Nurse Staffing and Patient Outcomes in the Rehabilitation Setting

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Nurse Staffing and Patient Outcomes in the Rehabilitation Setting Application of Production Function Theory
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1 online resource (12 p.)
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english
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Nason, Mary Margaret
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University of Florida
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Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Nursing Sciences, Nursing
Committee Chair:
NEFF,DONNA C
Committee Co-Chair:
AHN,HYO-CHOL
Committee Members:
GREGG,ANDREA C
HARMAN,JEFFREY SCOTT

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Subjects / Keywords:
fim -- nurse -- nursing -- outcomes -- rehabilitation -- staffing
Nursing -- Dissertations, Academic -- UF
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Nursing Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
As the United States (US) experienced a sustained nursing shortage, health care policy makers and health care administrators, legislators, and researchers increasingly focused on minimum nurse staffing standards, cost of nursing care, and the relationship between nurse staffing and patient outcomes. A model for nurse staffing that encourages both cost efficiency and outcome effectiveness is elusive. One approach is to use a production function to examine the relationship between nurse staffing and patient outcomes. Production function relationships are used extensively in business to determine a range of resources needed to produce a quality product. There is a paucity of research investigating the impact of nurse staffing on patient outcomes in the rehabilitation setting. Therefore, the specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting . Nurse staffing Registered Nurses (RNs), Non- RNs (Licensed Practical Nurses and Nursing Assistants), total nursing staff, and skill mix (RN Proportion and non-RNs) and its relationship with patient outcomes measured as length of stay (LOS) and functional independence (FIM) change was examined utilizing hierarchical linear modeling. This study was a secondary analysis of a parent study, Nurse Staffing and Patient Outcomes in Inpatient Rehabilitation Setting (Nelson, et. al, 2007). The hypothesis that there is a nonlinear relationship between RN HPPD and Non-RN HPPD with patient outcomes of LOS and FIM change is supported. Both HPPD estimates indicate that the relationships to LOS and FIM change direction. Therefore, the nature of the curvilinear relationship of nurse staffing and patient outcomes approximated a model of production function and diminishing returns. This study adds to the growing body of knowledge of nurse staffing and patient outcomes in the rehabilitation setting. This study provides further evidence that nurse staffing and patient outcomes have both a floor and a ceiling. These are both inflection points at which quality and efficiency are sacrificed. Further research is imperative to provide leaders in health care the ability to generate data-driven and evidence based practice decisions for optimal quality and efficiency.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Mary Margaret Nason.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: NEFF,DONNA C.
Local:
Co-adviser: AHN,HYO-CHOL.

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UFE0046647:00001


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1 NURSE STAFFING AND P ATIENT OUTCOMES IN T HE REHABILITATION SE TTING: APPLICATION OF PRODU CTION FUNCTION THEOR Y By MARY MARGARET NASON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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2 2014 Mary Margaret Nason

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3 This document is dedicated to sagacious and pertinacious advocates for nurses and those entrusted to their care.

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4 ACKNOWLEDGMENTS I thank my committee, Dr. Donna Neff, Dr. Andrea Gregg, Dr. Brian Ahn and Dr. Jeffery Harman. I am eternally grateful for my chair, Dr. Neff. Her mentoring and stalwart support got me through more trials in my doctoral journey than I had ever imagined. I am thankful for Dr. C. Garvan and Dr. K. Bloom for t he i r statistical help. I am particularly thankful for Dr. Niccie McKay, from the College of Health Services Research, Management nurses and others I am blessed with an amazing family. David have never left me and provided hope in times when none seemed in sight. Nina editing skills are the best and I am thankful for the love and support through this entire journey. Finally, I express my deepest gratitude to my Spirit Family

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRACT ................................ ................................ ................................ ................................ ..... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 11 Problem Statement ................................ ................................ ................................ .................. 11 Purpose ................................ ................................ ................................ ................................ ... 11 Variables ................................ ................................ ................................ ................................ 11 Background and Significance ................................ ................................ ................................ 12 Nur sing Home and Acute Care ................................ ................................ ........................ 14 Rehabilitation ................................ ................................ ................................ .................. 14 Nurse Staffing ................................ ................................ ................................ .................. 15 Theoretical Framework ................................ ................................ ................................ ........... 16 2 REVIEW OF THE LITERATURE ................................ ................................ ........................ 19 Purpose ................................ ................................ ................................ ................................ ... 19 Production Function Theory ................................ ................................ ................................ ... 19 Nurse Staffing ................................ ................................ ................................ ......................... 23 Acute Care ................................ ................................ ................................ ....................... 24 Long Term Care ................................ ................................ ................................ .............. 25 Rehabilitation ................................ ................................ ................................ .................. 26 Outcomes ................................ ................................ ................................ ................................ 27 Length of Stay ................................ ................................ ................................ ................. 27 Functional In dependence Measure ................................ ................................ .................. 28 3 METHODOLOGY ................................ ................................ ................................ ................. 31 Purpose ................................ ................................ ................................ ................................ ... 31 Hypothesis ................................ ................................ ................................ .............................. 31 Design ................................ ................................ ................................ ................................ ..... 31 Production Function ................................ ................................ ................................ ................ 32 Total Product ................................ ................................ ................................ ................... 32 Marginal Product ................................ ................................ ................................ ............. 33 Diminishing Marginal Returns ................................ ................................ ........................ 33 Production Function and Nurse Staffing ................................ ................................ ......... 34 Empirical Specification ................................ ................................ ................................ ... 35

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6 Procedure Methods ................................ ................................ ................................ ................. 35 Data ................................ ................................ ................................ ................................ ......... 36 Var iables ................................ ................................ ................................ ................................ 36 Predictor Variables ................................ ................................ ................................ .......... 37 Dependent Variables ................................ ................................ ................................ ....... 38 Length of stay ................................ ................................ ................................ ........... 38 Functional Independence Measure ................................ ................................ ........... 38 Patient Level Characteristics ................................ ................................ ........................... 39 Facility Level Characteristics ................................ ................................ .......................... 39 Data Analysis ................................ ................................ ................................ .......................... 39 4 RESULTS ................................ ................................ ................................ ............................... 48 Purpose ................................ ................................ ................................ ................................ ... 48 Description of Sample ................................ ................................ ................................ ............ 48 Nurse Staffing Characteristics ................................ ................................ ......................... 48 Patient Outcomes ................................ ................................ ................................ ............. 48 Length of stay ................................ ................................ ................................ ........... 48 ................................ ................................ ................................ ........... 49 Patient Characteristics ................................ ................................ ................................ ..... 49 Facility Characteristics ................................ ................................ ................................ .... 49 Hierarchical Linear Modeling Results ................................ ................................ .................... 50 Nurse Staffing and Patient Outcomes ................................ ................................ .............. 50 Explanatory Variables and Patient Outcomes: Length of Stay ................................ ....... 50 ................................ ....... 51 Production Function ................................ ................................ ................................ ........ 51 Length of stay ................................ ................................ ................................ ........... 51 ................................ ................................ ................................ ........... 52 5 DISCUSSION AND IMPLICATIONS ................................ ................................ .................. 57 Purpose ................................ ................................ ................................ ................................ ... 57 D iscussion ................................ ................................ ................................ ............................... 57 Production Function ................................ ................................ ................................ ........ 57 ................................ ................................ ................................ ................. 59 Length of Stay ................................ ................................ ................................ ................. 60 Limitations ................................ ................................ ................................ .............................. 61 Implica tions ................................ ................................ ................................ ............................ 62 Implications for Nursing Practice ................................ ................................ .................... 62 Implications for Theory ................................ ................................ ................................ ... 63 Implications for Future Research ................................ ................................ .................... 63 Conclusions ................................ ................................ ................................ ............................. 64 REFERENCES ................................ ................................ ................................ .............................. 66 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ......... 73

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7 LIST OF TABLES Table page 3 1 Stages of total product. ................................ ................................ ................................ ...... 44 3 2 Stages of marginal product. ................................ ................................ ............................... 44 3 3 Study variables and operational definitions. ................................ ................................ ...... 45 3 4 Study variables, data sources, values, and measures. ................................ ........................ 46 3 5 Hierarchical Linear Models. ................................ ................................ .............................. 47 4 1 53 4 2 Results from Hierarchical Linear Models for nurse staffing, length of stay, and ................................ ................................ ................................ ................... 54 4 3 Results from Hierarchical Linear Models for Length of Stay. ................................ .......... 55 4 4 ................................ ........... 56

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8 LIST OF FIGURES Figure page 3 1 Model of Production Function. ................................ ................................ .......................... 44

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9 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NURSE STAFFING AND PATIENT OUTCOMES IN THE REHABILITATION SETTING: APPLICATION OF PRODUCTION FUNCTION THEORY By Mary Mar garet Nason May 2014 Chair: Donna Felber Neff Major: Nursing Sciences As the United States (US) experienced a sustained nursing shortage health care policy makers and health care administrators, legislators, and researchers increasingly focused on mi nimum nurse staffing standards, cost of nursing care, and the relationship between nurse staffing and patient outcomes. A model for nurse staffing that encourages both cost efficiency and outcome effectiveness is elusive. One approach is to use a producti on function to examine the relationship between nurse staffing and patient outcomes. Production function relationships are used extensively in business to determine a range of resources needed to produce a quality product. There is a paucity of research i nvestigating the impact of nurse staffing on patient outcomes in the rehabilitation setting. The refore the specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outc omes in the inpatient rehabilitation setting Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed Practical Nurses and Nursing Assistants), total nursing staff, and skill mix ( RN Proportion and non RNs) ] and its relationship with patient outcomes measured as length of was examined utilizing hierarchical linear modeling This study was a secondary analysis of a parent study Nurse Staffing and Patient Outcomes in Inpatient Rehabilitation Setting ( Nelson, et al 2007).

