). If this were adjusted for the same utilization as Kaiser, the comparable figure would be $11.05 PPM. The 0PM model predicts a 23.9 percent decrease in cost would be possible for the three primary care departments. Assuming this reduction would also be possible in the remaining departments, the reduction would result in a cost of $8.42 PPM. According to Somers (31) the corresponding Kaiser figure was about $8.50 PPM in 1971. In summary, although the comparison to the Kaiser system could not be made in the same detail as with PGP, the comparison was useful. It showed that the manpower predictions and cost predictions are well within the range of the Kaiser system. Personal correspondence from Ms. Nina Wexler of Kaiser Foundation Health Plan of Southern California

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147 Case Exa mples Use of the Models in the Design of an HMO in Indianapolis , Indiana This section presents the results of an analysis performed regarding the Experimental Community Health Network (ECHN) proposed by the Metropolitan Health Council of Indianapolis, Indiana, Inc. (MHC) under O.E.O. Grant No. 50066E 7201. The ECHN is designed to provide medical care for people living in four poverty areas in the urban core of Indianapolis. One of these areas, the southeast area, was selected as the site for an analysis using the planning models. In the southeast area, the Southeast Health Center (SHC) has been operating since 1968. Several features of the SHC approach to health, care include an initial comprehensive patient evaluation, patient education, preventive medicine and the extensive use of nurse clinicians. Under the ECHN the SHC will be converted to primarily an HMO but additionally will continue to serve nonmembers on an episodic basis. Under the contract agreements the ECHN will be responsible for a comprehensive set of medical services while the SHC, as one component of the ECHN, will provide ambulatory care for the primary care areas. The involvement with and analysis of the SHC took on four phases: (a) initial problem definition and background needed to perform data collection; (b) data collection by the SHC and MHC and final definition of problem areas; (c) design and analysis through the use of the planning models; and (d) presentation of the results of the analysis.

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148 It should be noted that the alternatives and problem areas defined by the MHC are preliminary and do not necessarily represent the policy under which they will operate. The data requirements for the model helped to focus attention on the various types of information needed to calculate capitation rates and analyze manpower staffing levels. In addition, data reported in Chapter 4 were used in several places to replace data being used by MHC or to reinforce their data in areas of uncertainty. The data for this case example are presented in Appendix D. Several key aspects of the data are presented below: (a) the age-sex breakdown for the potential users of the HMO show that approximately 47 percent are under 15 years old and about 27 percent are femnle in the 15-44 age bracket; (b) the utilization rates used were 1.70, 1.28, and .66 office visits per person per year in adult medicine, pediatrics, and OB/GYN respectively; (c) the HMO subscriber size is projected in the range of 3000 to 8000; and (d) a fixed expenditure of $192,246 is incurred regardless of the subscriber level in the above size range. The flexibility of the models was demonstrated in the analysis of the SHC, since it had several properties which made manpower analysis

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149 difficult by traditional means. Some of the key factors involved were (a) extremely skewed demographic characteristics and utilization patterns which make comparison to staffing ratios of other plans difficult; (b) extensive use of nurse clinicians in the provision of medical care; (c) low subscriber levels which make integer restrictions important; (d) uncertainty as to role OB/GYN would play in the system; (e) possible limited use of General Practitioners in routine physicals and checkups in pediatrics and OB/GYN to help overcome integer manpower problems; (f) possible limited use of General Practitioners in routine prenatal and postpartum care to help overcome integer manpower problems; (g) use of nurse clinicians in both adult medicine and pediatrics; (h) use of nurse clinicians in traditional nursing function where indicated by integer constraints; (i) uncertainty as to subscriber levels; (j) possible use of pediatricians or OB/GYN' s on a half-time basis; and

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150 (k) continuation of episodic care in addition to HMO patients. All of these factors are within the range of the model's capabilities and the SHC was analyzed under the following parametric conditions: (a) assumption A allowed General Practitioners to perform routine examinations in pediatrics and OB/GYN and all other OB/GYN was on referral; (b) assumption B allowed General Practitioners to perform routine examinations in pediatrics and OB/GYN, routine prenatal and postpartum care in OB/GYN, and all other OB/GYN care was on referral; (c) assumption C was the same as B except that an OB/GYN specialist was included in the HMO; (d) designs were generated for full-time or half-time pediatricians and OB/GYN' s; and (e) designs were generated for subscriber levels of 3000, 5000, 6000 and 8000. The analysis was performed using the minimum cost model and the results are given in Table 17. Note that in general the level of nurse clinicians was fixed at three since that number is presently employed at the SHC. An explanation of the table follows: (a) runs are coded in 3 parts, the first digit is the number of subscribers in thousands, the second part refers to

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153 assumption A, B or C, and the third part is a run number which distinguishes between the full-time or half-time use of pediatricians and/or OB/GYN's; (b) the next five columns give the manpower levels for MD's in adult medicine, pediatrics and OB/GYN, nurse clinicians, and nursing; (c) the next six columns list the use of General Practitioners in routine exams for pediatrics (AMDPREVC) and OB/GYN (AMDPREVO) , and prenatal or postpartum care (AMDPREGO) (see Appendix C for derivation of the preceeding names) as well as the use of nurse clinicians in adult medicine, pediatrics and traditional nursing functions; (d) the next two columns list the maternity cases and OB/GYN office visit referrals; and (e) the last column lists the total monthly capitation. The following conclusions and recommendations can be drawn from the results in Table 17. 1. The fixed expenditures have a large effect on capitation at the lower levels — particularly at 3000 subscribers.

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154 2. For 3000 subscribers if a half-time OB/GYN specialist can be hired then OB/GYN services should be offered at SHC. If a half-time OB/GYN specialist cannot be hired then OB/GYN should be on referral with the General Practitioner providing routine physical exams and prenatal and postpartum care if suitable referral arrangements can be worked out. 3. For 5000, 6000 or 8000 subscribers a full-time OB/GYN specialist can be justified on an economic basis. For 8000 subscribers 1.5 OB/GYN 1 s can be justified but 2.0 cannot be. 4. For 3000, 5000, or 6000 subscribers only a half-time pediatrician is needed due to the extensive use of nurse clinicians in pediatrics. At 8000 a full-time pediatrician is needed. 5. The nurse clinicians are not used exclusively in their extended role. Their use in the traditional nursing role is shown to depend heavily on both the subscriber level and the hiring of full-time or part-time pediatricians. 6. The use of the General Practitioner in a limited role in pediatrics and OB/GYN has a positive effect on the system due to the added flexibility this lends to the integer or half-time

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155 manpower restrictions. Note thatMD's in adult medicine were not restricted to integer levels due to the more flexible staffing possibilities in that department. 7. Clinical assistants, who perform in the traditional nursing capacity, were not limited to integer values. Since they are at a much lower salary level, integer restrictions placed on them would have little economic impact on the system. 8. Within the same subscriber level, the cost of the alternatives varied as much as ten percent while for all cases the range from lowest to highest was fifty percent. 9. If OB/GYN services are excluded entirely from the capitation figure the capitation, assuming a full time pediatrician, would be $11.07, $8.23, $7.65, and $6.78 for 3000, 5000, 6000 and 8000 subscribers, respectively. Note that a detailed listing of the variable costs involved in the capitation analysis are listed in Table 18. Another point not yet discussed involves the possibility of the SHC providing care as an HMO and on an episodic basis. This possibility is especially likely in the first year of operation. To perform this analysis the maximum subscriber model was used and the number of physicians in adult medicine, pediatrics and OB/GYN was parameterized. A

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156 a w o

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157 o

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o

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159 o

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160 total of ten runs is listed in Table 19. Most headings were described previously but in addition the heading "slack" refers to idle time in FTE's. Conversion of the results to subscribers/MD is not strictly possible due to the use of General Practitioners across specialty lines and the use of the nurse clinicians, but some general conclusions can be listed. 1. With extensive nurse clinician utilization, one MD in adult medicine can care for approximately 5000 subscribers. 2. With extensive nurse clinician utilization, 1.45 MD's and one pediatrician can care for 6848 subscribers. 3. In the region near the optimal solution, with about 1-2 MD's in adult medicine, approximately 2500 subscribers per MD in adult medicine is implied. 4. Without aid from the General Practitioner, one OB/GYN specialist is limited to approximately 6000 subscribers. 5. One proposed manpower configuration consisted of 1.45 MD's in adult medicine, one pediatrician, and three nurse clinicians. Run E shows this configuration to be capable of providing care for 6848 subscribers. Note that the above results are listed in terms of subscribers for convenience. Patients visiting the center on an episodic basis can be converted to subscriber equivalents through the subscriber utilization

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161 eg

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162 rates of 1.70, 1.28, and .66 visits to adult medicine, pediatrics and OB/GYN, respectively. Table 19 can thus be used to examine the possibility of additional patient visits that could be handled by a staffing configuration. This would also lead to a recomputation of the capitation rate to include the additional revenue source. It is difficult to compare the results of the maximum subscriber analysis against other plans due to the use of nurse clinicians, but a rough comparison follows using RUN E. Using the subscriber utilization rates listed above RUN E predicts that 1.45 MD's in adult medicine, one pediatrician and three nurse clinicians can care for 6848 subscribers which can be converted to 20,200 patient visits. Assuming nurse clinicians in the expanded role can see an equivalent of about two-thirds the patients a physician sees (to be shown in Chapter 6) then the ratio is about 5050 visits per FTE MD. For adult medicine and pediatrics, Kaiser Permanente data* shows about 5500 visits per MD. Given the fact that SHC will have a low income group of subscribers who typically have more complicated and involved illnesses, these predictions seem to be very reasonable. In addition to the conclusions noted above, several other more general conclusions arose at various points in the design effort: (a) utilization figures for low income groups are sparse and a complete analysis is not truly possible, thus the SHC should collect *Personal communication from Ms. Nina Wexler of Kaiser Foundation Health Plan, Inc.

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163 utilization rates by age, sex and possibly income level to aid in future planning (especially critical in pediatrics); (b) the utilization data should include laboratory and x-ray utilization by type of test or series, cost or charges, department ordering test or series, and age and sex of patient; (c) the facility at SHC needs to be expanded to include more examination rooms or the capabilities of the medical personnel will be greatly hampered (there are presently eight examination rooms) ; and (d) since laboratory, x-ray and drug charges comprise about 50 percent of the variable costs in the system they should be examined for possible cost savings. Evaluation of the Indianapolis HMO Case Study The case study of the Indianapolis HMO and the Daytona Beach HMO (presented in the next section) were undertaken to show that the models are a valid means of developing staffing guidelines for HMO's. This section presents an evaluation of the results of the Indianapolis HMO study and includes three areas: (a) the reaction of the HMO planners to the results; (b) the differences between the model results

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164 and previous planning results; and (c) the effect the models and solutions had on the decision process. The HMO planners in Indianapolis felt the models were useful as decision aids in several areas: (a) the question of having OB/GYN at the HMO or referred out was quite unresolved and they felt the models had been useful in examining the alternatives; (b) they previously had no way to assess the effect of using General Practitioners in pediatrics or OB/GYN and the model showed the effect this could have on staffing; (c) the models were useful in assessing the effect the use of nurse clinicians would have on the need for a full-time pediatrician; (d) the models showed how many patients could be treated in an episodic manner in addition to the prepaid patients; and (e) the solutions highlighted the fixed cost problem which shows dramatically the high cost per subscriber resulting from operating at low subscriber levels.

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165 The above areas represented problems that were not amenable to an easy solution. The HMO planners felt the models were able to answer the manpower questions they had asked. Most importantly, in their estimation the results of the models were accurate. There were some differences in the results given by the models and the previous projected staff. These differences will be discussed for a subscriber level of 5000. The principal differences were that the models projected a need for one half-time pediatrician and a fulltime OB/GYN specialist whereas previous plans were for two half-time pediatricians and OB/GYN services on referral. The model found that only one half-time pediatrician was needed due to the extensive use of nurse clinicians in pediatrics and the limited use of General Practitioners in pediatrics. On the other hand, the models showed that a full-time OB/GYN specialist could be justified economically. In addition, the models showed that the nurse clinicians could only be used about 70 percent of the time in their extended role due primarily to the limited case selection. From an economic standpoint the previous manpower plans led to a capitation of $10.24 per person per month. Using the optimal solution from the models the cost would be $9.15 per person per month or a 10.6 percent reduction in cost. In addition, the model's solutions indicated all three primary care areas could be staffed at SHC, thereby obviating the need for outside referral for OB/GYN. At this point, the Indianapolis HMO is still several months from opening and staffing plans have not yet been finalized. Thus it is not possible to say with finality that the above staffing recommendations will be implemented. The planners did feel though that it had influenced

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166 their planning, particularly with regard to OB/GYN. They also felt that as a result of the use of the models they had assembled a much better and more consistent data base upon which to base future planning. In addition, they thought the parametric results of the models gave them very useful information with regard to capitation rates and staffing levels that they would use in their further planning. Case Study of Design of an HMO in Daytona Beach , Florida The case study of a design for the SHC presented in the previous section involved a neighborhood health center presently operational and planning to convert to an HMO. In this section an HMO in Daytona Beach, Florida named Florida Health Care Plan, Inc. (FHCP) is analyzed. There are three primary differences between these two HMO's: (a) FHCP is in its planning stages and has not yet provided medical care whereas SHC has operated as a NHC; (b) the SHC primarily was designed to provide care for low income groups whereas the FHCP has a different medical problem in that they project 50 percent of their subscribers as over 65 years of age; and (c) the FHCP is being started by a private group of physicians whereas the SHC is governmentally supported. When this analysis took place, the FHCP was well along in their planning and were about six months from opening. Consequently, the facility plans were relatively fixed, the benefits were fixed and an

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167 extensive cost and utilization analysis had been performed. Thus, the cost prediction capabilities of the models were of secondary importance and the primary question asked by FHCF involved manpower staffing levels. These questions involved two basic points: (a) how PE usage would affect MD requirements; and (b) how the two manpower groups would interact with the integer manpower restrictions as the HMO subscriber levels increased. Basically the FHCP wanted the above questions answered as part of their long range planning since they felt it would be at least a year before they would have enough subscribers to hire PE's. Before presenting the analysis and results for these two questions the data provided by FHCP will be briefly summarized. 1. The projected age-sex breakdown is given in Table 20. Note that 50 percent are over age 65. 2. Projected utilization rates per 1000 members were provided by FHCP and are listed in Table 21. Note that each column represents 1000 members. The combination of demographic characteristics and utilization rates lead to 11247, 459 and 672 office visits for adult medicine, pediatrics and OB/GYN respectively at a subscriber level of 3000.