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10 The hypothesis that there is a nonlinear relationship between RN HPPD and Non RN HPPD with patient outcomes of LOS and is supported. B oth HPPD estimates indicate that the relationships to LOS and FIM change direction. Therefore, the nature of the curvilinear relationship of nurse staffing and patient outcomes approximated a model of production function and diminishing returns. This study adds to the growing body of knowledge of nurse staffing and patient out comes in the rehabilitation setting This study provides further evidence that nurse staffing and patient and efficiency are sacrificed. Further research is i mperative to provide leaders in health care the ability to generate data driven and evidence based practice decisions for optimal quality and efficiency

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11 CHAPTER 1 INTRODUCTION Problem Statement As the United States (US) experienced a sustained nursing shortage; attention to healthcare reform from health care administrators, legislators, and researchers increasingly focused on minimum nurse staffing standards, cost of nursing care, and the relationship between nurse staffing and patien t outcomes. Despite this widespread attention, an efficient model for nurse staffing that is both cost efficient and outcome effective has proved to be elusive. Production function relationships are used extensively in business firms to determine a range o f resources needed to produce a product at acceptable cost and quality. There is a small body of research that suggests that a production function relationship between nurse staffing and patient outcomes may be plausible. In Chapter 1 the purpose, th e background and significance related to the phenomena of focus and theoretical framework will be discussed. Purpose The specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed Practical Nurses and Nursing Assistants), total nursing staff, and skill mix ( RN Proportion and non RNs) ] and its relationship with pat ient outcomes measured as length of stay (LOS) and functional was examined Variables The predictor variables are nurse staffing levels. The predictor variables are further delineated as staffing levels of Registered Nurse hours per patient day (RN HPPD), Non RN

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12 (THPPD), and skill mix ( RN Proportion and non RNs). The depe ndent variables are patient outcomes. Patient outcomes are measured in two ways in this study: Length of stay (LOS) and and calculated from the total Functional Independenc e Measure score on discharge and total Background and Significance Before the interest in medical errors was brought to the forefront in the Institute of To Err is Human: Building a Safer Health System (1999), nurses in the United States (US) reported that cost cutting and hospital redesign initiatives by hospitals reduced nurse staffing to unsafe levels (Shindul Rothschild, Berry, & Long Middleton, 1996). Subsequently, Congress expressed its concern f or the state of health care by mandating the Institute of Medicine to study nurse staffing adequacy in hospitals and nursing homes (Institute of Medicine, 1996). The IOM galvanized the importance of improving the work environment of in safe patient care in its third report, Keeping Patients Safe: Transforming the Work Environment of Nurses (2004). such as mortality) to nurse sensitive outcomes (decr eased length of stay or improvement of functional status) occurred when the American Nurses Association (ANA) published its pivotal study: Outcomes (1997). The ANA est these relationships. In reaction to the additional growing concern related to nurse staffing and qu ality of patient care, the American Nurses Association convened a nursing summit of national nursing

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13 organization representatives to develop a strategic and tactical plan. In Nursing Agenda for the Future: A Call to the Nation, (American Nurses Association 2002) evidence based research related to the quality, value, and cost of nursing services was prioritized. The value of nurse staffing to patient outcomes research was emphasized as a primary strategy. In testimony to the US Senate, the U.S. General Ac counting Office (2001) testimony united the concern to evaluate the efficiency of nursing practice, within the context of eroding resources. It also proactively and empirically addressed the impact of the range of nursing care hours at the bedside for opti mal patient care. Empirically, national and international systematic reviews of nursing and health services research have demonstrated that identifying the impact of nurse staffing to patient outcomes is paramount to support administrative, fiscal, and pol itical decisions regarding a safe and optimal care environment (Kane, Shamliyan, Mueller, Duval, & Wilt, 2007; Lang, Hodge, Olsen, Romano, & Kravitz, 2004; Lankshear, Sheldon, & Maynard, 2005) In spite of the progress made with health services and nursing researchers providing cogent data to inform evidence based decision making, the current political and fiscal focus on healthcare reform threatens to further erode the core of patient care. Garnered by the work produced until 2008, the IOM and the Robert W ood Johnson Foundation (RWJF), recognizing nursing as the largest portion of the US healthcare workforce, collaboratively initiated an investigation to assess and make recommendations to transform the future of nursing. Pivotal recommendations charged key stakeholders to expand opportunities for the conduction of research to improve practice environments, improve health outcomes, and reflect the contributions of nurses related to quality of care. More prescriptive recommendations were made related to the da ta collection for workforce requirements, including projecting for

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14 nursing workforce requirements by role, skill mix, region and demographics (The Institute Of Medicine, 2010, p. 6). Nursing Home and Acute Care Within federal mandates as early as 1987, a s part of the Omnibus Budget Reconciliation Act (OBRA), the federal Nursing Home Reform Act (NHRA) set minimum staffing levels for registered nurses (RNs) and licensed practical nurses (LPNs) and minimum training ides (NAs) in the nursing home setting. California lead the country in 1999 by establishing state mandates for minimum nurse patient ratios in acute care (Coffman, Seago, & Spetz, 2002). In response to the need for empirical data to support policy and ope rational decision making regarding these and subsequent mandates, research Although the volume of research in the nursing home setting and acute care setting is conclusions is the inconsistency of the data. Health care settings utilize a variety of software packages and manual systems to capture staffing and patient outcom e data. This has led to complicating this scenario is the varied and sometimes interchangeable use of the definitions and comparability and generalizability of the results. Rehabilitation The rehabilitation setting mirrors the circumstances discussed in the nursing home setting previously. Federally mandated staffing standar ds were implemented without empirical evidence to support the standards. Similar to the nursing home setting, a prospective payment system was implemented for the rehabilitation industry in January 2002. This system was established by the

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15 Centers for Medic are and Medicaid Services (CMS, 201 2 ) and was based on a patient classification system that was generated by research from the RAND Corporation. This patient classification system uses an Inpatient Rehabilitation Facility Patient Assessment Tool that is ba in the review of literature and methodology in Chapters 2 and 3 Prior to the work of Nelson et al. (2007) there were no published studies examining nurse staff ing and patient outcomes in the rehabilitation setting. A collaborative research study between the Uniform Data Systems (UDS), the Association of Rehabilitation Nurse (ARN) and the Veterans Health Administration was convened to investigate the relationshi p between nurse staffing and patient outcomes in inpatient rehabilitation settings (Nelson, et. al, 2007). This secondary analysis elucidates the production function of quality and nurse staffing as utilized in previous studies. More specifically, it adds to the gap in the literature related to the impact of nurse staffing in the rehabilitation setting on patient outcomes. Nurse Staffing There remains a critical lack of coherence in the definitions of what constitutes nurse staffing. In their reviews of n ational and international nurse staffing and outcomes research evidence, analysts all cited the lack of clear operational definitions of nurse staffing and inconsistencies in defining healthcare personnel as a concern (Heinz, 2004; Lang, Hodge, Olsen, Roma no & Kravitz, 2004; Kane, Shamiliyan, Mueller, & Wilt, 2007; Lankshear, Sheldon, & Maynard, 2005; Spetz, Donaldson, Aydin, & Brown, 2008; Unruh, 2008; Unruh & Zhang, 2012). Deepening the concern is emerging evidence that different nurse staffing measures c hange the association with patient outcomes (Kane et al., 2007, p. 1199). Despite the concerns, Spetz et al. (2008) concluded that recommending a single measurement strategy for studies of nurse staffing was not possible. These authors noted the constrai nts of data availability as a

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16 limitation. Further, the utilization of nursing personnel based on skill set and patient care need varies with health care settings. Theoretical Framework The environment of health care reform threatens the scarce and valued resource of nurses as both human and knowledge capital. Understanding the relationship between nurse staffing and patient outcomes will assist organizations to optimize this critical resource. The utilization of production function theory will provide a co nceptual framework for this study and elucidate the key factors that drive nurse staffing for patient outcomes in the inpatient rehabilitation setting. In spite of healthcare pressures and legislation to implement minimum staffing ratios, there remains a gap in the research providing health care administrators standards to execute previously. Given the inputs (staffing resources), as well as the outputs (patient, financia l, and profit outcomes) of health care organizations, it is a logical step to refine the approach of this research to incorporate an econometric methodology. Basic microeconomics principles dictate that a firm must decide on the combination of inputs to pr oduce its outputs, recognizing its constraints (Nicholson, 1978). Further, economic theory explicates that for any set of inputs, the production function is defined as the maximal realizable output or full range of outcomes (Shephard, 1970). Production fu nction, a fundamental economic theory, describes how a firm transforms resources (productive inputs) into outputs (goods, services to be sold to consumers). Decisions made by a firm related to input efficiency is correlated with outcome efficiency. Early s tudies of efficiency and productivity within the health care arena most commonly addressed cost and financial performance of hospitals (Bazzoli, Chan, Shortell, & D'Annouo, 2000; Garber, 1984; Granneman, Brown, & Pauly 1986). Later, Hendrix and Foreman (20 01) clearly describe the

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17 utilization of production function theory in decision making related to staffing and the production and supply of patient care in the long term care setting. They utilized production staffing level whereby quality is optimized, (Hendrix & Foreman, 2001, p. 164). A fundamental component of production function theory is the law of diminishing return s, also known as the principle of diminishing marginal productivity. This key economic law states that if one input in the production of a commodity is increased while all other inputs are held fixed, a maximum point will eventually be reached at which add itions of the input yield progressively smaller, or diminishing, increases in output. (Nicholson, 1995). Further, economists have extended the application of the principle of diminishing marginal productivity to include a point of minimum productivity wher e productivity and efficiency is decreased, sometimes to the point of inferior or useless product (Nicholson, 1978). Zhang, Unruh, Liu, and Wan (2006) hypothesized that there may be a production function relationship between nurse staffing levels and skill mix in nursing homes, such that an acceptable level of quality outcomes can be achieved within a range of minimum and maximum staffing They concluded that productio resources (productive inputs) are transformed into outputs. Nicholson and Snyder (2008) present production function as a statistical model formally expressed as: q = f ( k, l, ), where q represents the output: amount of product or goods during a period, and k, l, m represent the

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18 variables that affect the production process. Applicati on of production function as a statistical model is explicated in Chapter 3, Methods. While research in both nursing home and acute care settings demonstrated that increased levels of nursing staff have achieved improved outcomes; this approach has support ed the data do not assist health care administrators in determining standards that optimize both staffing and patient outcomes. This is further complicated by the influences of declining resources related to the nursing shortage, legislation, financial constraints, and profit incentives. As evidenced by the aforementioned research studies, nurse staffing levels and staffing skill mix are dynamics influenced by mult iple variables. Thus, managing care to achieve acceptable patient outcomes and safety is a challenge for nurse and health care administrators. identified relationship with improved patient outcomes. Limited studies have investigated the thresholds of staffing to achieve desired patient outcomes (Lang, Hodge, Olson, Romano, & Kravitz 2004; Lankshear, Sheldon, & Maynard 2005). Discerning if an ideal range of staffing leve ls and mix exists would support the reliability for staffing decisions to incorporate and influence patient outcomes.