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168 TABLE 20 Projected Demographic Characteristics for FHCP Age group 0-6 7-14 Male/15-20 21-34 35-49 50-64 65+ Female/15-20 21-34 35-49 50-64 65+ 3000 Subscribers 175 270 90 144 177 42 720 90 207 258 48 780 1000 Subscribers 583 900 300 480 590 140 2400 300 690 860 160 2600 3,000 10,000 TABLE 21 Projected Utilization Rates Per Thousand Members for FHCP Category

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169 $45,000for MD's, $12,000 for PE's, $10,000 for RN's and $6,000 for LPN's. 4. Ancillary costs were estimated at $7.00 for laboratory tests and $20 per x-ray series (including personnel costs) . 5. The FHCP will occupy 22,000 square feet which will be leased for $121000 per year plus $114000 per year for equipment. 6. Management costs are estimated to be $81000 and billing, receptionist etc. will cost from $47,400 to $55,000 depending on the subscriber level. 7. Cost of maintenance, utilities, etc. is estimated at $132,000 per year. 8. Co-payments will include a $1 per office visit charge. The analysis was carried out in three main parts: (a) continuous optimal solution using PE's with the minimum cost model; (b) integer manpower analysis for the 3000 and 10000 subscriber levels using the minimum cost model; and (c) a parametric analysis using the maximum subscriber model for various staffing patterns. The continuous optimal solution is presented in Table 22.

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170 TABLE 22 Continuous Optimal Solution for FHCP Subscribers

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171 The minimum cost solutions are 2 MD's and 1 PE at 3000 subscribers and 5 MD's and 5 PE's at 1000 subscribers. The FHCP is presently planning to open with 3000 subscribers and 2 or 3 MD's and no PE's in adult medicine. The above results predict that 2 MD's could provide care for approximately 2600 subscribers. The last part of the analysis involved a parametric analysis of integer staffing possibilities for adult medicine and the subscriber levels that could be handled. The results are presented for from two to eight MD's and from zero to six PE's. For low MD levels fewer than six PE's could be. used. The results are presented in Table 24. Several conclusions can be drawn from Table 24. 1. At maximum PE utilization levels the number of PE's is approximately equal to the number of MD's in adult medicine. 2. Whereas the MD's have a marginal productivity of approximately 1200-1400 additional subscribers per additional MD, the PE marginal productivity ranges from about 550-775 additional subscribers per additional PE . 3. The marginal productivity of PE's decreases as the number of PE's per MD is increased. 4. A suggested plan for growth and hiring can be derived from Table 24. This plan is given in Table 25.

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TABLE 24 Parametric Results for Various Integer Staffing Levels for FHCP 172

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17 3 TABLE 25 Suggested Dynamic Hiring Plan for Adult Medicine at FHCP Maximum Subscribers

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174 PE ' s ; and (b) their immediate objective is to try to establish a multi-specialty group practice so they can offer a comprehensive benefit package. However, they wanted the study performed to see how and when PE's might be of use in their HMO. They also examined the data base and the medical classification system and felt both were quite reasonable with several minor changes. The HMO planners were surprised at the effect PE's could have on their staffing patterns but did not disagree with the projected staff given by the models. They felt the model was able to respond very fully to the types of manpower staffing questions they had. Overall they viewed the model as giving them a better feeling for some of their projections. The PE analysis was viewed as an important input to their decision process and they felt it gave them something of substance to base further plans on. The staffing projections for MD's were in fairly close agreement with their previous projections. The model did show a slightly greater need for MD's in adult medicine and a lower demand for MD's in pediatrics and OB/GYN. Since no previous projections for PE staffing had been performed at FHCP no comparison can be made for PE staffing. As a result of the solutions the FHCP has started to more seriously consider using Family Practitioners to take care of most pediatric visits and referring more specialized cases to a pediatrician. This is due to the low projected requirements for a pediatrician. This is not as likely for OB/GYN due to the unavailability of an OB/GYN specialist

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175 for referral. They also feel it has very positively influenced them in the direction of hiring PE's as their subscriber levels increase. Concluding Remarks This chapter has presented a validation process; comparisons of the model solutions to two operating prepaid practices; nominal solutions for the models; and two case studies. Each of the above areas are related to the validation of the models. The validation process carried out in this dissertation can be summarized as: (a) internal validity, (b) face validity, (c) sensitivity testing, (d) parameter testing, (e) similarity testing, (f) subsystem validity, (g) data validity, and (h) event or time-series validity. Note that points (c) and (d) are addressed in Chapter 6 and the other points were addressed in this chapter. Sensitivity and parameter testing are included as a separate chapter since they represent major results of the study in addition to their role in the validation process.

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CHAPTER 6 PARAMETRIC AND SENSITIVITY ANALYSIS OF POLICY QUESTIONS Introduction This chapter presents an examination of the results which arise from changing some of the assumptions or input data from the nominal level. Two types of analysis are presented. Sensitivity analysis is used to examine the output response to changes in the input data. This type of analysis can be used to examine which inputs heavily affect the output and which inputs have little effect on the decisions being made by the models. Secondly, a parametric analysis is presented to examine the output response as the resources and requirements aspects of the model take on off nominal values. Both sensitivity and parametric analysis help to establish the validity of the models. Essentially, both types of analysis test aspects of the model. As more cases are examined more information is gathered as to the behavior of the model. This helps to pinpoint any inconsistencies that may arise as the model is tried under a systematic set of input values. The trends and changes that take place in the output of the models should be defensible in terms of the tradeoffs the models are making. In addition to their role in the validation procedure, sensitivity and parametric analysis can be used to examine an HMO in a systematic way and to draw conclusions from the models for various policy questions that arise not only for local HMO planners but also for national man176

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177 power and HMO planning. Specifically, this chapter will cover the following points: (a) sensitivity analysis of facility costs; (b) sensitivity analysis of optimal PE use as a function of PE salary; (c) a sensitivity analysis of the indirect supervision guidelines; (d) an analysis of the integer manpower restrictions for small HMO's; (e) a parametric analysis of manpower and cost for various subscriber levels; (f) a parametric analysis of optimal delegation under a scarcity of PE's; and (g) a parametric analysis of the maximum subscribers per physician under a scarcity of PE's. These are some representative and key issues that can be addressed by the models. However, as was shown in the analysis of the two case examples a large variety of other questions can also be answered. Sensitivity Analysis Facility Costs It was indicated in Chapter 5 that the effects of facility costs upon the decision process should be examined through sensitivity analysis. There are several points that can be stated with regard to the facility cost of an HMO. First, the models were intended to perform a cost analysis in addition to a manpower analysis. Since facility expenses are a fairly major expense in an HMO, they were included as a separate

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178 cost category. Secondly, although it seems reasonable that the facility costs would be affected by the number of physicians and PE's that would work in the HMO, a true cost function is not known. In addition, since the use of PE's increases the total number of employees providing medical care, a secondary tradeoff would involve the extra facility cost resulting from additional manpower. Thirdly, it was assumed that if facility cost data were collected for a facility of the approximate size indicated by the optimal solution, the cost could be assumed linear in that region. These three basic points are analyzed through response of manpower utilization to facility cost. In each of the cases analyzed, all inputs were held at their nominal level with the exception of the facility cost. The construction costs were increased by 25 percent, 50 percent, and 100 percent and the results are given in Table 26. TABLE 26 Manpower Utilization Response to Increases in Facility Cost

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179 and less PE utilization occurs as the facility costs increase. The reason for the shift to greater MD utilization can be deduced by recalling that the use of PE's leads to more manpower in the system. However, the solution is quite insensitive to the added space requirements and facility costs which implies the nominal solution will not be heavily affected by a detailed analysis of space utilization. As was noted in Chapter 3, one of the tradeoffs of the models involved the increase in the total time (MD plus PE) as PE's were used versus the greater MD time if PE's were not used. This analysis has shown this tradeoff as it is reflected in the facility cost to have a secondary effect on the decision making in that only a small number of delegations are so marginal that the facility cost increase is able to revise the delegation. This would be hoped for, not only because from a medical care standpoint it is definitely secondary, but also since a true cost function for facility cost is not known. These results show that in decision making with regard to facility costs the model behaves in a manner as one would expect the real system to behave. Thus this sensitivity analysis has further established the validity of the models. Physician Extender Salary The major tradeoff made in the model involves the use of PE's in some functions that are carried out by MD's in systems with no PE's. Although the PE still requires supervision from the MD for these functions the salary difference between the PE and MD frequently warrants the use of a PE where medically feasible. For the remainder of the discussion salary will be taken to mean salary plus fringe benefits .

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180 For the nominal case a salary of $16,500 for PE's was assumed as representative. However, there have been lower salaries and salaries as high as $21,000 reported. Thus it is desirable to examine the salary tradeoff by examining PE salaries that are -2000, +2000, and +4000 from the nominal salary. For all cases presented in Table 27 the PE salary is the only input revised from the nominal level. TABLE 27 PE Use As a Function of Salary Increment From the Nominal Manpower

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181 and 25 percent in pediatrics. 3. For all salary ranges above, the utilization of PE's in OB/GYN remains constant. This occurs at -2000 because the supervision constraint was reached in the nominal case. At +2000 or +4000 this indicates that PE's are still more cost effective; thus the OB/GYN solution is rather insensitive to salary in the region about the nominal. 4. For increment of +4000 the PE utilization in adult medicine declined about 50 percent and in pediatrics the decline was about 100 percent. 5. The delegation patterns for adult medicine and pediatrics can be summarized as follows: (a) at -2000 there was greater use of PE's in independent roles; (b) at +2000 PE utilization in independent roles ceased except for preventive services (PREV) and emotional disease (EDIS) ; (c) at +4000 MD-PE teams ceased and the only utilization of PE's was for preventive services and emotional disease in adult medicine. Thus it can be concluded that PE utilization tends to be more cost

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182 effective in the independent role as salaries decrease and tend to be cost effective only in the team role as salaries increase. The key tradeoff that explains this trend is the cost of supervision by the MD. As the PE salary rises ,the PE salary plus MD supervision cost tend to rule out the independent role except for those services with very low supervisory requirements such as preventive services. An analysis of the dual variables for the optimal solution at +4000 indicates that two or three thousand additional dollars in salary would eliminate all cost effective PE utilization in all three departments. As PE salaries increase one would expect that their use in the real system would become more restricted. Those activities which require much MD supervision would no longer be delegated and the MD-PE-RN teams that have little PE input would tend to be carried out by an MD-RN team. The services that required little or no MD intervention, such as preventive services, would remain attractive at relatively high PE salaries. Since the model gave the above intuitively plausible results, this raises the level of confidence in the ability of the model to make the correct economic tradeoffs with regard to the MD-PE cost comparison. Thus this sensitivity analysis helps to further validate the models. Indirect Supervision Guidelines In the Dele gation Guidelines section of Chapter 4 the indirect supervision guidelines were presented. They are repeated here for convenience. The nominal delegation guideline is: the PE may see those patients classified as mild (or not ill) or return visit patients designated as mild or moderate with indirect supervision. Five additional modes of indirect supervision are analyzed:

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183 (a) PE may see only mild cases in indirect supervision; (b) PE may see only mild and moderate return cases in indirect supervision; (c) PE may see only mild return cases in indirect supervision; (d) PE may see no patients in indirect supervision except for preventive services; and (e) no limits on PE utilization in the indirect supervision mode. These six cases were examined principally because there is uncertainty as to the exact role the PE will play in medical care. In some organizations the PE will only be used under the direct supervision of a physician in an MD-PE team while in other organizations the PE will not be used in an MD-PE team, but will act more independently in the indirect supervision mode. This analysis indicates the potential manpower utilization resulting from these various delegation patterns. For each of the six indirect supervision assumptions full use in the direct supervision mode was allowed. With the exception of the last case (no limits) it was assumed that MD's would spend a maximum of 20 percent of their time supervising PE's in the indirect supervision mode. For the cases presented in Table 28 the upper bounds on the X variables were revised in accordance with Table 6 of Chapter 4 and all other inputs were held at their nominal level. The following conclusions can be drawn from Table 28. 1. Nurse utilization is largely unaffected

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184 6 O -H 0)

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185 by the supervision and independent action assumptions principally because in most cases those functions for which nurses are trained to perform are done more cost effectively by nurse than by PE's regardless of the restrictions on PE usage. The exception is in OB/GYN where the assumption of a female PE obviates the use of a female nurse to accompany what is usually a male OB/GYN specialist in the examination room. 2. Cost varies only about plus or minus 1 percent as a function of the assumptions. This small change is in part induced by the ability of an optimization scheme to seek out the best solutions when new constraints are added. This is also partly due to the low effect the assumptions have on nursing costs (which account for about 25 percent of the medical personnel costs). An actual medical organization would probably show a larger cost response under the various delegation assumptions. 3. The two extremes for indirect supervision are included to show the upper and lower limits on PE utilization. The relative

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186 changes from the nominal in MD and PE utilization for these two extremes is given in Table 29. TABLE 29 Maximum Shifts From the Nominal in MD and PE Utilization Caused By Changes in the Indirect Supervision Guidelines Manpower Adult Medicine-MD -PE Pediatrics -MD -PE OB/GYN -MD -PE No indirect cases except preventive services +117= -16% + 3% 3% +15% -52% No limits on indirect cases 4% + 6% 2% + 2% -11% +37% Table 29 shows the PE and MD utilization tc be largely unaffected at even the extreme assumptions on indirect supervision with the exception of OB/GYN. 4. In Chapter 5 it was noted that after all tradeoffs are made, the model decides whether or not to use a PE in the indirect supervision mode for a given service. As long as the supervisory constraint is not reached this decision results in one of two alternatives: (a) do not use the PE independently

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187 in this particular service; or (b) use the PE to the upper bound for this particular service. This type of solution is a property of linear programming solutions and is quite reasonable in the context of these solutions. It can be noted that the tradeoffs are made somewhat independently of the upper bounds on independent PE use. Thus the delegation strategy given for the nominal OPM case with PE's in Chapter 5 is basically the same delegation strategy as the solutions given in Table 29. In particular, if the nominal case showed the desired delegation for a service to be PE and nurse up to the limit, then MD-PE and nurse to fulfill the remaining demand, it stays basically the same with just the upper limits changing. If on the other hand, the nominal solution shows the MD and nurse team to be optimal for a given service, this will not change regardless of the indirect supervision guidelines. The above statements assume that other constraints are not reached such as MD supervision or availability of MD's or PE's. Thus for adult medicine and pediatrics, manpower requirements are quite insensitive to the independent action assumption. In OB/GYN only

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188 the extreme assumptions show a significant utilization response. The only shift is that as independent action is more restricted in most cases it leads to greater use of MD-PE teams to provide the services. Thus it would seem that under economic optimality the independent versus dependent roles that a PE may eventually play will not have a major effect on the demand for PE's in prepaid group practice. This conclusion is important and perhaps unexpected but the detailed analysis given above of the tradeoffs and behavior of the model show that the model is again behaving in a justifiable manner, thereby contributing to the validation of the models. In addition to the analysis of the indirect supervision guidelines, a sensitivity analysis of the MD supervision time was performed. In the indirect supervision mode it is assumed that the MD will check over the PE's findings or confer with the PE regarding his findings. The MD may even briefly see the patient to confirm certain findings. A basic value of four minutes of MD time was used for indirect supervision. This value was modified by the fraction, f. ., depending on the difficulty of the service being performed. Values of f^. were arrived at based on the percent of time the PE would be used in the MD-PE team for each service (the smaller the PE usage the more difficult the service). In addition to the four minute basic time, values of six and eight minutes were also used. The results are presented in Table 30 with all inputs held at their nominal level with the exception of supervision time. The table shows there is almost no response as the supervision time is raised from four minutes to six minutes. However, it can also be seen that about a 20 percent shift in manpower requirements does occur

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189 TABLE 30 PE Utilization As a Function of Basic MD Supervision Time Manpower

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190 the addition of two extra minutes of MD supervision time would not overcome the cost savings for use of PE's. However, as the basic supervision time increases the MD is spending more of his time in supervision. Since supervision time is a limited quantity this would tend to rule out those services requiring the most supervision. Thus the analysis indicates the model is performing as one would expect the real system to perform. In conclusion it can be noted that MD supervision time and indirect delegation guidelines have some effect on overall manpower requirements, but the effect is not major except at the extreme assumptions. The supervision time and indirect delegation guidelines have a greater effect on the particular use of the medical manpower than they have on the number required for optimality. Parametric Analysis PE Utilization As a Function of Subscriber Levels and the Integer Re strictions Most of the solutions discussed to this point have focused on large scale HMO's. These solutions were designed to investigate the relationships between the various manpower categories and delegation results without the nuances of subscriber levels to cloud the results. However, many if not most HMO's will be operating with subscriber levels in the 8,000-30,000 range or for large HMO's many will have primary care centers in several locations serving subscriber levels in the above range. It should be noted that the models are directly capable of solving a multi-center HMO merely by defining additional departments such as adult medicine at clinic one, adult medicine at clinic two, etc.. If MD's

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191 are to be shared between clinics additional, simple constraints can be added to account for this. Another point is convenient to raise at this time. In most of the solutions presented, the subscriber size is used as a descriptive parameter since it has intuitive meaning. However, to completely describe the manpower and cost structure, subscriber size and patient utilization in terms of doctor office visits (DOV) per year is needed. Whereas many analyses work on the basis of subscriber size alone, without the explicit consideration of patient utilization, this analysis explicitly uses patient utilization in the models. Thus the analysis can be used for various patient utilization rates without in many cases rerunning the model. For example, the nominal DOV's per year used were .945, .866 and .218 for adult medicine, pediatrics and OB/GYN, respectively. Thus if one were analyzing a 10,000 subscriber level clinic but thought the utilization would be 20 percent higher than that given above, the desired solution could be found with the descriptor of 12,000 subscribers. Returning to the main point of this section, the interaction of small subscriber levels and manpower requirements are presented for subscriber levels of 8000, 10000, 12000, 16000, 20000, and 30000 and were investigated with the PM with two assumptions: (a) MD and PE levels are restricted to integer values; and (b) MD levels are continuous while PE levels are integer. The first assumption arises from the desirability of having full-time employees who can give their undivided practice to the subscribers of

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192 the plan. The second assumption recognizes there may be instances where hiring only full-time MD's would be wasteful of a scarce talent and expensive to the subscribers. In the present medical setting however, it is not as easy for a PE to carry on a separate practice independent of the HMO on a part-time basis. Thus their integer restriction was maintained. The results from assumption (a) and (b) are summarized in Table 31. Nurses are not restricted to full-time and PE's are assumed to not be involved in inpatient care; thus the hospital MD time must be added in as was previously discussed. Table 31 shows the effect of lower subscriber levels on the cost and manpower requirements. All of the nominal tradeoffs are in effect in these solutions and in addition the integer manpower tradeoff is in effect. The results from Table 31 are summarized below. 1. Assumption (a) leads to a maximum of 8.5 percent higher cost per subscriber and has its greatest effect at low subscriber level with negligible effect at 30,000 subscribers. 2. Under assumption (a) the cost is 13.3 percent higher at 8,000 subscribers than at 30,000 subscribers. Under assumption (b) the corresponding margin is 3.9 percent. 3. Integer restrictions have the effect of requiring more high level personnel. MD's replace PE's in some functions and PE's replace nurses in some functions in order to use the higher cost manpower as fully

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193 u

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194 as possible. Assumption (a) leads to lower nurse levels than assumption (b) . Essentially PE's are being used less efficiently by taking over functions a person with less training could perform. 4. The most important result of Table 31 is the implications for regional or national manpower planning. Table 31 shows that future requirements forMD's and PE's in HMO's are quite dependent on the size of HMO's being built and the particular integer restrictions used. For the large clinics discussed in the nominal solutions, the ratio of PE/MD was 1.31, 2.02, and .51 for adult medicine, pediatrics and OB/GYN, respectively . For illustration purposes assume that an equal number of 8000, 10000, 12000, 16000, 20000 and 30000 clinics are used in some geographical territory. Then by correcting Table 31 for hospital practice and weighting the results equally the new ratios are 1.24, 1.12 and .37 for assumption (a) and .83, .59 and .13 for assumption (b). This indicates a 5 percent, 45 percent and 27 percent reduction for assumption (a), and a 37 percent,

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195 71 percent, and 75 percent reduction for assumption (b), for PE's in adult medicine, pediatrics and OB/GYN, respectively. Thus it can be seen that the size of clinics and the integer restrictions have a major effect on the future PE requirements. This also points out the inherent error in quoting PE to MD ratios without explicitly considering the operational circumstances. In summary, it can be noted that the integer restrictions and small subscriber sizes have the effect of raising MD/subscriber ratios and usually has the effect of lowering PE/MD ratios. This is especially true under the part-time assumption for MD's and full-time assumption for PE's. In many instances the integer manpower tradeoffs act to transcend all other tradeoffs. Thus this tradeoff which was shown to be quite unimportant in the nominal cases in Chapter 5 is extremely important for low subscriber levels. Optimal Delegation With a Scarcity of PE' s Results presented in previous sections were found under the assumption that whatever manpower is needed could be hired. Although, this information is relevant to the extent of showing the optimal operating conditions it is also relevant to examine the solutions in light of the present manpower market. Since PE programs did not exist in significant numbers until 1971 or 1972, the number of graduate PE's is quite small. It will take several more years before the number of PE's gradually builds up to a sizable quantity (32). Thus an HMO may

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196 not be able to hire the number of PE's they may wish to. Thus given a scarcity of PE's one can ask: (a) how many MD's are needed; (b) what is the new cost figure; and (c) what functions should be delegated first to minimize cost? The results are given in Table 32 and have been adjusted for hospital MD time. The results are for a subscriber level of 82,000 but approx-. imations for other sizes can be found by using proportions. Several points about the table require expository remarks. The column headed "new services delegated" refers to those new services that are delegated to a PE-RN or MD-PE-RN team as an additional PE is added. The nomenclature for the service and manpower names can be found in Tables C-l and C-2 of Appendix C. A dash under that heading means that the additional PE is being used for services previously listed. The term "maximum PE utilization" refers to the economic limit for PE utilization. A summary of the results is given below. 1. Table 32 shows the decrease in MD requirements as additional PE's are used. The marginal savings for adding PE's are given in Table 33. Thus initially a PE can replace about twothirds of an MD however as the upper limit for PE utilization is reached the replacement rate is about .4. This does point out the fact that PE use tends to i:icrease the total number

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197 TABLE 32 Optimal Delegation and MD Requirements Under a Scarcity of PE's # of PE's

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TABLE 32 Continued 198 # of PE's

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199 TABLE 33 Marginal MD and Cost Savings As Additional PE ' s Are Used Number of PE' s per department

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200 services, such as well child care or routine physical exams are the first services to be delegated from an economic viewpoint. Diseases with a high emotional content and chronic disease generally followed in delegation. Diseases with high emotional content are first delegated to MD-PE-RN teams where the PE can save the MD much time by performing the initial workup and then assisting the physician in carrying out a therapeutic regimen. Diseases with a high emotional content are also delegated to a PE-RN team if the condition is not severe such as routine ulcers, failure to adjust in school, inaturity, malingering, sleeping problems, etc.. In OB/GYN routine prenatal care was also high on the list. These services, aside from the economic issues, are the services PE's are best qualified to handle. For patients with chronic diseases, the MD can determine the diagnosis in the first visit and in most cases turn the patient over to the PE to carry out the prescribed regimen of treatment. Additionally, the delegation tends to initially lead to formation of MD-PE teams with the exception of preventive

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201 services and other services with verylow supervisory requirements. As more PE's become available the PE's are used increasingly in an indirect supervision mode. In summary, the results are intuitively appealing and represent feasible delegation patterns. The results of this section are useful for HMO planning in the present manpower market with a scarcity of PE's. The results show that from a marginal cost and manpower savings the first several PE's hired are the most effective. As more PE's are hired the marginal cost savings become very small but significant MD savings are still realized. Maximum Subscribers Per Physician Under a Scarcity of PE' s Although economics plays a major role in many decisions, including medicine, there is an additional significant factor in the medical field. While there is some disagreement as to whether there is a shortage of MD's, a maldistribution of MD's, or a misutilization of MD's, most would agree there is not an oversupply of primary care MD's available for recruitment for HMO's. Thus the question may arise as to how to maximize the number of subscribers an HMO could provide care for per MD. This section will examine the additional constraining factor of a shortage of PE's. The PE scarcity will be examined parametrically by taking the number of MD's and PE's to be fixed and the Subscriber Maximization (SM) model will then find the delegation pattern which maximizes the number of subscribers served. The results are obtained for relatively small

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202 departments of one, two or three MD's and are displayed in Table 34. Note that the MD levels are not adjusted for the additional MD inpatient requirements. The term "Max PE" in Table 34 refers to the point at which additional PE's added to the system are idle. Essentially the tradeoffs used in the analysis for Table 34 are the nominal tradeoffs with the exception that saving MD time is the key tradeoff rather than saving money. Thus those activities which required the least MD supervision or those which replaced the most MD time for the relative least PE time were delegated first. The results of Table 34 are presented graphically in Figure 10 which shows the subscribers per MD as a function of the PE to MD ratio. The ratios in Figure 10 have been corrected for MD hospital utilization. The figure shows the substantial gains in subscribers per MD that are possible if PE's are used extensively in the system. For example, at one PE per MD a 51 percent and 60 percent increase in subscriber size in adult medicine and pediatrics is possible. At one PE per two MD's in OB/GYN a 29 percent increase is possible. Thus Figure 10 displays the potential manpower impact that could occur if PE's become widely available and are extensively used. Remarks This chapter has presented a wide variety of sensitivity and parametric analysis through the use of the mathematical models. It is in this type of analysis that mathematical models display their maximum usefulness. With a mathematical model one can ask many questions and receive answers quickly and at low cost. This type of experimentation is simply not possible with the physical system. In fact, the points

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203 CO

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204 20 19 18 17 16 15 14 13 12 11 10 Pediatrics .4 .6 .8 1. 1.2 1.4 1.6 1. RATIO PE/MD FIGURE 10 Subscribers Per MD As A Function of PE/MD Ratio 2. 2.2 2.4 2.6

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205 raised in this chapter are representative of the types of analyses that may be performed with the models, but there remains a large number of special cases or particular questions that can be approached with the models. Examples, of this were given in Chapter 5 with the particular form of questions and analyses dictated by the particular case examples under study. In summary, this chapter served three major purposes. First the sensitivity analysis showed the solutions to be relatively insensitive to several of the secondary factors involved in the models and the parametric analysis established trends and used tradeoffs in a consistent and defensible manner. Secondly, various aspects of the sensitivity and parametric analysis established results of a more general policy making level. Some of the results not only give guidelines for HMO manpower use but also suggest possible national manpower implications. Third, the sensitivity and parametric analysis helped to further validate the models. The models were tested under systematic sets of input values and the models performed as one would expect the real system to perform. The results of the models were intuitively plausible and could be justified in terms of the tradeoffs made.

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CHAPTER 7 SUMMARY OF RESULTS AND CONCLUSIONS Introduction This last chapter has two principal functions. First the results and conclusions and the validation process given in the previous chapters are summarized here. This largely takes the form of a restatement of previous results and conclusions, but in addition, more general conclusions are derived from the overall results of the research. Secondly, several areas requiring further research are stated. These were either initially defined as outside the scope of the analysis or are subsidiary to the main thrust of this dissertation. Several of these additional areas are difficult but it is hoped that the results obtained in this dissertation will aid in their resolution. Results and Conclusions Development of the Models and Data Base The results and conclusions can be divided into two sections: those results which carried through the development of the models and those results which arose from the solution of the models. The results are stated in a generally chronological order. Chapter 2 presented a definition of the PE that could be used for further analysis and development. Chapter 2 also presented a systems framework in which HMO design could be carried out. The conception of 206

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207 HMO planning developed in Chapter 2 served as the basis of the model development. Three preliminary models were developed in Chapter 3 which served as the basis for the development of four final models with diverse objectives. The Overall Planning Model was developed to solve the general class of problems defined by: given a fixed capitation rate and projected subscriber base find (a) manpower to be hired, (b) delegation of services, (c) services to be provided (d) facilities required, and (e) particular technology innovations to be used. Next the Minimum Cost model was developed to solve the following basic class of problems: given a fixed set of medical departments and a fixed subscriber base, find the optimal staffing, delegation and facility requirements to minimize the capitation rate. In addition to the two minimum cost models two additional models were developed to analyze the use of MD's in HMO's. The Subscriber Maximization model solves the following basic class of problems: given a fixed professional staff and subscriber fee, find the optimal delegation, facility requirements, and

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208 hiring policy for allied personnel to maximize the number of people who can be served. Lastly, the Minimal Use of Professional Manpower Model was developed to solve the following basic class of problems: given a fixed subscriber base, a fixed fee, and a fixed set of services, find the optimal staffing, delegation and facility requirements to minimize the professional level personnel used. The above four models are solved using mixed integer programming techniques or linear programming techniques if the integer restrictions are removed. In Chapter 4 an analysis of the shortcomings of some existing medical classification systems was carried out. This resulted in the formulation of a new medical classification system. This new classification system is a three-level hierarchial system which relates to the following manpower planning considerations: (a) training and delegation, (b) morbidity statistics, and (c) manpower utilization. A computer program was then developed to use the new classification system to define time requirements, delegation possibilities and utilization data. The delegation analysis was performed in terms of the new medical classification system which enabled the delegation to be specified on both a detailed and broad level. Since a comprehensive

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209 and consistent data set for these three areas was not previously available, both the technique of generating the data set and the data set itself are major results of this research. In addition medical cost data were collected at a major prepaid group practice. Data relating to both direct and indirect costs are presented to fulfill the data requirements of the models. Results From the Models Chapter 5 presented results relating to nominal solutions of the models and the validation process. An eight point plan for the validation of normative mathematical models was presented. The validation process used in this research was then summarized in terms of the general validation process. A comparison between the Overall Planning Model and the PGP actual system was performed. This comparison showed a very close prediction by the model compared to the operating system. The model then predicted that a 23 percent cost savings could result at PGP if nominal productivity rates were assumed. The model also predicted a further 4 percent cost reduction and a 40 percent MD reduction would be possible if PE's were extensively used. A comparison of the nominal results to Kaiser-Permanente was also performed on a less detailed level and a very close comparison resulted. A delegation analysis showed the following general guidelines for delegation of services to PE's: (a) preventive services have a low supervision requirement and should be delegated to PE's;

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210 (b) chronic illnesses are primarily delegated to MD-PE teams and in some cases to PE's; (c) acute illnesses are primarily delegated to MD's or to PE's and seldom to MD-PE teams; (d) symptoms of undiagnosed diseases are delegated to MD-PE teams; and (e) diseases with high emotional content are delegated to MD-PE teams or to PE ' s . Nominal solutions for the Subscriber Maximization model showed the following results: (a) a 41 percent decrease in MD requirements and 1.55 PE's per MD could be used in adult medicine; (b) a 53 percent decrease in MD requirements and 2.1 PE's per MD could be used in pediatrics; (c) a 22 percent decrease in MD requirements and .47 PE's per MD could be used in OB/GYN. The model was also used in two case studies in HMO planning. These studies were performed to show that the models are a valid representation of an HMO system and that these models can be used for aids to decision makers in planning HMO's either in the early stages of their development or in subsequent staffing decisions. The first case study

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211 demonstrated the flexibility of the models, since many special provisions were specified. The results showed the effect subscriber level had on the capitation rate. It also was used to demonstrate under what conditions an OB/GYN and pediatrician could be justified economically. The model was able to demonstrate how a 10 percent cost reduction could be made through a revision of previously projected staffing patterns. In addition several projected staffing levels were examined with the Subscriber Maximization model to see how many patients could be handled in an episodic manner in the neighborhood health center role. The second case study was primarily concerned with the manpower effect PE's would have on the HMO. The results indicated very low requirements for MD's in pediatrics and OB/GYN and high requirements in adult medicine and was in general agreement with previous projections for MD requirements. In addition, no previous results had been established in the HMO regarding the use of PE's and the models showed that for 10,000 subscribers a staff of five MD's and five PE's was optimal. In addition as a result of the parametric analysis, a dynamic hiring plan was suggested. Both case studies were performed to help validate the models and thus they were presented to the HMO planners for evaluation. In summary, the planners felt the models were accurate; that the results were useful to them; and that they influenced their decision process in several areas. Chapter 6 presented sensitivity and parametric analysis which was used to analyze policy questions and to further validate the models. The sensitivity analysis showed that the facility cost affected the total cost of the HMO but affected the model's decision making in only

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212 a secondary manner. The PE salary plus benefits figure was analyzed for its effect on PE utilization. A nominal PE salary to MD salary ratio of about .42 was used but it was shown that for the region of .37 to .47 there was little effect on the decision making. However, at .52 and above a very definite impact was felt and PE's rapidly lost their cost effectiveness. At lower ratios the models used PE's more extensively in the indirect supervision mode whereas at higher ratios they were only used in MD-PE teams. The exception was for those services requiring very low supervision, such as preventive services, where PE's were used in the indirect supervision mode at all salary ratios up to the point where they lost their cost effectiveness entirely. A total of six indirect supervision guidelines were investigated. The results showed that, except at the extreme guidelines, total PE use was relatively unaffected. Instead, as the guidelines were made more restrictive, MD-PE teams were used to a greater extent. An analysis of the indirect supervision time requirements showed that PE use was not greatly affected until the nominal supervisory time was doubled. It was shown that the integer manpower restrictions have definite cost implications for small HMO's or small HMO clinics. The integer restrictions also have the following effects on PE utilization: (a) integer MD and integer PE restrictions would possibly decrease PE requirements by 5 percent to 45 percent for small HMO's; and (b) continuous level MD's and integer PE restrictions would possibly decrease PE requirements by 37 percent to 75

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213 percent for small HMO's. In the present manpower market there are very few PE's; thus the use of less than the optimal number of PE's was investigated. This showed the following results: (a) a marginal savings of about .6 MD per PE as few PE's are added to the system and a cost savings of about 60 percent _ of the difference in salary between the MD and PE per PE used; (b) a marginal savings of about .4 MD per PE as the maximum number of PE's is reached and a corresponding negligible cost savings; and (c) if few PE's are available they should first be used in those areas requiring the least supervision, then in mild or moderate cases of diseases with a high emotional content and chronic disease. The maximum number of subscribers that could be served was also analyzed with the number of available PE's used as the parameter. The results showed for example that at one PE per MD a 51 percent and 60 percent increase in subscriber size in adult medicine and pediatrics is possible. At one PE per two MD's in OB/GYN a 29 percent increase is possible. Results of the Validation Process Although segments of the validation process were stated in the

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214 previous section in the course of presenting the results of the models, this section is included to explicitly summarize the validation results. As a preliminary step in the validation of the models Chapter 3 presented a careful development of the models from a very basic resources and requirements model to a detailed representation of the HMO and manpower system. This helped to establish the internal validity of the models and also presented the models similarities and dissimilarities with previous models. Then a consistent data base to use in the models was carefully established in Chapter 4. In Chapter 5 an eight step validation process was formulated. As part of the validation process, subsystems of the model were compared to two operational prepaid group practices. The results were in very close agreement with the actual system. In addition the models were tested in two case studies. An evaluation of the results by the HMO planners indicated the results were accurate and the models were a useful aid to decision making. Thus the results of Chapter 5 helped to establish the subsystem validity and face validity of the models. In Chapter 6 two more validation steps were carried out. A sensitivity and parametric analysis was used to test the models for inconsistencies under systematic changes in the inputs. In particular, results were analyzed and justified in the following areas: (a) the decisions made by the model under a range of facility costs; (b) the delegation and manpower utilization resulting from a range of PE to MD salary ratios; and

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215 (c) the delegation and manpower utilization resulting from several indirect supervision guidelines. In addition the behavior of the model was investigated parametrically as a function of the integer manpower restrictions, size of the HMO, and under a scarcity of PE's. In each case the analysis indicated that the model performed as one would expect the real system to perform. An Overview of the Results and Conclusions The above results and conclusions were taken explicitly from the first six chapters of the research. However, it is possible to present a concluding overview of the results: (a) a comprehensive and consistent data set was assembled and presented; (b) a new medical classification system for manpower analysis was presented; (c) normative mathematical models were developed and were shown to be a valid representation of an HMO system; (d) the models can be used as an aid to decision makers in planning HMO's either in the early stages of their development or in subsequent staffing decisions; (e) PE's have been shown to be very useful in HMO's for replacing MD's in some specific functions;

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216 (f) PE's will probably have less than a 10 percent effect on the cost of medical care; (g) PE's can be used most effectively in large HMO's; and (h) in general PE's could reduce MD requirements in HMO's by 22-53 percent depending on the specialties and size of the HMO. Areas for Further Research At the outset, there were several areas of HMO planning that were defined to be outside the scope of this research. As the research progressed, several additional areas that are subsidiary to the main direction of the research, but nevertheless important areas, where identified as requiring further research. Some of the more important topics requiring further research are given below. There are four principal areas that were defined as outside the scope of the study. 1. The models are presently capable of decision making for all medical departments, however the specialties were generally excluded from the study not only to make the research more manageable, but also because of the scarcity of data for medical specialties. As HMO's grow in size

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217 the analysis of specialty care will become quite important. 2. Ancillary departments such as laboratory and x-ray were treated as special cost categories while other ancillary services were treated as other expense or as overhead.. These other ancillary services such as pharmacy, physical therapy, family planning, dietary counseling, podiatry, etc., as well as laboratory and x-ray, can be examined in the model as a medical department in the same manner the primary care departments were examined in this research. In high capital areas such as laboratory and x-ray the model is especially suited to aid in a minimum cost analysis. However much more analysis of manpower and technology capabilities in these areas must first be performed. In addition data is sparse for these departments. 3. Dentistry falls within the scope of the models that were developed. Since expanded duties dental auxilliaries of various levels are being proposed it

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218 would seem natural that dental manpower and cost analysis could proceed in a similar manner. What is needed is a dental classification system, delegation analysis, time requirements and cost data in a parallel fashion to the medical analysis in this research. 4. The inpatient portion of the HMO was excluded from this study. Presumably, it could also be included but the model structure would possibly have to be revised to include an inpatient analysis. Here again, the data requirements are of principal concern. 5. There are several possibilities for revisions in the structure of the model that may result in a more accurate representation of the system. For example, the facility cost function was assumed linear in some region about the optimal solution. As more data becomes available it may be possible to develop a more universal facility cost function. Since this function may be nonlinear it would make the models more difficult to solve. Also the productivity was taken as constant for a given level of technology. The produc-

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219 tivity could be modeled as a stochastic function of the patient load, staffing pattern, facility design, etc.. These and other changes in the models are useful additions if they allow the model to answer questions the present models are unable to. However, to make the above changes would require a greater amount of data and kno T .?ledge of how medical care is delivered and would probably require additional solution techniques, more advanced than those presently existing, to solve the resulting models. There were many areas of a subsidiary nature that require further research. Only the major points are listed below. 1. Through the use of the models presented in this research and the medical classification system developed, it is possible to examine manpower training programs as to their potential manpower and cost effect on the system for which the training programs are provided. Thus it may be possible to use the models to aid in the development of training programs.