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19 CHAPTER 2 REVIEW OF THE LITERATURE Purpose The specific aim of this study was to apply production function theory to examine the nature o f the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed Practical Nurses and Nursing Assistants), total nursing staff, and skill mix ( RN Proportio n and non RNs) ] and its relationship with patient outcomes measured as length of stay (LOS) and functional was examined In C hapter 2 the review of literature related to the theory and variables will be discussed. Production Function Theory Production Function, a fundamental economic theory, states that the decisions made by a firm related to input efficiency is correlated with outcome efficiency. Early s tudies of efficiency and productivity within the health care arena most commonly addressed cost and financial performance of hospitals (Bazzoli, Chan, Shortell, & D'Annouo, 2000; Garber, Fuchs & Silverman, 1984; Granneman, Brown, & Pauly 1986). Later, thresholds for optimal staffing levels were identified in the study conduct ed by Abt Associates (Abt Associates, 2001). In their report to Congress, staffing levels below the threshold demonstrated a negative impact on the quality of care and those above the threshold demonstrated no significant impact on quality outcomes. Leadi ng the foray to incorporate economic theory, health services, and nursing research, are two studies that clearly link the theoretical framework of production function theory to research and conclusions to support the relationship between optimized maximum and minimum staffing resource allocation and optimal patient outcomes (Hendrix & Foreman, 2001;

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20 ptimal care. Hendrix and Foreman (2001) were among the first to utilize production function theory in the health care setting related to nurse staffing. Their study is the most frequently cited in subsequent studies, establishing their research as a semin al work in this area. They clearly describe the utilization of production function theory in decision making related to staffing and the production and supply of patient care in the long term care setting. This study was a secondary analysis of two nation al data sets commonly utilized in health services research related to nursing homes: Area Resource File (ARF) and the Online Survey Certification and optimum staffi ng level whereby quality is optimized, personnel are conserved, and public burden previous studies had generally found that increased nurse staffing improved patient out comes; the results of this study supported the theoretical model and the concept of diminishing returns. Zhang, Unruh, Liu, and Wan (2006) utilized the theory of production function in their research to model the relationship between nurse staffing and qua lity in nursing homes. They sought to empirically identify minimum nurse staffing levels to achieve reasonable quality and efficiency. According to production function theory, the inputs in this study were operationally defined as RN hours per patient day, Licensed Practical Nurses (LPN)/Licensed Vocational Nurses (LVN) hours per resident day, NA hours per resident day, total licensed staff (RN + LPN/LVN) hours per resident day, and total nurse (RN + LPN/LVN + NA + administrator) hours per resident day. Th e output was operationally defined as a researcher generated quality

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21 index based on the OSCAR measures of the presence of indwelling catheters, pressure sores, physical restraints, and a calculated weight for incidence rate. Zhang and colleagues (2006) rec ognized that the most efficient production occurs within the region of decreasing marginal returns to labor. They hypothesized that the desired staffing point (unit of input) to be within the area of diminishing marginal returns in relationship to quality improvement and efficiency (outputs). They defined the ranges of quality improvement within the area at which quality is still improving and efficiency to be where returns to additional staffing are still positive. The minimum point of operation was deter und diminishing marginal returns to nursing labor in relationship to quality. Although production function theory was not specified, the results of subsequent studies have revealed a nonlinear relationship between nurse staffing and patient outcomes. Commi ssioned by the Centers for Medicare & Medicaid Services (CMS) under the Omnibus Budget and Reconciliation Act of 1990, Abt Associates, Inc. (2001) studied the appropriateness of establishing minimum nurse staffing standards in long term care. The report co ntends that RN, LPN, and NA staffing improves quality to a threshold where there is no further significant improvement. Zhang and Grabowski (2004) purported a nonlinear relationship between nursing s of staffing may have a strong influence (Zhang & Grabowski, p. 19).

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22 Mark, Harless, McCue and Xu (2004), in their longitudinal study of 422 hospitals, conc unconditionally (p. 279) to the point of marginal return. Staffing increases in the lowest staffed 25% of hospitals showed the largest improvement in patient outcomes. Conversely, increases i n staff in the best 25% of hospitals (mean 8.9 hours per patient day) demonstrated marginal returns, and deterioration in some outcomes. With findings consistent with Zhang and Grabowski (2004), their study provides some of the most compelling evidence tha t a production function for nurse staffing and patient outcomes exists. An a priori assumption of Nelson and colleagues in their rehabilitation study was that a linear relationship existed between nurse staffing and patient outcomes (Nelson, et. al, 2007 ). However, their findings suggest a non linear relationship between nurse staffing and patient outcomes. Their findings were consistent with those studies conducted in long term care settings a production function relationship explained the diminishing returns of increased nurse staffing on patient outcomes (Hendrix & Foreman, 2001; Zhang, Unruh, Liu & Wan, 2006). Statistically and clinically significant associations between nurse staffing and patient outcomes were identified in the international system atic review by Lankshear, Sheldon & returns to increased RN level s and skill mix has more face validity than the linear relationship p. 172 ). Further, the systematic review and analysis of Kane and research team (2007) were consistent with identifying a curvilinear association between staffing and outcomes.

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23 Pallas (2009) studied the effects of nurse staffing and work environment variables on patient outcomes in 24 Canadian cardiac and cardiovascular in patient units. The y sought to test the Patient C are Delivery Model a conceptual model which emphasizes th e multiple facto r s influencing patient outcomes They hypothesized that staffing levels and patient outcomes wer e nonlinear. The results demonstrate d that patient knowledge, status and behavior improved as staffing levels increased then changed direction with a pattern of diminishing marginal return. The recognition by researchers that a curvilinear relationship between nurse staffing and patient ou tcomes may exist has evolved over time. In addition, it has been demonstrated in a variety of health care settings. The application of production function theory becomes a logical progression of this area of health services research. Nurse Staffing Several early studies used large multi institutional databases to examine the effects of nurse staffing and mortality along with other characteristics. Three found that higher RN proportion was associated with lower mortality rates (Aiken, Smith, & Lake, 1 994; Hartz et al., 1989; Flood, Ewy, Scott, Forrest, & Brown, 1976). Three additional studies found no statistically significant relationships between nurse staffing and mortality (Al Hider & Wan, 1991; Shortell & Hughes, 1988; Shortell et al., 1994). The measures of nurse staffing and setting varied from study to study. In their later study, Shortell and colleagues (1994) utilized data directly from intensive care units. Unruh (2008), in her literature review of nurse staffing and patient, nurse, and fin ancial outcomes, noted improved research methodologies. Recent studies continue to support that lower nurse to patient ratios (higher RN staffing) were associated with lower mortality (Aiken, Clarke, Sloane, Lake, and Cheney, 2008; Aiken et al., 2010; Nee dleman et al., 2011).

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24 Acute Care Unruh (2008) conducted a literature review of research exploring the relationship of nurse staffing and patient outcomes in the hospital setting. Of the 45 studies conducted in the United States, she focused on 21 studies c onducted since 2002. Her rationale includes the issues presented in the critique above methodological issues have improved over time Furthermore 2002 was a considered a p. 65 ). Aiken et al. (2002) examined patient nurse ratios and found that each additional patient in complications. In their landmark multidisciplinary study, nursing administration researchers collaborated wit h public health researchers to quantify and elucidate nurse staffing levels and the quality of care in hospitals (Needleman, Buerhaus, Mattke, Stewart, & Zelevinsky, 2002). The researchers found that a higher proportion of hours of nursing care provided by registered nurses and a greater number of hours of care by RNs per day are associated with better care for hospitalized patients. Patient outcomes of interest were urinary tract infection, pneumonia, LOS, upper gastrointestinal bleeding and shock in medic al patients and failure to rescue for major surgery patients. These studies are considered seminal works for the utilization of patient outcomes that are considered specifically sensitive to nursing care. Most subsequent studies also utilized hours per pat ient day and/or nurse to patient ratios. Some studies also addressed the concept of skill mix or proportion of RN to non RN staffing, finding that higher RN proportion resulted in improved patient outcomes (Cho, Katfian, Barauskas, and Smith, 2003; Hall et al., 2003 ; Needleman, Buerhaus, Mattke, Stewart, & Zelevinsky, 2002 ; Tourangeau, Giovanetti, Tu, & Wood, 2002; Unruh, 2003). Cho et al. (2003) found that RN proportion significantly reduced pneumonia such that a 10% increase in RN proportion resulted in a 9.5% reduction in pneumonia. Similarly, c onsistent with Needleman et

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25 al. (2002), Unruh (2003) reported that both higher numbers and proportion of licensed nurses is statistically related to lower incidenc e of adverse events. This study also supported th at an increase in RN proportion significantly reduces pneumonia. A richer RN skill mix was related to a lower 30 day mortality rate for patients with the primary diagnosis of acute myocardial infarction, stroke, pneumonia or septicemia in Canadian hospita ls (Tourangeau et al. 2002). Lang et al. (2004) concluded that the literature offers little support for specific minimum nurse patient ratios in hospitals and recommends future research include skill mix and case mix adjustment as important variables. To that point, this study is the first to examine the production function relationship between nurse staffing, including skill mix (RN proportion) and patient outcomes. Additionally, case mix adjustment utilizing rehabilitation impairme nt category (RIC) grou ps further strengthens this study. Long Term Care Two studies of nurse staffing in the nursing home setting utilized production function as the underlying theoretical model. Hendrix and Foreman (2001) examined the number and mix of RNs, LPNs, and NAs in relation to the prevalence and severity of decubitus ulcers as a measure of patient outcome and quality. The results suggest that the number of RNs and NAs reduces the cost of decubitus care, while LPNs tended to increase the cost. These results underscore the importance of clearly defining the various staffing levels of care in the study setting. Additionally, the results also supported that increasing levels of nursing staff only continued to improve outcomes to a point. In doing so, this study was among the first to elucidate that nurse staffing and patient outcomes were functions of marginal productivity and diminishing marginal returns. Zhang, Unruh, Liu, and Wan (2006) utilized the theory of production function in their research to model the relation ship between nurse staffing and a quality index generated from the

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26 incidence rates of indwelling catheters, pressure sores, and physical restraints in nursing homes. Nurse staffing measures utilized were RN hours per patient day (sic), LPN hours per reside nt day, NA hours per resident day, total licensed staff per resident day, and total nurse (RN, LPN, NA and administrator) hours per resident day. Nurse staffing levels were positively correlated with the quality index. In their systematic review of studies of nurse staffing and quality in nursing homes, Bostick, Rantz, Flesner, and Riggs (2006) identified three consistent themes in the studies: staffing measures, quality measures, and risk adjustment variables. The authors reported that staffing measures st udied included the ratio of staff to residents and the number of hours per resident day (HPRD). In fact, over half the studies used some measure of the two. Staff mix was also identified as an important variable, although the operational definition was inc onsistent: ratio of licensed to unlicensed staff, number of RN, LPN and NAs per total nursing staff, and others. These staffing measures most closely align the current study of nurse staffing and patient outcomes in the rehabilitation setting. Rehabilita tion The rehabilitation setting mirrors the circumstances discussed in the long term care setting previously: in spite of federal mandated staffing standards, there was no empirical evidence to support these standards. Prior to the work of Nelson and colleagues (2007), to our knowledge, there were no published studies examining nurse staffing, minimum staffing levels, or patient outcomes in the rehabilitation setting. Nelson et al. utilized staff mix, defined as RN Proportion and non RN staff, overall nursing H PPD, RN HPPD, and Non RN staff HPPD as staffing measures. Significant correlations were found between total nursing HPPD and case

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27 the research findings, as the per cent of nurses certified in rehabilitation increased, the case mix adjusted length of stay decreased. Outcomes Length of Stay Mortality and length of stay were common variables in early outcomes research. These data were consistently generated in hosp ital registration and administrative databases and therefore readily available. Several early research studies examined the relationship between hospital registered nurse staffing and length of stay. Increased numbers of RNs and RN hours per patient day d ecreased patient LOS (Flood & Diers, 1988; Needleman, Buerhaus, Mattke, Stewart, & Zelevinsky, 2002; Schultz, Van Servellen, Chang, McNeese Smith, & Waxenberg, 1998). In a systematic review of the effect of hospital nurse staffing and patient outcomes publ ished between 1980 and 2003, authors found that few studies included LOS and no clear recommendations were made (Lang, Hodge, Olsen, Romano & Kravitz, 2004). In a later systematic review Thungjaroenkul, Cummings, and Embleton (2007) encompassed studies pub lished between 1990 and 2006. The effect of hospital nurse staffing on length of stay were variables of interest in 11 studies. Higher ratios of RNs was significantly related to reduced length of stay in hospital settings, including the intensive care uni t (Amaravadi, Dimick, Pronovost, & Lipsett, 2000; Barkell, Killinger, & Schultz, 2002; Lassnigg, Hiesmayr, Bauer, & Haisjackl, 2002; Needleman, Buerhaus, Mattke, Stewart, & Zelevinsky, 2002). RN hours per patient day was also statistically related to LOS ( Cho, Ketefian, Barkauskas, & Smith, 2003). Further, high RN levels may prevent adverse events that cause an increase in length of stay. Cho and colleagues (2003) reported that each adverse event (falls, adverse drug events, pneumonia urinary tract infect ion, wound infection and sepsis) resulted in significantly prolonged length of stay. I ncreases in RN proportion were associated with a

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28 decrease in the probability of pneumonia. Unruh (2003) also attributes higher RN proportion to decrease probability of p neumonia and LOS. These results were corroborated by Kane et al. (2007, p. 1198 ). In their systematic review and meta analysis, an increase by one RN per patient day was associated with a decreased LOS of 24% in ICUs (OR, 0.76; 95% CI, 0.62 0.94) and 31% in surgical patients (OR, 0.69; 95% CI, 0.55 0.86). Synthesizing studies examining the relationship between changes in RN hours per patient day and changes in nurse sensitive outcomes (NSO), Dall, Chen, Seifert, Maddox, and Hogan (2009) reflected the econ omic value of professional nursing. Using 2005 Nationwide Inpatient Sample (NIS) hospital discharge data along with the RN HPPD, and NSO, they concluded that as nurse staffing levels increase, length of stay decreased. The impact of nurse staffing increas es decreased length of stay via mitigation of nosocomial complications. Additionally, the economic value of additional RNs depends on staffing levels, such that, at low staffing levels, incremental additions of RN staff make larger contributions to patient care. As staffing levels improve, the value added is positive, but declining. Although the authors do not explicate it in the presentation of the study, these results underscore that recent research implicates that production function theory applies to nu rse staffing and patient outcomes. Functional Independence Measure The Uniform Data System for Medical Rehabilitation (UDSMR) developed the ivities of daily living. It is intended to stratify the patient on a continuum from a minimum score, which indicates dependence in all areas evaluated, to a criteria for admission, discharge, and maintenance of rehabilitation gains (Kelly Hayes &

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29 Facility Patient Assessment Instrument which is used to determine prospective payment rate s for all Medicare rehabilitation patients. The association between functional status and rehabilitation length of stay is well documented (Harada, Kominski, & Sofaer, 1993; Heinemann, Linacre, Wright, Hamilton, & Granger, 1994; Hosek et al., 1986; Stinema n (1995); Stineman & Williams, 1990). Over the health care reforms have decreased length of stays, national rehabilitation data from 2000 2007 indicate the assoc (Granger et al., 2010). Regardless of patient diagnosis, high functional status is associated with tays (Atalay & Turhan, 2009; Eastwood, Hagglund, Gordon, & Marino, 1999; Kennedy et al. 2006; McClure et al., 2011; San Segundo, Aguilar, Santos, & Usabiaga, 2007; Yeung, Davis, & Soric, 2010). The research of the association of nurse staffing and functio nal status in acute care and in long term care is meager. In their systematic review of evidence on nursing workload and staffing on health work environments, Pearson et al. (2006) cited only one study examining by Hall and colleagues (2003) utilized a repeated measures design to examine nurse registered Specifically, staff mix was a significant predictor of functional independence ( Hall et al., 2003). Two studies examined the relationships between staffing intensity and changes in FI scores. Johnston, Wood, and Fiedler (2003) found that correlations between staff hours per

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30 patient day (direct RN and therapy staff) and functional gain in rehabilitation hospitals were small, less than 2% of variance. Similarly, Jette, Warren, and Wi rtalla (2004) reported positive associations with higher nursing staff level and therapy intensity and the average change in FIM in skilled nursing facilities. However, the staffing intensity variables contributed only 3% of the variance to the model. Var iations in the definitions of nurse staffing in the studies also confound the results. Clearly, these gaps call for current and future research related to nurse staffing and functional health outcomes. The study of nursing staffing and patient outcomes in acute and long term care has progressed exponentially over the past decade. Variables have become more refined. Systematic reviews have identified the concept of diminishing returns as nurse staffing and patient outcomes were examined. The application o f production function theory to the contributes to the gaps identified in previous studies.

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31 CHAPTER 3 METHODOLOGY Purpose The specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting. Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed P ractical Nurses and Nursing Assistants), total nursing staff, and skill mix ( RN Proportion and non RNs) ] and its relationship with patient outcomes measured as length of stay (LOS) and functional was examined. C hapter 3 disc usses the study design, application of the production function to the study, the empirical specification, the parent study (setting, subjects, sample, and data collection methods), operationalization of variables utilized in the secondary analysis, and dat a analysis methodologies. Hypothesis The following hypothesis was tested: There is a non linear relationship between nurse staffing levels for RNs, Non RNs, total nursing staff, and skill mix (RN proportion) with patient production function relationship is elucidated Design This study was a secondary analysis of data that was collected in the parent study entitled It was a collaborative research study between the Uniform Data Systems (UDS), the Association of Rehabilitation Nurses (ARN) and the Veterans Health Administra tion (VHA) for the purpose of examining nurse characteristics (experience and certification in rehabilitation), nurse staffing, and patient outcomes in the inpatient rehabilitation setting.

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32 n a previous study to test the use of large data sets has been common in the health services research arena, this approach is recently gaining ground as an accept ed methodology for nursing researchers (Kneipp & Yarandi, 2002; Magee, Lee, Giuliano, & Monro, 2006; and Smaldone & Connor, 2003). This study will further elucidate the previous study by applying the theory of production function to the parent study data t o estimate a production function with nurse staffing as the predictor variables and patient outcomes as the dependent variables. Production Function In standard economic theory, the production function describes how a firm transforms resources (productive inputs) into outputs (goods, services to be sold to consumers) (Nicholson & Snyder, 2008). Formally, a production function can be expressed as: q = f (x 1 x 2 n ) where q represents the output (amount of goods or services produced during a period), and x 1 x 2 n .where x i function thus measures how much output is obtained from a given set of input. Total Product Total product (TP) is another term for the total amount of output that a firm produces from all inputs. (Nicholson, 1978). Most commonly total product is analyzed when one variable input, such a s labor, changes while all other inputs are held constant. The upper portion of Figure 3 1 illustrates total product as a function of a variable input: Q = Quantity of outputs as a function of L = Labor (variable inputs). The TP curve is typically S shap ed, starting at zero when zero units of labor are used. Then, as illustrated in Figure 3 1 and described in Table 3 1 as units of labor are added, TP first

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33 increases at an increasing rate (Stage I), then increases at a decreasing rate (Stage II), and the n eventually begins to decrease (Stage III). Marginal Product (Nicholson & Sn yder, 2008, p. 296). When total product is analyzed as a function of one input (typically labor), holding all others constant, marginal product of labor can be expressed as: = ( ) or = ( ) Thus, marginal product describes how output changes when the labor input changes by one unit. The lower portion of Figure 3 1 illustrates marginal product and shows the relationship between total product and marginal prod uct. Because MP is the slope of the TP curve at a given point, the shape of the MP curve is determined by the shape of the TP curve. As indicated in Table 3 2 MP initially is positive and increasing (Stage I), then is positive and decreasing (Stage II), and eventually becomes negative (Stage III). Note that a firm would not hire or utilize labor units beyond L3 because in this range using more labor would actually cause a reduction in output. Diminishing Marginal Returns A fundamental component of product ion function theory is the law of diminishing returns, also known as the principle of diminishing marginal productivity. This principle states that if one input in production is increased (i.e. labor) while all other inputs are held fixed, a maximum point of marginal return will eventually be reached, after which additions of the input