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220 2. Throughout the research, the need for good data was of constant concern. Essentially, much of the data collected in the medical field is too piecemeal and ill-defined to be of any use in analysis of the medical system. A systematic data collection procedure needs to be developed if HMO and manpower planning is to advance. One useful aspect of models of a system is that they can give an exact definition of the data required to analyze the system. 3. Techniques to evaluate HMO efficiency could be developed using the models to analyze the medical manpower and cost aspects.

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APPENDICES

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APPENDIX A MEDICAL CLASSIFICATION SYSTEMS TABLE A-l Principle Sections of the International Classification of Diseases* I. Infective and Parasitic Diseases II. Neoplasms III. Endocrine, Nutritional, and Metabolic Disorders IV. Diseases of Blood and Blood-Forming Organs V. Mental Disorders VI. Diseases of the Nervous System and Sense Organs VII. Diseases of the Circulatory System VIII. Diseases of the Respiratory System IX. Diseases of the Digestive System X. Diseases of the Genitourinary System XI. Complications of Pregnancy, Childbirth, and Puerperium XII. Diseases of the Skin and Subcutaneous Tissue XIII. Diseases of the Musculoskeletal System and Connective Tissue XIV. Congenital Anomalies XV. Certain Causes of Perinatal Morbidity and Mortality XVI. Symptoms and Ill-Defined Conditions XVII. Accidents, Poisonings, and Violence *Source International Classification of Diseases , Adapted for Use in the U.S., Department of Health, Education and Welfare, Public Health Service Publication No. 1693, 1962. 222

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223 CO > > . QJ E X

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224 TABLE A-3 Major Categories of a Medical Service Classification System for General Practice* SERVICES NUMBER PER 1000 CASES PHYSICAL EXAMINATION Well Child (age 0-1) 40 Well Child (age 1-16) 141 Abbreviated 30 Complete Female 24 Complete 55 Complete with ECG 14 PRENATAL EXAMINATION Routine 42 With Genetic Counseling 14 FIRST VISIT—PREGNANCY 10 BIRTH CONTROL-FEMALE PROBLEM 10 DE SENSITIZATION SHOTS 56 SKIN ALLERGY 30 IMMUNIZATION SORE THROAT SINUSITIS THROMBOPHLEBITIS WARTS HEART DISEASE HYPERTENSION FRACTURES LACERATIONS MUSCLE PAIN BURNS ABCESS WOUND INFECTIONS ARTHRITIS 47 54 OTITIS EXTERNA AND MEDIA 47 30 2 HEMATOMA • 1 REMOVE EAR WAX I 5 14 URINARY INFECTION 4 2 EXOGENOUS OBESITY 21 14 18 50 MUSCLE CONTUSION 13 8 8 8 12 6 ALL OTHER SERVICES 176 *Source Golladay, F.R. , Smith, K.R. , and Miller, M. , "Allied Manpower Strategies: Estimates of the Potential Gains From Efficient Task Delegation," Health Economics Research Center, Report No. 5, U. of Wisconsin, November 1971.

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225 TABLE A-4 Patterns of Medical Care for the Primary Care Specialties* Well child service Infectious childhood disease Physical diagnostic service Prenatal first visit Prenatal other Postpartum service Family Planning Counseling Contraception service Gynecology service Otitis media Sore throat Gastroenteritis Emotional difficulty Upper respiratory infection Urinary tract infection Gastrointestinal upset Muscle or joint discomfort Skin disorder Maintenance service-chronic disease Minor emergency Physical counseling Injection Adult physical exam Follow-up exam or care Heart and arterial disease History Patient preparation *Source "Personnel and Time Requirements for Delivery of Health Care Services," GEOMET, Inc., Report HF-145, September 1972.

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501 513 Chronic Sinusitis 573 600 605 Cystitis 609 226 TABLE A-5 Diagnostic Categories for Which GEOMET Specifications of Care Were PreparedNo. of ICDA Number Name Prototypes 030 Acute or Unspecified Gonorrhea 2 051 Streptococcal Sore Throat 2 087 Chickenpox 1 092 Infectious Hepatitis 2 131 Dermatophytosis 3 240 Hay Fever 2 241 Asthma 4 260 Diabetes Mellitus 3 287 Obesity Not Specified As of Endocrine Origin 2 291 Iron Deficiency Anemias (Hypochromic) 1 293 Anemia of Unspecified Type 3 324 Psychoneurotic Disorders 4 326 Sociopathic Personality Disturbance 4 353 Epilepsy 2 370 Conjunctivitis and Ophthalmia 3 391 Otitis Media 3 420 Arteriosclerotic Heart Disease Including Coronary Disease 4 434 Other and Unspecified Diseases of Heart 7 442 Hypertensive Heart Disease with Arteriolar Nephrosclerosis 2 447 Other Hypertensive Disease 2 450 General Arteriosclerosis 3 470 Acute Nasopharyngitis (Common Cold) 2 472 Acute Pharyngitis 2 473 Acute Tonsillitis _ 2 475 Acute Upper Respiratory Infection of Multiple or Unspecified Sites 3 481 Influenza With Other Respiratory Manifestations and Influenza, Unqualified 3 492 Primary Atypical Pneumonia 3 493 Pneumonia, Other and Unspecified 3 Bronchitis, Unqualified ^ 4 540 Ulcer of Stomach 3 543 Gastritis and Duodenitis 3 560 Hernia of Abdominal Cavity Without Mention of Obstruction 4 571 Gastroenteritis and Colitis, except Ulcerative, Age 4 Weeks and Over ^ Functional Disorders of Intestines 5 Infections of Kidney "J Other Diseases of Urethra and Urinary Tract 3 *Source "Simulation Model for the Evaluation of an Ambulatory Health Care Delivery System," GEOMET Inc., Report No. HF-43, June 1971.

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227 ICDA Number TABLE A-5 Continued Name No. of Prototypes 626 Diseases of Parametrium and Pelvic Peritoneum (Female) 630 Infective Diseases of Uterus, Vagina, and Vulva 634 Disorders of Menstruation 692 Other Cellulitis and Abscess Without Mention of Lymphangitis 695 Impetigo 698 Other Local Infections of Skin and Subcutaneous Tissue 703 Other Dermatitis 714 Diseases of Sweat and Sebaceous Glands 722 Rheumatoid Arthritis (or Polyarthritis) and Allied Conditions 723 Osteoarthritis (Arthrosis) and Allied Conditions 780 Certain Symptoms Referable to Nervous System and Special Senses 782 Symptoms Referable to Cardiovascular and Lymphatic System 783 Symptoms Referable to Respiratory System 785 Symptoms Referable to Abdomen and Lower Gastrointestinal Tract 786 Symptoms Referable to Genitourinary System 787 Symptoms Referable to Limbs and Back 788 Other General Symptoms 789 Abnormal Urinary Constituents of Unspecified Cause 790 Nervousness and Debility 791 Headache 795 Ill-defined and Unknown Causes of Morbidity and Mortality 873 Other and Unspecified Laceration of Face 884 Open Wound of Finger (s) 910 Superficial Injury of Face, Neck, and Scalp 918 Superficial Injury of Other, Multiple, and Unspecified Sites 998 Complications of Surgical Procedures in General Y00 Medical or Special Examination Y00.5 Well-Baby and Child Care Y02 Persons Receiving Prophylactic Inoculation and Vaccination Y06 Prenatal Care Y07 Postpartum 0bseryation_ ____________________ 260/287 Diabetes Mellitus and Obesity Not Specified as of Endocrine Origin 260/447 Diabetes Mellitus and Other Hypertensive Disease 287/447 Obesity Not of Endocrine Origin and Other Hypertensive Disease 391/475 Otitis Media and Acute Upper Respiratory Infection of Multiple or Unspecified_Sites_ _____________

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228 TABLE A6 Sample Listing of Elements of Care for Pediatrics'' DESCRIPTION ELEMENT NUMBER Allergy hypo-sensitization Catheterization, residual Cholangiography, intravenous (I) Cholecystography, oral (I) Conference, patient history Conference with physician Conference with RN, Brief, less than 5 minutes Conference with RN, 5-20 minutes Counseling, dietary Culture, screening for organism, pus Culture, definitive for organism, cellulitis EKG with interpretation & report (I) Exam, comprehensive, preliminary Exam, comprehensive Exam, intermediate, preliminary Exam, intermediate Exam, limited, preliminary Exam, limited Exam, routine physical, preliminary Exam, routine physical Exam, well-baby, preliminary Exam, well-baby Eye discharge Immunization and test check Immunization, DPT Immunization, measles Immunization, tetanus Incision and drainage Injection, intramuscular Intravenous therapy Minor surgery Microscopic exam, initial wet mount, skin scrapings Nasal smear for eosinophiles Packing to control epistaxis Phenylketone, urine Proctoscopy 01 01114 04 09 90650 04 00 74310 03 00 74290 03 09 90104 04 09 90008 00 09 90101 04 09 90102 04 09 90400 04 00 87080 11 00 87090 41 00 93000 01 08 10001 00 08 20001 00 08 10002 00 08 20002 00 08 10003 00 08 20003 00 08 10004 00 08 20004 00 08 10005 00 08 20005 00 00 99000 51 09 90100 04 01 01202 14 01 01202 34 01 01202 44 01 12600 04 01 OHIO 04 09 90700 04 01 12605 04 00 87010 21 01 22130 04 01 20210 04 00 84040 04 01 01125 00 *Source "Personnel and Time Requirements for Delivery of Health Care Services," GEOMET Inc., Report No. HF-145, Sept. 1972

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229 TABLE A-7 Sample Specification of Care' Diagnostic Category 051 Prototype Number 1 of 2 Name Streptococcal Sore Throat Description Moderate Percentage This Prototyp e 95 Element of Care Regional Examination Throat Swab and Culture Prescription, Bulk Pills Exit Interview Visit Number 1 1 1 1 Days to Next Visit 7 to 10 Brief Examination Throat Swab and Culture Exit Interview ^Source "Simulation Model for the Evaluation of an Ambulatory Health Care Delivery System," GEOMET Inc., Report No. HF-43, June 1971.