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34 yield progressively smaller, or diminishing, increases in output (Nicholson & Snyder, 2008). Note that diminishing returns (Stage II) is different from negative marginal pro duct (Stage III). That is, diminishing returns refers to the situation in which additional units of the input do result in added output, but the marginal contribution declines. Production Function and Nurse Staffing While the production function approach is widely used to analyze business firms, Newbold (2008), in his discussion paper regarding production economics of nursing, asserts that there is little adoption of production function theory in mainstream nursing workforce research. Given that nursing i s a fundamental input into the production of healthcare services, the approach can readily be adapted to the study of nurse staffing. The standard application of production function would be to examine the effect of nurse staffing (inputs) on the amount o f healthcare services produced (output). Nicholson and Snyder (2008) note that the model is commonly modified in empirical work by measuring output ( q nurse staffing, value added can be int erpreted as quality, or patient outcomes. Thus, this study examined how additional nurse staffing (labor input) affected quality (patient outcomes). For example, Zhang et al. (2006) took this approach by examining a production function with quality as a function of the number of nurses or nursing hours. Returning to Figure 3 1 the expectation is that initially as incremental units of nurse staffing are added, patient outcomes will increase at an increasing rate, then increase at a decreasing rate, and eventually will begin to decrease. The implications of this model are that at low levels of staffing, increases in staffing lead to levels of quality that increase at an increasing rate (increasing marginal returns to staffing), where quality is measured b y patient outcomes

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35 returns to staffing. Finally, increases in staffing wi ll result in a decrease in patient outcomes and negative marginal returns to staffing. The maximum level of nurse staffing is exemplified as L3 in Figure 3 1 because adding nurse staffing beyond this point would result in increased LOS and change. Empirical Specification The next step is to transform the general form of the production function: where Q (patient outcomes) = f [L (nurse staffing); X (covariates)] into the empirical specification to be used in the data analysis. The standard linear specification, which would be: Q = a + bL + cX, cannot be used here, because it would not allow the TP curve (patient outcome as a function of nurse staffing) to be S=shaped. To allow for that possibility, a curvilinear model was specified. Procedu re Methods Following dissertation committee approval, paperwork was processed to gain approval of the University of Florida Institutional Review Board (IRB 01). Exempt review was requested and approved, as subjects were fully de identified in the data set provided to the recipient investigators and in compliance with the Health Information and Portability and Accountability Act of 1996. A confidentiality agreement with the primary investigator of the original study was obtained and submitted assuring that t he recipient investigators will not be provided access to the identities of the subjects or to information through which the identities of subjects could be readily ascertained. Included in the packet were copies of the approval letters for the parent stud y from the Tampa Veterans Administration (VA) Medical Center IRB and the Un iversity of South Florida IRB.

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36 Data The data for this study come from research conducted by Nelson, et al. (2007). That study randomly selected a sample of 54 rehabilitation units f rom a pool of 806 rehabilitation units in the United States participating in Uniform Data System for Medical Rehabilitation (UDSMR), stratified by the USDMR geographical regions. Patient level data were extracted from the USMR database for a one month p eriod and were de identified prior to transmission to investigators at the coordinating site, the Tampa Veterans Administration (VA) Medical Center. Nurse level variables were collected via surveys and logs for a one month period. Data collection occurred over a 24 month period in 2005, staggered by site and reported as unit aggregated data. Variables Study variables and operational definitions are presented in Table 3.3. The predictor variables are nurse staffing and the dependent variables are patient outcomes. The facility staffing variables were further delineated as staffing levels of Registered Nurse hours per patient day (RN HPPD, Non A), total staffing (THPPD), and skill mix (PROP RN). Patient outcomes are measured in two ways in this Association of Rehabilitation Nurses ( 2004, 2005 ) describes the h igh priority research issues in their second edition of the Rehabilitatio n Nursing Research Agenda Under one of the categories, outcomes in relation to the type, intensity, and duration of rehabilitation nursing services required as a high priority agenda item. This agenda item supports the selection of both length of Study variab les, data sources, values, and measures are reflected in Table 3 4.

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37 The explanatory patient level variables utilized were gender, age, race, marital status, and Rehabilitation Impairment Category (RIC) groups. Facility level variables were facility types (freestanding rehabilitation hospital versus a rehabilitation unit in an acute care facility) and number of operational beds. Predictor Variables Nurse s taffing RN hours for patient day (RNHPPD) is the total number of direct patient care RN hours during the study month divided by the total midnight census during the study month, Values range from 0 to 36. Non RN hours for patient day (NONRNHPPD) is the total number of direct patient care LPN/LVN/NA hours during the study month divided by the total midnight census during the study month, Values range from 0 to 24. Total Hours per patient day (TOTHPPD) is the total number of direct patient care hours during the study month divided by th e total midnight census during the study month, Values range from 1 to 48. Skill mix proportion of RNs, (PROP_RN) is the per cent of RN and LPN/LVN/NA use. Ne l son et al. (2007) utilized staff mix, defined as proportion of RNs and non RN staff, overall nu rsing hours per patient day (HPPD), RN HPPD, and Non RN staff HPPD as staffing measures. This study differs from some previously discussed where licensed staff is defined to include LPNs with RNs when examining skill mix and proportion. For this study, exa mining RN to non RN (combining LPN and NA) best addressed the functional roles of the RN and LPN in the rehabilitation setting. This study is further strengthened by the utilization of case mix adjustment as recommended by Lang et al. (2004). For these rea sons, this study utilized the same

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38 Dependent Variables Length of stay Length of stay is the duration of a single episode of inpatient rehabilitation hospitalization. LOS is a continu ous measure calculated by subtracting the day of admission from the day of discharge. Values are actual days, ranging from 1 to 32. Descriptive statistics, including means, standard deviations, and ranges (minimum and maximum) are presented. F unctional In dependence Measure outcomes in the rehabilitation setting throughout the United States and the world (Duchene, 2008). This 18 item scale is appropriate for measuring cog nitive and motor functions for patients reliability, validity, and sensitivit y. Internal consistency reliability coefficients have been reported as above 0.90 for all subscales, with the exception of 0.68 for the locomotion subscale (Dodds, Martin, & Stolov, 1993). in 3 days of discharge. The higher the values, the greater the improvements in functional independence during the rehabilitati on stay. Descriptive statistics, including means, standard deviations, and ranges (minimum and maximum) are presented. D ischarge FIM adjusted by admission is described as a dependent variable in data analysis, later in Chapter 3

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39 Patient Level Characteristics Rehabilitation Impairment Category (RIC) classifies patients into one of 21 categories based on inpatient rehabilitation admission reason. The RIC is the highest level of classification for payment groups for CMS. The RIC is considered a pr oxy measure for patient mix and staffing levels ( Nelson et al. 2007 ). Once initial descriptive statistics were generated, it was determined that the RIC vari able values needed to be transformed. Like diagnoses were categorized into eight RIC groups: 1 (Stroke), 2 (Brain Injury), 3 (Spinal Cord Injury), 4 (Neurological), 5 (Replacement lower extremity), 6 ( Amputation ), 7 (Other, orthopedics) and 8 (Other, misce llaneous). These groupings are consistent with the parent study (Nelson, 2007). Frequency data are presented with a number and percentage for each group. Additional patient characteristics are age marital status, race and gender Age is presented in desc riptive statistics, including means, standard deviations, and ranges (minimum and maximum). Values range from 5 to 101. Marital status, race, and gender are presented as frequency data: number and percentage for each category of variable. Facility Level C haracteristics The two facility specific variables are the facility type and size. The facility type is categorical: 1 (freestanding rehabilitation hospital) and 2 (rehabilitation unit within an acute care facility). Facility type is reported as number a nd percentage. Facility size is expressed by number of operation beds Values range from 8 82. Data Analysis SAS version 9.3 (Cary, N.C.) was used for all statistical analyses. A level of significance of .05 was used for all hypothesis testing. Nelson and colleagues (2007) maximized strategies to

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40 limit missing data in the parent study. In spite of stringent steps such as through training of data collectors, minimizing the burden of data collection, and weekly reviews of daily logs with immediate follow up to complete missing data, some data were lost ( p. 188 ). Nurse staffing and facility data utilized in this secondary analysis had a less than 5% missing data rate. Patient data t burdensome ( Nelson et al., 2007, p. 188). Descriptive statistics included means, standard deviations, minimum and maximum ranges for continuous variables. Categorical variables wer e statistically represented in frequency distributions and percentage distributions. The following hypothesis was tested: There is a non linear relationship between nurse staffing levels for RNs, Non RNs, total nursing staff, and skill mix (RN proportion) with patient production function relationship is elucidated First, to allow for a nonlinear relationship in the statistical model, variables representing the me ans and squared means of the staffing variables RN HPPD and Non RN HPPD were generated. These staffing variables are referred to as linear and quadratic terms, respectively. Next t o allow for a curvilinear result, both the lin ear and the quadratic staffin g variables were utilized in the statistical modeling. Hierarchical Linear Modeling (HLM) is the most appropriate statistical technique to analyze multilevel data where one level is nested within the other (Raudenbush & Bryk, 2002). In this study, p I n social science research it is recognized that subjects may be clustered in organizational units (i.e. students in schools or patients in hosp itals) where there may be s ome influence on one level of analysis that eff ects the other level of

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41 analysis by virtue of residing with in the same organizational context (Hofmann, Griffin, & Gavin, 2000). HLM allows researchers to develop models to adjust for these influences. HLM was also utilized to account for the hierarchical nature of the data A key methodological assumption of HLM is that lower level units of data are nested within identifiable higher level units of data (Hofmann, et al.). HLM also allows the researcher to simultaneously model the impact of both individual (patient, lower) and institutional (facility, higher) variables on the dependent variables of interest (McCoach, 2010, p. 125). In this study, patient level characteristics ( admission gender, race, marital status, and RIC group) are cons idered level 1 explanatory variables. The facility level characteristics (number of operational beds and facility type) are the level 2 explanatory variables. ). The predictor staffing variables were RN hours and non RN hours The dependent variables of i nterest modeled were l ength of stay and These are represented in Table 3 3 and 3 4. Key statistical assumptions for hierarchical linear modeling were examined. Data were checked for outliers and implausible values. For each of the HLM model s, the convergence criteria were met. Fit statistics 2 Residual log likelihood, the Bayesian information criterion AIC C ) were examined. Level 1 (patient level) observations are assumed to be independent. The Level 2 (facility) variables are also assumed to independent both facility level characteristics and patient level characteristics, separate models were identified. Initi ally, the nurse staffing predictor variables (level 2 variables) were modeled separately: RNHPPD, Non RN HPPD, Total HPPD and Proportion RN. HLMs for each of the dependent variables were run with each of the staffing predictor variables and explanatory

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42 va riables. All variables were entered and run simultaneously for each model. Nurse staffing variables, (RN HPPD, non RN HPPD, total HPPD, and RN Proportion) were not significant predictors of length of stay. RN proportion and the proportion RN squared te rm significantly predicted FIM The relationship of RN proportion to change was such that both the linear and quadratic terms were significantly related to change ( p = 0.0169 and p = 0.0155 respectively ). Therefore, both the linear and the curvilinear relationships of proportion RN and change were statistically significant. Finally, more parsimonious models were selected. RN HPPD and Non RN HPPD (controlling for total HPPD and RN proportion) were modeled with each dependent va riable. Next, RN HPPD and Non RN HPPD squared terms were included the models for each DV. For length of stay, t he nurse staffing predictor variables (level 2 variables) RN HPPD and Non RN HPPD were run with explanatory variables of gender, race, marital status, RIC group, operational beds and facility type. A second model was run with the predictor variables RN HPPD, Non RN HPPD and their quadratic terms with the explanatory variables of gender, race, marita l status, RIC group, operational beds and facility type. HLMs for were run with staffing predictor variables of RN HPPD and Non RN HPPD in one model and RNHPPD, Non RNHPPD and their quadratic terms in the other. Discharge functioned as th e dependent variable. The explanatory variables of gender, race, marital status, RIC group, operational beds and facility type were included in both models. In addition, admission was included as a covariate to adjust for discharge All variable s were entered an d run simultaneously for each model. The models are presented in Table 3 5. The last variables entered into each model were selected by the statistical program as the reference variable for each of the categorical patient and facility char acteristics. Rehabilitation

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43 Impairment Category group was the only variable with clinical or research rationale for order entry into the model. Stroke was selected as the reference variable because of the volume of patients post stroke was second only to replacement lower extremity S troke is a commonly used diagnosis in rehabilitation research lower extremity replacement surgeries. There was no particular research interest or priority for de signating the reference variable for marital status. Age, g ender, race and facility type are dichotomous variables with no compelling rationale to enter one variable over the other. The reference variable s are identified in the HLM results T ables 4 3 and 4 4

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44 Table 3 1. Stages of total product. Stage Units of l abor Description Stage I 0, L1, L2 TP of zero when zero units of labor are used, after that TP increases at an increasing rate Stage II L2 L3 TP increases at a decreasing rate Stage III >L3 TP decreases Table 3 2. Stages of marginal product. Stage Units of labor Slope representation Stage I 0 L2 MP > 0 and increasing Stage II L2 L3 MP > 0 and decreasing Stage III >L3 MP < 0 Figure 3 1. Model of Production Function

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45 Table 3 3. Study variab les and operational definitions. Variable level Variable category Variable Definition Predictor variables Staffing characteristics RN hours per patient day Total number of direct patient care nursing hours divided by total midnight census Day, Eve, Night Non RN (LPN/NA) hours per patient day Total number of direct patient care LPN/LVN/NA nursing hours divided by total midnight patient census Total hours per patient day Total number of direct patient care nursing hours divided by total midnight patient census Skill Mix RN Proportion Proportion of nursing hours contributed by registered nurses Dependent variables Patient outcomes Length of s tay Duration of single episode of hospitalization (calculated by subtracting day of admission from day of discharge) Functional Independence discharge adjusted by Level 1 E xplanatory variables Patient characteristics Rehabilitation Impairment Category (RIC) Highest level of classification for payment (case mix) group categories. Age Actual age in years Gender Gender: male/f emale Marital s tatus Reported marital status on admission Race Reported race on admission Level 2 E xplanatory variables Facility characteristics Facility t ype Freestanding rehabilitation h ospital Rehabilitation unit in acute care f acility Size Numbe r of operational b eds

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46 Table 3 4. Study variables data sources values, and m easures. Variable level Variable category Variable Data source Values Measure Predictor variables Staffing characteristics RN hours per patient day Daily log Calculated 0 36 Scale Non RN (LPN/NA) hours per patient day Daily log Calculated 0 24 Scale Total hours per patient day Daily log Calculated 1 48 Scale Skill mix RN Proportion Daily log Calculated .02 1.0 Scale Dependent variables Patient o utcomes Length of s tay (LOS) database Actual days LOS 1 32 Continuous Scale database Discharge score 18 125 Continuous Level 1 Explanatory variables Patient characteristics Admission score Database Admission score 18 124 Continuous Rehabilitation Impairment Category (RIC) Groups Database 1 = Stroke 2 = Brain injury 3 = Spinal cord injury 4 = Neurological 5 = Replacement lower extremity 6 = Amputation 7 = Other orthopedic 8 = Other miscellaneous Categorical Age database 5.0 101.0 Nominal Continuous Gender database 1 = Male 2 = Female Categorical Dichotomous Marital status database 1 = Never married 2 = Married 3 = Widowed 4 = Separated 5 = Divorced Categorical Race/ethnicity database 0 = Other 1 = White Categorical Dichotomous Level 2 Explanatory variables Facility characteristics Facility type database 1 = Freestanding rehab ilitation hospital 2 = Rehab ilitation unit in acute care facility Categorical Dichotomous Size Operational beds database 8 82 Nominal Continuous

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47 Table 3 5. Hierarchical Linear Models. Model Dependent variable Staffing variable s Explanatory variables Level 1 and 2 1 Length of s tay RN HPPD Non RN HPPD Age, gender, marital status, race, facility type, operational beds 2 Length of s tay RN HPPD Non RN HPPD RN HPPD RN HPPD Non RN HPPD Non RN HPPD Age, gender, marital status, race, facility type, operational beds 3 Change Discharge RN HPPD Non RN HPPD Admission a ge, gender, marital status, race, facility type, operational beds 4 Change Discharge RN HPPD Non RN HPPD RN HPPD RN HPPD Non RN HPPD Non RN HPPD Admission a ge, gender, marital status, race, facility type, operational beds *Squared term for each variable

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48 CHAPTER 4 RESULTS Purpose The specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed P ractical Nurses and Nursing Assistants), total nursing staff, and skill mix ( RN Proportion and non RNs) ] and its relationship with patient outcomes measured as length of stay (LOS) and functional was examined C hapter 4 presents the sample descriptives and results of the hierarchical linear models. Description of Sample The descriptive statistics for the nurse staffing characteristics, patient outcomes, patient characteristics, and facility characteristics are presented i n table 4 1. Nurse Staffing Characteristics The total nursing care hours per patient day averaged 6.9 ( SD =3.5) with a range of 0.7 21.4. The average RN HPPD were 3.6 ( SD =2.2) and Non RN HPPD were 3.3 ( SD =1.9). The proportion of RNs was 50% ( SD =0.1). Patient Outcomes Length of s tay A total of 1529 patients had their full length of stay, admission to discharge, during the data collection period. The average LOS was 9.7 days ( SD = 5.1).

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49 c hange SD = 16. 7). The average d ischarge SD change SD = 13.3). Patient Characteristics The average patient age was 69.7 ( SD 15.3), with a range from 5 to 101 years. Just over half (57.10%) of the patients were female. The patients were predominantly white (85.22%) ere married (49.17%). Lower extremity joint replaceme nt (i.e. knee replacement) represented the majority of patients : 25.87% Next s troke accounted for 18.14% of the patients The miscellaneous RIC oup (fractured lower extremity, arthritis) was 17.03%. The remainder of the RIC groups, brain injury, spinal cord injury, neurological and amputation accounted for less than 7% of the patients each Facility Characteristics There were 54 rehabilitation facilities included in the study. Of those, 49 (90.74%) were identified as rehabilitation units within acute care facilities. Only 5 facilities (9.26%) were identified as free standing rehabilitation hospitals. The mean number of operational beds was 28 .1 ( SD =17.5). Because of the difference in the nature of the facilities (units within hospitals versus free standing rehabilitation hospitals), the range of operational beds was broad: 8.0 82.0.

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50 Hierarchical Linear Modeling Results Results for the hier archical linear models for all variables are presented in tables 4 2 through 4 4 Variables, regression estimates, standard errors, and p values are presented for each model. Nurse Staffing and Patient Outcomes HLM results for nurse staffing and the depen dent variables, length of stay and change are presented in table 4 2. Nurse staffing variables (RNHPPD, NON RN HPPD, and their quadratic terms ) were not significant predictors of length of stay or FIM Therefore, neither the linear nor the curvilinear relationships nurse staffing LOS and change are statistically significant. Explanatory Variables and Patient Outcomes: Length of Stay Hierarchical linear modeling results for explanatory variables and length of stay are presented in T able s 4 3 For staffing models ( RNHPPD, NONRNHPPD and RNHPPD, NONRNHPPD, RNHPPD*RNHPPD, NONRNHPPD*NONRNHPPD ), RIC group, age, and race significantly predicted length of stay. For RNHPPD and NONRNHPPD operational beds significantl y predicted LOS : the more operational beds in a facility, the longer the length of stay Rehabilitation Impairment Category Group was significantly related to length of stay for all staffing models ( p = <.0001). When compared to patients with strokes, le ngth of stay was lower than stroke for all RIC groups. Older patients had higher (longer) LOS ( p = <.000 9 ) than younger patients. There was a statistically significant positive relationship between LOS and patient race ( p <.023) for all staffing models. White patients had shorter LOS than all patients of other races. There was a statistically significant positive relationship between length of stay and operational beds ( p < 0.0 4 ) for RNHPPD and NONRNHPPD In facilities with a greater number

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51 of beds, patients had longer LOS when compared to other facilities with a lower number of operational beds. However, Facility type did not demonstrate a statistically significant relationship with length of stay ( p = 42 ). Explanatory Variables and Patient Outcome s: C hange Hierarchical linear modeling results for explanatory variables and are presented in T able 4 4. For staffing models (RNHPPD, NONRNHPPD and RNHPPD NONRNHPPD, RNHPPD*RNHPPD, NONRNHPPD*NONRNHPPD ), admission RIC group, age, gen der, facility type, and operational bed size significantly predicted Admission significantly predicted at discharge/ change ( p <.0001). When compared to patients with strokes, brain injury, othe r orthopedic and replacement lower extremities (e.g. knee replacement ) and lower for patient post amputation extremities and neurological and spinal cord injuries There was a statistically significant inverse relationship between and patient age ( p <.0001) Older patients had lower than younger patients. for males was significantly lower than females ( p = .00 3 ), such that women had improved functional outcomes. Additionally, for patients in fr eestanding rehabilitation hospitals was significantly higher than for patients in rehabilitation units in acute care hospitals ( p = 0.018 ). There was a statistically significant inverse relationship between and operational beds ( p = 0.00 21 ). P atients in facilities with a higher number of operational beds had lower Production Function Length of stay The results show that length of stay decreases as the number of RNHPPD increases. However, the rate of decrease in LOS slows down as more and more RN hours are added, as