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230 TABLE A-7 Continued Diagnostic Category 051 Prototype Number 2 of 2 Name Streptococcal Sore Throat Description Severe Percentage This Prototype 5_ Element of Care Regional Examination Throat Swab and Culture Injection, Penicillin Prescription, Bulk Pills Exit Interview Visit Number 1 1 1 1 1 Days to Next Visit 7 to 10 Regional Examination Venous Blood Sample, CBC, Erythrocyte Sed. Rate, Mononucleosis Screening Complete Urinalysis Throat Swab and Culture Prescription, Bulk Pills Exit Interview 5 to 10 Brief Examination Throat Swab and Culture Exit Interview

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231 TABLE A-8 Assignment of Proxy Specifications of Care* ICDA For Which Specifications Not Prepared Specification of Care Assigned ICDA 056 096 214 217 226 243 244 245 292 325 328 354 387 390 396 422 464 467 474 491 527 544 578 Diagnosis Whooping Cough Other Diseases Attributable to Viruses Uterine Fibromyoma Benign Neoplasm (Female Genital Organs) Lipoma Urticaria Allergic Eczema or Dermatitis Other Allergic Disorders Other Anemias of Specified Type Personality Pattern and Trait Disturbance Transient Situational Personality Disorders Migraine Glaucoma Otitis Externa Other Diseases of Ear and Mastoid Process Other Myocardial Degeneration Phlebitis and Thrombophlebitis Other Diseases of Circulatory System Acute Laryngitis and Tracheitis Bronchopneumonia Other Diseases of Lung & Pleural Cavity Disorders of Function of Stomach Other Diseases of Intestines & Peritoneum ICDA 481 481 634 634 Y00 703 703 370 293 324 324 791 Y00 391 391 434 782 782 475 493 501 540 573 Diagnosis Influenza Influenza Disorders of Menstruation Disorders of Menstruation Medical or Special Examination Other Dermatitis Other Dermatitis Conjunctivitis and Ophthalmia Anemia of Unspecified Type Psychoneurotic Disorders Psychoneurotic Disorders Headache Medical or Special Examination Otitis Media Otitis Media Other & Unspecified Diseases of Heart Symptoms Referable to Cardiovascular & Lymphatic System Symptoms Referable to Cardiovascular & Lymphatic System Acute Upper Respiratory Infection Pneumonia, Other & Unspecified Bronchitis, Unqualified Ulcer of Stomach Functional Disorders of Intestines *Source "Simulation Model for the Evaluation of an Ambulatory Health Care Delivery System," GEOMET, Inc., Report HF-43, June 1971.

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232 TABLE A-8 Continued ICDA For Which Specification Not Prepared ICDA Diagnosis 583 603 607 617 633 635 637 650 689 690 691 700 701 706 720 741 781 784 847 851 883 891 912 920 924 Other Diseases of Liver Other Diseases of Kidney & Ureter Urethritis, Nonvenereal Other Diseases of Male Genital Organs Other Diseases of Uterus Menopausal Symptoms Other Diseases of Female Genital Organs Abortion Mastitis & Disorders of Lactation Boil and Carbuncle Cellulitis of Finger and Toe Seborrheic Dermatitis Eczema Psoriasis & Similar Disorders Acute Arthritis Synovitis, Bursitis & Tenosynovitis Other Symptoms Referable to Nervous System & Special Senses Symptoms Referable to Upper Gastrointestinal System Sprains & Strains of Other & Other Unspecified Parts of Back Contusion &. Hematoma of Scalp Open Wound of Hand(s) Open Wound of Knee, Leg & Ankle Superficial Injury of Shoulder & Upper Arm Contusion of Face and Neck Contusion of Elbow, Forearms & Wrist Specification of Care Assigned ICDA 092 600 605 609 634 634 634 Y07 Y07 692 692 703 703 703 722 722 780 785 787 873 884 884 918 918 918 Diagnosis Infectious Hepatitis Infections of Kidney Cystitis Other Diseases of Urethra & Urinary Tract Disorders of Menstruation Disorders of Menstruation Disorders of Menstruation Postpartum Observation Postpartum Observation Other Cellulitis & Abscess Other Cellulitis & Abscess Other Dermatitis Other Dermatitis Other Dermatitis Rheumatoid Arthritis Rheumatoid Arthritis Certain Symptoms Referable to Nervous System & Special Senses Symptoms Referable to Abdomen & Lower Gastrointestinal Tract Symptoms Referable to Limbs & Back Other & Unspecified Laceration of Face Open Wound of Finger(s) Open Wound of Finger(s) Superficial Injury of Other, Multiple & Unspecified Sites Superficial Injury of Other, Multiple & Unspecified Sites Superficial Injury of Other, Multiple & Unspecified Sites

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233 TABLE A-9 Clinical Subgroups in the Kaiser Clinical Behavior Disease Classification System* Preventive services (01) DISEASES Diseases not generally requiring hospitalization Diseases with high emotional component Emotionally produced or aggravated diseases (21) Diseases secondary to social or psychological disorganization (22) Emotional disease (23) Diseases without high emotional component Chronic disease With symptoms Symptoms completely controlled under treatment (31) Symptoms treatable, nonmalignant Systemic or general (41) Internal (CNS, intrathoracic, intraabdominal) (42) Other (43) Obesity (44) Symptoms treatable, malignant Systemic or general (46) Without symptoms (33) Complications of other illnesses (45) Acute disease Microorganism-produced Viral Systemic or general (51) Internal (CNS, intrathoracic, intraabdominal) (52) Other (53) Bacterial Internal (CNS, intrathoracic, intraabdominal) (55) Other (56) Other Internal (CNS, intrathoracic, intraabdominal) (58) Other (59) Non-microorganism-produced Internal (CNS, intrathoracic, intraabdominal) (62) Other (63) Symptoms of undiagnosed disease (71) PREGNANCY Prenatal and postnatal services (81) Complications (82) TRAUMA AND ADVERSE EFFECTS OF EXTERNAL CAUSE Burns and traumatic injuries and adverse effects of chemicals and other external causes Hospitalization not usually required (92) *Source Hurtado, A.V. and Greenlick, M.R. , "A Disease Classification System for Analysis of Medical Care Utilization, with a Note on Symptom Classification," Health Services Research 6, p. 235-250 (1971)

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234 TABLE A-10 Ancillary Task Listing for General Medical Practice* RECEPTION AND RELATED TASKS Make Chart New Patient Patient Check-in Patient Check-out Prepare Hospital List Reception Telephone Calls PRELIMINARY AND POSTPROCESSING TASKS Call Patient from Waiting Room Chief Complaint Diet Counseling Draw Blood Escort Patient to Examining Room Hospital Admission Procedure Nurse Consultation on Telephone Obtain Urine Sample Prepare and Administer Injection Prepare Chart to Call Next Patient Prick Finger Record Blood Pressure Record Temperature Record Weight and Height LABORATORY, X-RAY AND RELATED TASKS Bilirubin Blood Differential Count Blood Sugar Blood Urea Nitrogen Cholesterol DAP Test Diathermy Treatment Globulin Gram Stain Hematocrit Hemoglobin Mononucleosis Test Occult Blood Test Pack Samples Prepare Culture Record EKG Spray Pap Smear Total Protein Uric Acid Urinalysis Visual Examination White Blood Cell Count X-ray *Source Freeman, J., "Manpower Analysis of General Medical Practice," Health Systems Research Division, University of Florida, 1970.

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APPENDIX B PHYSICIAN EXTENDER DELEGATION DATA TABLE B-l OBSTETRICS History Examination Physicians' Willingness To Delegate Activities to a Trained OB/GYN Assistant"** Assistant Sex not Mentioned* 85.7% (including Pap smear)

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236 TABLE B-2 Summary of Tasks for a Physician's Assistant* 1. Receives assigned patients, interviews them for social, family and medical history, noting down patient's chief complaint, description of condition, symptoms, summarizing and reporting salient data, following physician's format. 2. Carries out such administrative details as preparing insurance forms, scheduling patient laboratory tests (obtaining and reporting results) . 3. Explains and interprets physician's instructions to patient and/or family. 4. Conducts visit, and visits physician's patients in hospital, checking on their condition (questioning and conducting parts of the physical examination as needed) and reporting on their condition (changes) to the physician (memo or phone call) . 5. Conducts full range of physical examination, eliciting and maintaining patient's cooperation throughout (coaching/diverting). 6. Observes and reports on patient's appearance, general condition. 7. Observes and examines patient's body systems, using range of technique and equipment as required, detecting, describing and reporting on anv abnormalities/pathologies. (The analysis is based on the knowledge' and application of criteria for detecting normal /abnormal conditions in each system or part of the system, e.g., metabolic, cardio-respiratory, etc.). The physician's assistant analyzes conditions by applying criteria. 8. The physician's assistant may follow a checklist or other guide in reporting the results of the physical examination to the physician. *Source Powers, L., "The Systems Approach to Functional Job Analysis: Task Analysis of the Physician's Assistant, The Bowman Gray School of Medicine, Wake Forest University, 1970.

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237 TABLE B-2 Continued 9. Performs (or schedules) laboratory tests, procedures on blood, urine, etc., summarizing and reporting results to the physician. 10. Treats patients, administering medication, and helps them in carrying out steps of treatment plan under the direction of a physician. 11. Administers first aid to patients, ranging from treating lacerations which may require simple suturing to prevention of serious bleeding (using tourniquets, tying bleeders, if necessary). 12. Performs triage and critical tasks such as cardio-respiratory resuscitation needed to restore, maintain normal conditions. 13. In emergency situations, when physician is not present, performs life saving tasks exercising own discretion, until physician can be contacted.

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238 TABLE B-3 Survey by Physicians Specialty for Possible Duties of Physician's Assistant* Definition of Possible Duties 1. Take a routine medical history 2. Perform preliminary physical examinations 3. Emergency room procedures (suture lacerations, extracting superficial foreign bodies, changing routine dressings, measurement of venous pressure^ 4. On an emergency basis and until the physician arrives, support vital functions, including cardiopulmonary resuscitation, inhalation therapy, administer intravenous fluids 5. Operate certain diagnostic and therapeutic instruments such as electrocardiographs, respirators, cardiac monitors, and defibrillators 6. Carry out certain laboratory examinations 7. Identify the needs for appropriate laboratory and radiological studies and ordering such studies 8. Perform diagnostic activities, i.e., EKG, pulmonary function tests, audio and visual test, maintenance of patient medical records 9. Conduct well-baby checkups, including injections 10. Cast application and removal 11. Prescribe therapeutic regimen under physician's supervision 12. Monitor health status of chronically ill or postoperative patients through visits to hospitals, home or nursing facility 13. Routine prenatal checkups 14. Uncomplicated or emergency deliveries *Source Borland, B.L. , Williams, F.E. , and Taylor, D. , "A Survey of Attitudes of Physicians on Proper Use of Physician's Assistants," Health Services and Mental Health Administration Health Services Reports 87, p. 467-472 (1972).

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TABLE B-5 Feasible Delegation of Elements of Care 251 Element Code Element Name Delegate OHIO Injection, Intramuscular 01114 Allergy Hypo-Sensitization 01125 Proctoscopy 01202 Immunization, Tetanus 01202 Immunization, Rubella 01202 Immunication, Oral Polio 01202 Immunization, Measles 01202 Immunization, DPT 01204 Vaccination, Smallpox 06065 Scraping for Fungus. 06070 Wood's Glass Examination 10001 Exam, Comprehensive, Preliminary 10002 Exam, Intermediate, Preliminary 10003 Exam, Limited, Preliminary 10004 Exam, Routine Physical, Preliminary 10005 Exam, Well-Baby, Preliminary 10006 Exam, Prenatal, Preliminary 10009 Exam, Postpartum, Preliminary 12600 Incision and Drainage 12605 Minor Surgery 20001 Exam, Comprehensive 20002 Exam, Intermediate 20003 Exam, Limited 20004 Exam, Routine Physical 20005 Exam, Well-Baby 20006 Exam, Prenatal 20009 Exam, Postpartum 20210 Packing To Control Epistaxis 22130 Nasal Smear For Eosinophiles 40000 Conference, Exit Interview 40001 Referral To Hospital, Inpatient Self-Care 40002 Referral To Hospital, Normal Inpatient Care 40003 Referral To Hospital, Intensive Inpatient Care 40004 Referral To Hospital, Emergency Yes Yes No Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Some Initial Initial Yes Yes Yes Yes No Yes Yes Yes No No No Some

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TABLE B-5 Continued 252 Element Code Element Name Delegate 40010 Referral To Dental Clinic 40015 Referral To ENT Specialist 40020 Referral To General Surgeon 40025 Referral To Allergist 40030 Referral To Dermatologist 40035 Referral To Psychiatrist 40040 Referral To Endocrinologist 40045 Referral To Urologist 40050 Referral To Gynecologist 40055 Referral To Physical Therapist 40060 Referral To Orthopedic Specialist 40065 Referral To Nephrologist 40070 Referral To Neurologist 40075 Referral To Ophthalmologist 40080 Referral To Cardiologist 58100 biopsy, Endometrial 70130 X-Ray, Mastoids, Complete and Bilatersl 70220 X-Ray, paranasal Sinuses, Complete (I) 70260 X-Ray, Skull, Complete (I) 71010 X-Ray, Chest, Single View (I) 71020 X-Ray, Chest, Two Views (I) 71030 X-Ray, Chest, 4 Views Min. (I) 74000 X-Ray, Abdomen, Kub (I) 74010 X-Ray, Abdomen, With Oblique or Cone View (I) 74020 X-Ray, Abdomen, Complete (I) 74240 X-Ray, GI Tract, Upper, Without Kub (I) 74245 X-Ray, GI Tract, Upper, With Small Bowel (I) 74270 X-Ray, Colon, Barium Enema (I) 74290 Cholecystography, Oral (I) 74310 Cholangiography, Intravenous (I) 74400 Urography, Excretory, IVP (I) 81040 Urinalysis-Dipstick Only 84040 Phenylketone, Urine 86460 Skin Test, Blastomycosis Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No No No No Yes Yes Yes

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253 TABLE B-5 Continued Element Code Element Name Delegate 86490 Skin Test, Coccidioidomycosis 86510 Skin Test, Histoplasmosis 86580 Skin Test, Tuberculosis, PPD 86585 Skin Test, Tuberculosis, Tine 87010 Microscopic Exam, Initial Wet Mount, Urethra 87080 Culture, Screening For Organism, Pus 87090 Culture, Definitive For Organism, Sputum 87095 Culture + Sensitivity, Urethra Exudate 88100 Cytopathology Smears, Genital Source 88200 Cornification Tests 90008 Conference With Physician 90009 Conference, Family Planning 90100 Immunization and Test Check 90101 Conference With RN, Brief, Less Than 5 Min. 90102 Conference with RN, 5-20 Min. 90103 Conference With RN, 20-45 Min. 90104 Conference, Patient History 90105 Screening 90200 Taking of Blood Pressure, Temperature, Pulse 90201 Taking of Weight, Height 90202 Taking of Temperature 90400 Counseling, Dietary 90450 Counseling, Exercise 90500 Conference With LPN 90601 Wound Care Dressing 90602 Wound Care Removal of Sutures 90603 Wound Care Clean, Suture, Dress 90604 X-Ray of Affected Area, Limbs or Back (I) 90605 Wound Care Clean and Dress 90606 X-Ray of Affected Area, Face (I) 90607 X-Ray of Affected Area, Joints (I) 90650 Catheterization, Residual 90700 Intravenous Therapy 92080 Visual Fields With Medical Interpretation 93000 EKG With Interpretation & Report (I) 99000 Nasal Discharge Yes Yes Yes Yes Exudate Yes Yes Yes No Yes No No No Yes No No No Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No Yes No No Yes Yes No No Yes (I) Interpret

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APPENDIX C PRINCIPAL MODEL INPUTS AND NOMENCLATURE FOR PROBLEM VARIABLES TABLE C-l Names Assigned to Personnel Classes MD PE RN LPN MD & RN MD & PE MD & RN & LPN PE & RN PE & RN & LPN Adult

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255 o o o >< 55 H WHO CJ U O U

PAGE 276

256 8| S o Ph o o u o o o u u uu oiHP cam OO Zft 6h J3 H 3H S3 H H 2 CO M O MO MO O E* <:<:<$ < < < < • M -O 3 0) co h S3 pa ca >i z H s H CO M O MO < < <; < < < < < CO

PAGE 277

257 cu

PAGE 278

TABLE C-3 Principal Input Data Coefficients For The Mathematical Models 258 Variable

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TABLE C-3 Continued 259 Variable

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TABLE C-3 Continued 260 Variable

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APPENDIX D DATA COLLECTION FOR THE INDIANAPOLIS, INDIANA HMO This appendix presents the data that were used in the case history for the Indianapolis HMO. Most of the data used were supplied by the MHC or SHC except where otherwise noted. The key data inputs for use in the model are given below. 1. Specialty referral consists of 22 percent of all office visits.* 2. An age-sex breakdown for the potential users of the HMO is given in Table D-l. Of special note is that approximately 47 percent are under 15 and about 27 percent are female from ages 15-44. TABLE D-l Age-Sex Breakdown for Potential Enrollees in the SHC Under 15

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262 3. A report by Sparer and Andersen (121) listed utilization rates for several HMO's and showed low income groups have a higher utilization reported than the norm. From their report it was noted that the low income group at Group Health of Puget Sound had the most similar demographic characteristics to Table D-l above. The utilization rate for the low income group at Group Health of Puget Sound was 4.66 MD visits plus mid-level or nurse visits. This figure was multiplied by .78 to arrive at 3.64 visits per person per year to Adult Medicine, Pediatrics, and OB/GYN. These visits were then broken down through an age-sex adjustment of Kaiser-Permanente data* to give 1.70, 1.28, and .66 office visits per person per year to adult medicine, pediatrics and OB/GYN, respectively. Thus, the projected visits per year as a function of subscriber number is given in Table D-2 below. 'Personal communication from Dr. M. Greenlick and Ms. Vicky Burnham, Kaiser Health Services Research Center

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TABLE D-2 Projected Visits Per Year For SHC As a Function of Subscriber Level 263 Departments

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264 encounter at $18.76 each. In addition one laboratory test per encounter at $3.85 was estimated. 6. Medical equipment costs were estimated to be $10,000 per FTE MD with a seven year average lifetime to give a yearly cost of $1855 per FTE MD. 7. Medical records and medical supplies were estimated to cost $.51 and $.50 respectively per patient encounter. 8. Drug costs were estimated to be $3.60 per patient encounter. 9. Referral costs for OB/GYN were taken to be $250 plus laboratory and x-ray for maternity and $20 plus laboratory and x-ray for other office visits.

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265 TABLE D-3 Fixed Expenditures at SHC Cost Description Monthly Capitation Average yearbased Full Time ly cost on 5,000 Equivalent or salary Enrollment Administrative and Clerical Administrative Assistant Industrial Engineer Receptionists Financial Interviewer Appointment Scheduler Clerk Medical Records Sub total Community and Ancillary Director Community Services Secretary Community Services Family Planner Chaplain Caseworker Health Educators Charge Nurse Sub total 1. 1. 1. 1. 1. 1. 3^ 9. .4 1. 1. 1. 1. 2. 1. 7.4 15155. 14774. 5482. 6636. 5793. 5793. 16589. 70222.

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REFERENCES 1. Somers, A.R. , Health Care in Transition : Directions for the Future , Chicago: Hospital Research and Education Trust, 1971. 2. "Health Manpower: Perspective 1967," Public Health Service, Department of Health, Education and Welfare, Washington, D.C. , Government Printing Office, 1967. 3. Egeberg, R.O., "Engineers and the Medical Crisis," Proceedings of the IEEE 57, p. 1807-1808 (1969). 4. Garfield, S.R. , "The Delivery of Medical Care," Scientific American 222, p. 15-23 (April 1970). 5. Consumer Price Index , Bureau of Labor Statistics, U.S. Dept. of Labor, Washington, D.C., Government Printing Office, Feb. 1970. 6. Nixon, President Richard M. , "The State of the Union," Washington, D.C., January 22, 1971. 7. Fenderson, D., "A Manpower Evaluation Protocol," Bulletin of the New York Academy of Medicine 48, p. 966-973 (1972). 8. Lashof, Joyce C, "The Neighborhood Health Center: A Model for the Organization of Services," National Health Forum, Meeting the Crisis in Health Care Services in Our Communities, Washington, D.C. , Feb. 23, 1970. 9. Balfe, Bruce E., "A Survey of Group Practice in the United States, 1965," Public Health Reports 84, No. 7, p. 597-604 (1969). 10. "Summary of Discussions at 1970 National Health Forum, Meeting the Crisis of Health Care Services in Our Communities," National Health Forum, Washington, D.C, 1970. 11. Glasgow, J., "Prepaid Group Practice as a National Health Policy: Problems and Perspectives ," Inquiry 9, p. 3-15 (1972). 12. Prussin, J., "This is Prepaid Group Practice Medical Care," paper presented at meeting of Medical Group Management Association, Las Vegas, Nevada on March 6, 1972. 13. Williams, G., "Kaiser: What is It? How Does It Work? Why Does It Work?" Modern Hospital 117 , p. 71 (Feb. 1971). 266

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267 14. Saward, Ernest W. , "Prepaid Group Practice in the Health Crisis," paper presented at National Health Forum, Meeting the Crisis in Health Care Services in Our Communities, Washington, D.C. , Feb. 23, 1970. 15. Kennedy, Sen. Edward M., "National Health Insurance and Health Security, S.4297," Congressional Record , Proceedings and Debates of the 91st Congress, Second Session, Washington, D.C., Government Printing Office, 1970. 16. Nixon, President Richard M. , "Proposals on Health Care Sent to the Congress of the United States," Washington, D.C., Government Printing Office, 1971. 17. Myers, B.A., "Health Maintenance Organizations: Objectives and Issues," Southern Health Bulletin 8, p. 5-11 (Nov. 1971). 18. "Comparison of Major National Health Insurance Proposals," Research and Development Division, Blue Cross Association, June 1971. 19. "Health Maintenance Organization Act of 1971, H.R. 5615 (Congressmen Staggers and Springer) and S. 51182 (Senator Javits) ," Washington, D.C., Government Printing Office, 1971. 20. "Health Maintenance Organization Act of 1971, H.R. 11728 (Congressmen Rogers and Roy)," Washington, D.C, Government Printing Office, 1971. 21. "Health Maintenance Organization and Resources Development Act of 1972, S.3327 (Senator Kennedy)," Washington, D.C, Government Printing Office, 1972. 22. "Hearings before the Subcommittee on Public Health and Environment on the Committee on Interstate and Foreign Commerce," House of Representatives, Ninety-Second Congress, Second Session on H.R. 5615 and H.R. 11728, Washington, D.C, Government Printing Office, April 1972. 23. Rothfield, M.B., "Sensible Surgery for Swelling Medical Costs," Fortune 87, p. 110-119 (April 1973). 24. Ellwood, Paul, "The Health Maintenance Strategy," Health Services and Mental Health Administration, DHEW, Washington, D.C, Government Printing Office, March 1970. 25. "Towards a Comprehensive Health Policy for the 1970' s A White Paper," DHEW, Washington, D.C, Government Printing Office, May 1971. 26. "Resolutions Adopted by the Governing Council of the APHA," American Journal of Public Health 61, p. 2528-2536 (1971).

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268 27. "HMO's As Seen by the AMAAn Analysis," Division of Medical Practice, American Medical Association, Chicago, 111., May 1971. 28. Williams, J.J., "Family Medical Care Under Three Types of Health Insurance," School of Public Health and Administrative Medicine, Columbia University, 1962. 29. "Report of the Medical and Hospital Advisory Council to the Board of Administration of the State Employees Retirement System," Medical and Hospital Advisory Council, State of California, June 1964. 30. "The Kaiser Foundation Medical Care Program," in Report of the National Advisory Commission on Health Manpower , Vol. II , Appendix IV , Washington, D.C., Government Printing Office, Nov. 1967. 31. Somers, A.R. (ed.), The Kaiser-Permanente Medical Care Program : A Symposium , New York: The Commonwealth Fund, 1971. 32. "Manpower Report of the President," The White House, Washington, D.C., Government Printing Office, March 1972. 33. Powers, L. , "The Systems Approach to Functional Job Analysis: Task Analysis of the Physician's Assistant," The Bowman Gray School of Medicine, Wake Forest University, 1970. 34. Adamson, E., "Critical Issues in the Use of Physician Associates and Assistants," American Journal of Public Health 61 , p. 1765-1779 (1971) . 35. Estes, E., "Task Oriented Versus Degree Oriented Training," Military Medicine 134 , p. 386-389 (1969). 36. Breytspark, L. and Pondy, L. , "Sociological Evaluation of the Physician Assistant's Role Relations," Group Practice 18, p. 32-40 (1969). 37. Smith, R.A. , "MEDEX: A Demonstration Program in Primary Medical Care," Northwest Medicine 68, p. 1023-1030 (1969). 38. Silver, H.K. , Ford, L.G. , and Steerly, S.G. , "A Program to Increase Health Care for Children: The Pediatric Nurse Practitioner," Pediatrics 39, p. 750-760 (1967). 39. "Guidelines on Short-Term Continuing Education Programs for Pediatric Nurse Associates, A Joint Statement of the American Nurses' Association and the American Academy of Pediatrics," American Journal of Nursing 71, p. 509-512 (1971) and Pediatrics 47, p. 1075-1079 (1971). 40. Yankauer, A., Tripp, S., Andrews, P., and Connelly, J. P., "The Outcomes and Service Impact of a Pediatric Nurse Practitioner Training Program — Nurse Practitioner Training Outcomes," American Journal of Public Health 62, p. 347-353 (1972).

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269 41. Schiff, D.W. , Fraser, C.H. , and Walters, H.L. , "The Pediatric Nurse Practitioner in the Office of Pediatricians in Private Practice," Pediatrics 44, p. 62-68 (1969). 42. Stearly, S. , Noordenbos, A., and Crouch, V., "Pediatric Nurse Practitioner," American Journal of Nursing 67 , p. 2083 (1967). 43. Record, J.C. , and Cohen, H.R., "The Introduction of Midwifery in a Prepaid Group Practice," American Journal of Public Health 62 , p. 354-360 (1972). 44. "Report on Licensure and Related Health Personnel Credentialing," Department of Health, Education, and Welfare, Publication No. (HSM) 72-11, Washington, D.C., Government Printing Office, June 1971. 45. "Model Legislation Project for Physician's Assistants," Department of Community Health Services, Duke University, June 1970. 46. Willig, Sidney H. , "The Medical Board's Role in Physician Assistancy," Federation Bulletin 58, p. 126-159 and p. 167-201 (1971). 47. Curran, William J., "New Paramedical Personnel — to License or Not to License?" New England Journal of Medicine 282 , p. 1085-1086 (1970). 48. Carlson, R.J., Health Care , Ed. C.C. Havighurst, Dobbs Ferry, New York: Oceana Publications, Inc., 1972. 49. "Certification in Allied Health Professions," National Institutes of Health, Department of Health, Education, and Welfare, Publication No. (NIH) 73-246, Washington, D.C., Government Printing Office, 1971. 50. "State Licensing of Health Occupations," Department of Health, Education, and Welfare, Public Health Service Publication No. 1758, Washington, D.C. , Government Printing Office, October 1967. 51. "American Medical Association. Licensure of Health Occupations," Journal of the American Medical Association 208 , p. 2154-2155 (1969). 52. Golden, A.S., Carlson, D.G., and Harris, B., "Non Physician Family Health Teams for Health Maintenance Organizations," presented at 99th Annual American Public Health Assoc, meeting, October 1971. 53. Sidel, V.W. , "The Feldsher in the U. S.S.R. ," Annals of the New York Academy of Science 166 , p. 957-966 (1969). 54. Sidel, V.W. , "Health Services in China," International Journal of Health Services 2, p. 385-395 (1972). 55. Horn, J., Teamwork for World Health , Ed. G. Wolstenholme and M. O'Connor, London: J. and A. Churchill, 1971.