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52 evidenced by the positive coefficient for the squared terms. See Table 4 2 The inflection point, x = 10.3969 is the point at which adding more hours would actually lead to longer length of stay. This suggests that there is a U shaped relationship between RN hours and LOS. The inflection point for NONRNHPPD x = 8.7875, is the point at which adding more hours would actually lead to longer length of stay. This suggests that there is a U shaped relationship between Non RN hours and LOS. change The results show that as the number of RNHPPD increases, increases Yet the rate of increase in is decreasing as more and more RN hours are added, as evidenced by the positive coefficient for the squared terms. See Table 4 2. The inflection point, x = 7.1750 is the point at which adding more hours would actually reduce This suggests that there is a n upside down U shaped relationship between RN hours and change The inflection point for NONRNHPPD x = 8.7006, is the point at which adding more hours would actually reduce This suggests that there is an upside down U shaped relatio nship between Non RN hours and

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53 Table 4 1. Sample c haracteristics Variable category Variable Frequency % Mean SD Minimum Maximum Staffing characteristics RN hours per patient day 3.6 2.2 0 .2 12.0 Non RN (LPN/NA) hours per patient day 3.3 1.9 0 .0 9.3 Total hours per patient day 6.9 3.5 0.7 21.4 Skill mix RN Proportion 0.5 0.1 .02 1.0 Patient o utcomes Length of s tay (LOS) 9.7 5.1 1 .0 32 .0 score on admission 71.4 16.7 18 .0 124 .0 score on discharge 91.2 20.9 18.0 125.0 discharge minus admission 20.1 13.3 77 .0 66 .0 Patient characteristics Rehabilitation Impairment Category (RIC) Groups Stroke 277 18.14 Brain injury 119 7.79 Spinal cord injury 82 5.37 Neurological 80 5.24 Replacement lower extremity 395 25.87 Amputation 44 2.88 Other orthopedic 260 17.03 Other miscellaneous 270 17.68 Age N = 1529 69.7 5 .0 101 .0 Gender Male 656 42.90 Female 873 57.10 Marital status Never married 186 12.34 Married 741 49.17 Widowed 421 27.94 Separated 16 1.06 Divorced 143 9.49 Race/ethnicity Other 226 14.78 White 1303 85.22 Facility characteristics Facility type N = 54 Freestanding rehab ilitation hospital 5 9.26 Rehab ilitation unit in acute care facility 49 90.74 Operational beds 28.1 17.5 8 .0 82 .0

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54 Table 4 2 Results from Hierarchical Linear Models for nurse staffing, length of stay, and Length of stay change Variable Estimate SE p Estimate SE p RN HPPD 0.08605 0.1399 0.5414 0.2289 0.3183 0.4754 NONRNHPPD 0.1278 0.1399 0.4272 0.06554 0.3638 0.8578 RN HPPD 0.4768 0.5420 0.3835 1.2549 1.2367 0.3154 RNHPPD* RNHPPD 0.04586 0.06084 0.4548 0.1749 0.1409 0.2207 N ON RNHPPD 0.7943 0.6679 0.2403 0.6691 1.5051 0.6587 NONRN HPPD NONRNHPPD 0.09039 0.08694 0.30 3 8 0.07691 0.1960 0.6965 SE = standard error ; RNHPPD RNHPPD NONRNHPPD NONRNHPPD = quadratic terms

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55 Table 4 3 Results from Hierarchical Linear Models for Length of Stay RN HPPD NONRNH PPD RNHPPD NONRNHPPD RNHPPD* NONRNHPPD Variable Estimate SE p Estimate SE p Rehabilitation Impairment Category (RIC) Groups < .000 1 < 0.000 1 Stroke 0 0 Brain injury 0.2525 0. 5371 0.2734 0.5376 Spinal cord injury 0.6917 0.6132 0.7051 0.6135 Neurological 1.2391 0.6192 1.2520 0.6196 Replacement lower extremity 3.347 0.4009 3.3414 0.4013 Amputation 0.05381 0.7796 0.04536 0.7798 Other orthopedic 0.9686 0.4275 0.9715 0.4278 Other miscellaneous 2.0095 0.4271 2.0156 0.4280 Age 0.03332 0.01006 0.0009* 0.03341 0.01006 0.0009* Gender 0.1657 0.1719 Male 0.3774 0.2685 0.3719 0.2686 Female 0 0 Marital status 0.6025 0.6189 Never married 06507 0.5528 0.6306 0.5533 Married 0.4184 0.4415 0.4086 0.4416 Widowed 0.3335 0.4869 0.3255 0.4870 Separated 0.9774 1.2726 0.9842 1.2728 Divorced 0 0 Race/ethnicity 0.0232* 0.0262* Other 0.9485 0.4014 0.9294 0.4023 White 0 0 Facility type 0.4253 0.4507 Freestanding rehabilitation hospital 0.8337 1.0369 0.7998 1.0516 Rehabilitation unit in acute care facility 0 0 Operational beds 0.03688 0.01716 0.0365* 0.03289 0.01783 0.0713 SE = standard error ; RNHPPD *, NONRNHPPD = quadratic terms; *p < .05 ; 0 or = reference variable

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56 Table 4 4 Results from Hierarchical Linear Models for RN HPPD NONRNH PPD RNHPPD NONRNHPPD RNHPPD* NONRNHPPD Variable Estimate SE p Estimate SE p 0.9303 0.02177 <.0001* 0.9301 0.02177 <.0001* Rehabilitation Impairment Category (RIC) Groups 0.0002* 0.000 2 Stroke 0 0 Brain injury 0.8522 1.4433 0.8368 1.4444 Spinal cord injury 2.3992 1.6519 2.3846 1.6524 Neurological 3.0578 1.6658 3.1313 1.6664 Replacement lower extremity 3.2887 1.1024 3.2284 1.1025 Amputation 0.1566 2.1076 0.1733 2.1074 Other orthopedic 0.9525 1.1515 0.8870 1.1519 Other miscellaneous 1.0962 1.1550 1.2167 1.1572 Age 0.1470 0.02727 <.0001* 0.1486 0.02727 <.0001* Gender 0.00 32 0.00 32 Male 2.2333 0.7241 2.2333 0.7243 Female 0 0 Marital status 0.3582 0.3664 Never married 2.5843 1.4856 2.5568 1.4864 Married 1.7244 1.1894 1.7205 1.1897 Widowed 2.2468 1.3135 2.2430 1.3135 Separated 0.5239 3.4258 0.5002 3.4253 Divorced 0 0 Race/ethnicity 0.8287 0.7987 Other 0.2308 1.0595 0.2722 1.0599 White 0 0 Facility type 0.0 176* 0.0256 Freestanding rehabilitation hospital 5.5193 2.2464 5.1509 2.2346 Rehabilitation unit in acute care facility 0 0 Operational beds 0.1218 0.03745 0.0021* 0.1154 0.03818 0.0040* SE = standard error ; RNHPPD *, NONRNHPPD = quadratic terms; *p < .05 ; 0 or = reference variable

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57 CHAPTER 5 DISCUSSION AND IMPLICATIONS Purpose The specific aim of this study was to apply production function theory to examine the nature of the relationship between nurse staffing and patient outcomes in the inpatient rehabilitation setting Nurse staffing [ Registered Nurses (RNs), Non RNs (Licensed Practical Nurses and Nursing Assista nts), total nursing staff, and skill mix ( RN Proportion and non RNs) ] and its relationship with patient outcomes measured as length of stay (LOS) and functional was examined. Chapter 5 presents the discussion of the results, limitations, and conclusions of this study and implications for future utilization and research. Discussion The following hypothesis was tested: There is a non linear relationship between nurse staffing levels for RNs, Non RNs, total nursing staff, and skill mix (RN proportion) with patient setting such that a production function relationship is elucidated Production Function The hypothesis that there is a nonlinear relationship between RN HPPD and Non RN HPPD with patient outcomes of LOS and is supported. The relationship s of RN HPPD and Non RN HPPD with LOS and are such that neither the linear or quadratic terms are significant However, both HPPD estimates indicate that the direction of the relationships to LOS and FIM change as evidenced by the reverse coefficient for the squared terms This is consistent with published literature indicating that a nonlinear relationship between nurse staffing and patient outcomes exists (Lankshear, Sheldon &Maynard, 2005; Kane et al., 2007; Nelson et al., 2007; Zhang & Grabowski, 200 4).