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270 56. Navarro, V., "Health, Health Services, and Health Planning in Cuba," International Journal of Health Services 2, p. 397-432 (1972). 57. Sidel, V.W. , "The Barefoot Doctors of the Peoples Republic of China," New England Journal of Medicine 286 , p. 918-923 (1972). 58. Adetoro, J.E. , "The Nigerian Medical Auxiliary," Journal of National Medical Association 63, p. 192-196 (1971). 59. Stephen, J., "Lessons from the U.S.S.R.," Practitioner 208 , p. 824831 (1972). 60. Tornig, J., "The Paramedical Courses in Denmark," Danish Medical Bulletin 19, p. 194-197 (1972). 61. Riddick, F.A. , "Use of Allied Health Professionals in Internists' Offices," Archives of Internal Medicine 127 , p. 924-931 (1971). 62. Yankauer, A., "Pediatric Practice in the United States," Pediatrics 45, p. 521-554 (1970). 63. Coye, R.D. and Hansen, M.F., "The Doctor's Assistant," Journal of the American Medical Association 209, p. 529-533 (1969). 64. Estes, E.H. , and Howard, D.R. , "The Physician's Assistant in the University Center," Annals of the New York Academy of Science 166 , p. 903-910 (1969). 65. Silver, H.K. , "The Pediatric Nurse Practitioner and the Child Health Associate: New Types of Health Professionals," Annals of the New York Academy of Science 166 , p. 927-933 (1969). 66. Borland, B.L. , Williams, F.E. , and Taylor, D. , "A Survey of Attitudes of Physicians on Proper Use of Physician's Assistants," HSMHA Health Service Reports 87, p. 467-472 (1972). 67. Fairweather, J.L. , and Kifolo, A., "Improvement of Patient Care in a Solo OB-GYN Practice by Using an RN Physician's Assistant," American Journal of Public Health 62, p. 361-363 (1972). 68. Yankauer, A., Connelly, J. P., and Feldman, J.J. , "Task Performance and Task Delegation in Pediatric Office Practice," American Journal of Public Health 59, p. 1104-1117 (1969). 69. Yankauer, A., Jones, S.H. , Schneider, J., and Hellman, L.M. , "Performance and Delegation of Patient Services by Physicians in Obstetrics-Gynecology," American Journal of Public Health 61 , p. 15451555 (1971). 70. Silver, H.K. , "Use of New Types of Allied Health Personnel," American Journal of Diseased Child 116, p. 486-490 (1968).

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271 71. Braun, J. A., Howard, D.R., and Pondy, L.R., "The Physician's Associate: A Task Analysis," Department of Community Health Sciences, Duke University, November 1971. 72. Freeman, J., "Manpower Analysis for General Medical Practice," Health Systems Research Division, University of Florida, 1970. 73. Golladay, F.L., Smith, K.R., and Miller, M. , "Allied Manpower Strategies: Estimates of the Potential Gains from Efficient Task Delegation," Health Economics Research Center, Report No. 5, University of Wisconsin, November 1971. 74. "Personnel and Time Requirements for Delivery of Health Cafe Services," GEOMET, Inc., Report HF-145, September 1972. 75. Shuman, L.J., Mathematical Models for Health Manpower Planning , Dissertation, Johns Hopkins University, 1969. 76. Shuman, L. J., Young, J. P., and Naddor, E. , "Manpower Mix for Health Services: A Prescriptive Regional Planning Model," Health Services Research 6, p. 103-119 (Summer 1971). 77. Reinhardt, U.E., An Economic Analysis of Physician's Practices , Dissertation, Yale University, 1970. 78. Goldstein, H.M., and Horowitz, M.A., "Paramedical Manpower: A Restructuring of Occupations," paper presented at the 99 th Annual APHA meeting, 1971. 79. Kershaw, J. and McKean, R.N., "Systems Analysis and Education," Research Memorandum at the Rand Corporation, Santa Monica, October 30, 1959. 80. Jewell, W.S., "Optimal Flow through Networks with Gains," Operations Research 10, p. 476-499 (1962). 81. Pondy, L., "Utilization and Productivity of the Duke Physician's Associate," School of Business Administration, Duke University, May 1972. 82. Charnes, A., and Cooper, W.W., "Programming with Linear Fractional Functionals," Naval Research Logistics Quarterly 9, p. 181-186 (1962). 83. Geoffrioan, A.M., "Progress in Large-Scale Optimization," paper presented at 39th National ORSA meeting, May 1971. 84. Hurtado, A.V., and Greenlick, M.R., "A Disease Classification System for Analysis of Medical Care Utilization, with a Note on Symptom Classification," Health Services Research 6, p. 235-250 (1971).

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272 85. Tyroler, H.A. , Conceptual Issues In the Analysis of Medical Care Utilization Behavior , Ed. M.R. Greenlick, Rockville, Md.: National Center for Health Services Research and Development, 1969. 86. International Classification of Diseases , Adapted for use in the U.S. , Department of Health, Education and Welfare, Public Health Service Publication No. 1693, 1962. 87. Current Procedural Terminology , 2nd Ed., Chicago: American Medical Association, 1970. 88. 1969 California Relative Value Studies , 5th Ed., San Francisco: California Medical Association, 1969. 89. "Simulation Model for the Evaluation of an Ambulatory Health Care Delivery System," GEOMET Inc., Report No. HF-43, June 1971. 90. "Simulation of an Ambulatory Health Care Delivery System," GEOMET Inc., Report No. HF-119, June 1972. 91. Schneider, D., Roberts S., and Kilpatrick, K. , "A Systems Analysis of Health Maintenance Organizations," paper presented at the Joint Meeting of ORSA-TTMS-AIEE, Fall 1972. 92. Patterson, P.K. , and Bergman, A.B., Time-Motion Study of Six Pediatric Office Assistants," The New England Journal of Medicine 281 , p. 771774 (1969). 93. Bergman, A.B., Dassel, S.W. , and Wedgexvood, R.J. , "Time-Motion Study of Practicing Pediatricians," Pediatrics 38 , p. 254-263 (1966). 94. Parrish, H.M. , Bishop, F.M. , and Baker, A.S., "Time Study cf General Practitioners' Office Hours," Archives of Environmental Health 14 , p. 892-898 (1967). 95. Bergman, A.B., Probstfield, J.L. , and Wedgewood, R.J. , "Performance Analysis in Pediatric Practice: Preliminary Report," Journal of Medical Education 42, p. 249-253 (1967). 96. Silver, H.K. , Duncan, B. , "Time-Motion Study of Pediatric Nurse Practitioners: Comparison with Regular Office Nurses and Pediatricians," The Journal of Pediatrics 79, p. 331-336 (1971). 97. Feldman, M., "Pediatric Nurse Practitioner's Role in a Large Group Practice," Hospital Topics , p. 38 (March 1972). 98. Parker, H.J. and Delahunt, J.C., "Delegating Tasks to a P. A. : Physician's Reactions," Texas Medical Journal 68, p. 69-79 (Oct. 1972). 99. Perlman, M. , Adams, J., Wolfe, H. , and Shuman, L. , "Methods for Distributing the Costs of Non-Revenue Producing Centers," University of Pittsburgh, August 1972.

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273 100. Berman, H.J. , and Weeks, L.E., The Financial Management of Hos pitals , Ann Arbor, Michigan: Bureau of Hospital Administration, The University of Michigan, 1971. 101. Wagner, H.M. , Principles of Operations Research With Applications to Managerial Decisions , Englewood Cliffs, New Jersey: PrenticeHall Inc. , 1969. 102. Ackoff, R.L. and Sasieni, M.W. , Fundamentals of Operations Re search , New York: John Wiley and Sons, Inc., 1968. 103. Llewellyn, R.W. , Linear Programming , New York: Holt, Rinehart and Winston, 1964. 104. Hadley, G. , Linear Programming , Reading, Massachusetts: AddisonWesley Publishing Company, Inc., 1962. 105. "Introduction to Mathematical Programming System-Extended (MPSX) ," IBM Report No. GH 20-0849-2, March 1972. 106. Gomory, R.E., "An Algorithm for the Mixed Integer Problem," Rand Report P-1885, February 1960. 107. Hu, T.C., Integer Programming and Network Flows , New York: Addison-Wesley, 1969. 108. Lasden, L.S. , Optimization Theory for Large Systems , London: MacMillan Company, 1970. 109. Davis, R.E. , Kendrick, D.A. , and Weitzman, M. , "A Branch and Bound Algorithm for Zero-One Mixed Integer Programming Problems," Oper ations Research 19, p. 1036-1044 (1971). 110. Driebeek, N.J. , "An Algorithm for the Solution of Mixed Integer Programming Problems," Management Science 12 , p. 576-587 (1966). 111. Beale, H.M.L. and Small, R.E., "Mixed Integer Programming by a Branch and Bound Technique," in Proceedings of the IFIP Congress, Ed. W. A. Kalenich, Washington, D.C.: Spartan Press, 1965. See also Beale, E.M.L. , Mathematical Programming in Practice , London: Pittman and Sons, 1968. 112. Revelein, P.R. , "An Extension of the Algorithm of Driebeek for Solving Mixed Integer Programming Problems," Operations Research 16. p. 193-196 (1968). 113. Land, A.H. and Doig, A.G., "An Automatic Method of Solving Discreet Programming Problems," Econometrics 28 , p. 497-520 (1960). 114. Shareshian, R. , "Branch and Bound Mixed Integer Programming," IBM Corporation, April 1967.

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274 115. Naylor, T.H., Balintfy, J.L. , Burdick, D.S., Chu, K. , Computer Simulation Techniques , New York: John Wiley and Sons, Inc., 1966. 116. Wigan, M.R., "The Fitting, Calibration, and Validation of Simulation Models," Simulation , p. 188-192 (1972). 117. Friedman, M., Essays in Positive Economics , Chicago: University of Chicago Press, 1953. 118. Koopmans, T.C. , Three Assays on the State of Economic Science , New York: McGraw-Hill Book Co., 1957. 119. Hermann, C, "Validation Problems in Games and Simulations," Behavioral Science 12, p. 216-230 (1967). 120. Emshoff, J.R. and Sisson, R.L. , Design and Use of Computer Simu lation Models , New York: The Macmillan Company, 1970. 121. Sparer, G. and Andersen, A. , "Utilization and Cost Experience of LowIncome Families in Four Prepaid Group Practice Plans 1970-1971," paper presented at Annual Conference of American Public Health Association, November 1972. 122. "Annual Report of St. Louis Labor Health Institute," St. Louis Labor Health Institute, St. Louis, Missouri, 1972.

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BIOGRAPHICAL SKETCH Donald Paul Schneider was born November 4, 1945 in Streator, Illinois. He received his elementary and secondary education in the Streator school system, graduating from Streator Township High School in June, 1963. He attended the University of Cincinnati from 1963 to 1968 and received a bachelor's degree in aerospace engineering in June, 1968. While a student at the University of Cincinnati, he worked as a student trainee at the Manned Spacecraft Center in Houston, Texas, from 1965 to 1967. After graduating from the University of Cincinnati, Donald Schneider worked for Martin-Marietta Corporation in Orlando, Florida, where he also started a part-time graduate program at the University of Florida. In January, 1970, he enrolled full time in the. Industrial and Systems Engineering Department at the University of Florida and received a Master of Engineering degree from the University of Florida in August, 1970. Donald Schneider was employed by the Health Systems Research Division at the University of Florida from June, 1971, to July, 1972 ? and as an Operations Research Analyst for the National Institutes of Health in Bethesda, Maryland from July, 1972^0 January, 1973. He is presently a faculty member of the General Engineering Department at the University of Illinois. Donald Schneider is a member of Tau Beta Pi honorary engineering 275

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276 society, the American Institute of Industrial Engineers, and the Operations Research Society of America professional societies. He is married to the former Ester Lizcano of Houston, Texas, and is the father of one son, David.

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I certify that I have read_this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ~/u
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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. n Richard C. Reynolds Professor and Chairman of Community Health and Family Medicine This dissertation was submitted to the Dean of the College of Engineering and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August, 1973 Dean, Graduate School

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