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58 In fact, the inflection points for HPPD and both LOS and change indicate the point at which adding more hours would actually change the direction of the relationships. This suggests that there is a U shaped relationship between HPPD and patient outcomes. This result indicates that the relationships are curvilinear and approximate a production function curve. The seminal work of Aiken et al. (2002) and Needleman et al. (2002) set the stage for robust studies of nurse staffing and nurse sensitive patient outcomes over the past decade While many studies supported that RN proportion resulted in improved outcomes (more is better) the literature has offered little support fo r minimum nurse patient ratios ( Lang et al. 2004). This minimum to more is better view is what has commonly been assumed and studied as a linear relationship of nurse staffing to patient outcomes. relationship of nurse staffing to patient out comes indicates that a floor and ceiling exists. That is, there is a minimal level of nurse staffing where lower levels result in inferior care or outcomes. Similarly, at some range of staffing, a maximum point is reached such that further increases in s taffing no longer produce improved outcomes (ceiling). This is the fundamental principle of production f unction and diminishing returns: at incremental changes in labor (staffing), variations in productivity (outcomes) occur on the trajectory. The result s of this study are important in that there is a curvilinear relationship between HPPD and the patient outcomes of LOS and FIM change. This is the first step in indicating that a production function with diminishing returns is plausible. W hen the nature of the relationships between HPPD with LOS and are further examined in this study both gave evidence of the increasing or decreasing slope patterns typical of production function models. The existence of diminishing marginal ret urns to

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59 additional HPPD was supported although the relationship was not statistically significant. This is consistent with the published literature utilizing production function to model the relationship of nurse staffing and patient outcomes which found increased nurse staffing improved quality and patient outcomes to t he point of diminishing returns (Hendrix & Foreman, 2001; Zhang et al. 2006; Mark, Harless, McCue & Xu, 2004; Meyer, Wang, Li, Thompson, & Obrien Pallas, L., 2009) The lack of statistical ly significant estimates in this study does not mean that a production function curve does not exist The results are in keeping with the traditional slopes of a typical production function model. The lack of statistical support for a model of diminishing returns may have been influenced by the limitations of this study. Decisions related to centering of the variables could have influence d the results. In the same way, different approaches for modeling production function may produce statistically signifi cant results. C hange HLM models including admission as a covariate demonstrated a curvilinear relationship between RNHPPD and patient outcomes. As the number of RNHPPD increases, increases. The relationship between RNs and change is consistent with nursing staff in Canadian hospitals was found to be a significant predictor of functional status. In this study, as the number of RNHPPD increases, increases. However, the rate of increase in is decreasing as more and more RN hours are added, as evidenced by the positive coefficient for the squared terms. The inflection point, x = 7.1750 is the point at whi ch adding more hours would actually reduce This suggests that there is an upside down U shaped relationship between RN hours and

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60 This is consistent with the results of with Meyer et al. (2009), where the linear relationship betwe en nurse staffing and Omaha Scale knowledge and status changed direction at 88%. A s staffing levels exceeded 88% there were diminishing returns on patient Omaha Scale knowledge, status and behavior scores Additionally, Meyer and colleagues reported inc reasing levels of nurse staffing had an increasing influence on status change to a point of marginal returns. These findings suggest that further investigation into production function modeling as applied to functional status and positive patient outcomes such as knowledge achievement is warranted. Length of S tay N urse staffing levels for RNs and Non RNs were not significant predictors of length of stay. Nelson (2007) found a significant relationship between hours of total nursing care and RN HPPD with LOS in the rehabilitation setting. The difference in results may be related to an adjustment of the length of stay (n=304) : deleting patients with immediate discharge from the sample. In addition t h e researchers utilized an iterative process for model de velopment, deleting independent variables found to be nons ignificant The scope of this current study did not allow for the adjustments in LOS and could be considered for future investigation of these data. Thi s is in contrast to a large volume of liter ature supporting the relationship between nurse staffing and LOS. Higher ratios of RNs and RN HPPD were significantly related to reduced length of stay in hospital settings, including the intensive care unit (Amaravadi, Dimick, Pronovost, & Lipsett, 2000; Barkell, Killinger, & Schultz, 2002; Cho, Ketefian, Barkauskas, & Smith, 2003 ; Lassnigg, Hiesmayr, Bauer, & Haisjackl, 2002; Needleman, Buerhaus, Mattke, Stewart, & Zelevinsky, 2002). One explanation may be that the nature of the rehabilitation setting is not as amenable to changes in length of stay as acute care setting. Also, economic

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61 pressures encourage early transfer to rehabilitation facilities having the effect of reducing the LOS in acute care setting may be reduced. When examining the relationship of RN HPPD and LOS the hypothesis of a production function curve of diminishing marginal returns was supported. The results of this study show that length of stay decreases as the number of RNHPPD increases. Additionally, the rate of decrease in LOS slo ws down as more and more RN hours are added, as evidenced by the positive coefficient for the squared terms. The inflection point, the point at which adding more hours would actuall y lead to longer length of stay suggests that there is a U shaped relatio nship between RN hours and LOS. This shape approximates the shape of a typical production function curve. Limitations Several limitations of this study should be acknowledged. First hierarchical linear e of the variables in this study. Variables were not centered in the HLM models in the current study. There are many considerations for the selection of variables to center and which centering method to use (e.g., group centering, grand mean centering, e tc.). Centering selection choices can affect statistical results. In future work, selection of variables to center and centering method will be incorporated in the development of HLM models. Second, t he HLM modeling results have shown a curvilinear relationship of RN HPPD and Non RN HPPD with patient outcomes of LOS and . The methodology for examining diminishing marginal returns with nurse staffing a nd patient outcomes is limited, but approaches are varie d. For the scope of this study, one approach to approximate the inflections points of the curvilinear relationship was utilized. The HLM estimates for HPPD and the

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62 squared terms were calculated for the value of x. Further exploration of the nature of th e curvilinear relationships will be part of future investigation. Third, a n argument may be made that the sample consisted exclusively of rehabilitation centers, possibly affecting generalizability of the results. However, nurse staffing has been identified as having a curvilinear relationship and diminishing returns with patient outcomes in the literature in the acute and long term settings. This study of the rehabilitation setting is additive to that body of work. Implica tions Implicat i ons for Nursing Practice Nursing administrators are once again challenged to justify registered nurse staffing in lean economic times. With nurse staffing being one of the largest budget expenses of health care facilities, historical staffi ng models and hours per patient day are called into question. Empirical data to support staffing decision is needed. In particular, higher costs related to higher RN staffing must be justified. Hall et al. (2003) and Meyer et al. (2009) support that highe r RN proportion/ staff utilization is a significant predictor of functional independence. These studies help elucidate the unique nature of nurses influence on the outcomes of patient s in their care. T he evidence to support optimizing both minimum staffi ng and maximum staffing resource allocation and optimal patient outcomes is growing. Since Hendrix & Foreman, (2001) and Zhang, Unruh, Liu and Wan (2006) the body of literature revealing diminishing returns to nurse labor in acute and long term care has gr own. This study indicates that the pattern of diminishing returns also exists in the rehabilitation setting. This adds to the conundrum for health care administrators and policy makers that, in addition to concerns related to minimal nurse staffing, ther e is a point at which additional staffing no longer promotes quality or

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63 efficiency. Implications for Theory Prod uction function theory was utilized to provide the underpinnings and guide this research study. This theory has been utilized to address staffing resources and patient outcomes (Hendrix & Foreman, 2001; Zhang et al., 2006). As previously stated, the existence of diminishing returns has been demonstrated repeatedly in a variety of settings over the past decade. Nonetheless, the volume of research has not reached a tipping point at which decision makers and policy makers are c onvinced by the evidence. T his theory can provide the conceptual framework for utilizing alternate statistical approaches to the questions of staffing efficiency as it relate s to quality of care and patient outcomes, as well as other efficiency concerns i n the health care setting today Perhaps Hendrix and Foreman portended the future when in 2001 they utilized level whereby quality is optimized, personnel are conserved, and public burde 164). Implications for Future Research In their study of nurse staffing and patient outcomes, Meyer, Wang, Li, Thompson, & Obrien Pallas, L. (2009) noted a knowledge, behavior a nd status scores were less likely to show improvements at discharge. Further analysis of the rehabilitation scores or consideration in future analysis for other outcomes, as well. Although research of nurse staffing and patient outcomes has surged in the last decade, few studies have applied the theory of production function to examine the nature of those

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64 relationships Methodological issues in nurse staffing research continue to be refined, including outcomes within facilities. S tudies including large data sets in all settings ( acute care, long term care, and rehabilitation ) could further substantiate if the relationship of nursing labor and patient outcomes consistently demonstrates diminishing returns. These data are important to support decision makers and policy makers in t ight fiscal environments such as health care today. another growing body of work for researchers and quality measurement specialists. For example, higher RN proportion decreased probability of pneumonia and a subseque nt reduction in LOS (Cho et al., 2003; Unruh, 2003). They attribute RN proportion as specifically influencing the interventions aimed at the prevention of pneumonia Nelson et al. (2007) noted that further r esearch is needed to articulate the rehabilitation RN work processes that affect patient outcomes. T he work of Hall et al. (2003) reported RN proportion/staff mix as a significant predictor of functional independence. Further research is needed to continu e to substantiate the influence rehabilitation RN staffing and interventions have on functional outcomes. Conclusions The hypothesis that there is a nonlinear relationship between RN HPPD and Non RN HPPD with patient outcomes of LOS and is supported. The relationships of RN HPPD and Non RN HPPD with LOS and are such that neither the linear or quadratic terms are significant. However, both HPPD estimates indicate that the relationships to LOS and FIM change direction, as evidenced b y the reverse coefficient for the squared terms. Therefore, the nature of the curvilinear relationship of nurse staffing and patient outcomes approximated a model of production function and diminishing returns was demonstrated

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65 This study provides furth er evidence that nurse staffing and patient outcomes have both a sacrificed. Concerns about the economy and the state of health care in general have reached a Z eitgeist in the United States. Further research is imperative to provide leaders in health care the ability to generate data driven and evidence based practice decisions for optimal quality and efficiency.

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70 McClure, J. A., Salter, K., Meyer, M., Foley, N., Kruger, H., & Teasell, R. (2011). Predicting length of stay in patients admitted to stroke rehabilitation wit h high levels of functional independence. Disability and Rehabilitation, 33 (23 24), 2356 2361. doi:10.3109/09638288.2011.572225 McGillis Hall, L., Doran, D., & Pink, G. H. (2004). Nurse staffing models, nursing hours, and patient safety outcomes. Journal of Nursing Administration, 34, 41 45. McCoach, D. B. (2010) Hierarchical Linear Modeling. In G. R. Hancock &R. O. Mueller (Eds.), (pp 123 140). New York: Routledge. Meyer, R.M., Wang, P., LI, X., Thompson, D., Obrien Pallas, L. (2009). Evaluation of a patient care delivery model: patient outcomes in acute care. Journal of Nursing Scholarship, 41 (4), 399 410. doi: 10.1111/j1547 5069.2009.01308.x Needleman, J., Buerhaus, P., Mattke, S., Stewart, M., & Zelevinsky, K. (2002). Nurse staffing levels and the quality of care in hospitals. New England Journal of Medicine, 346, 1715 1722. Needleman, J., Buerhaus, P., Pankratz, V. S., Leibson, C. L., Stevens, S. R., & Harris, M. (2011). Nurse staffing and inpatient m ortality. New England Journal of Medicine, 364 (11), 1037 1045. Nelson, A., Powell Cope, G., Palacios, P., Luther, S. L., Black, T., Hillman, T.,...Gross, J. C. (2007). Nurse staffing and patient outcomes in inpatient rehabilitation settings. Rehabilitatio n Nursing, 32 (5), 179 202. Newbold, D. (2008). The production economics of nursing: a discussion paper. International Journal of Nursing Studies, 45, 120 128. Nicholson, W. (1978). Production Function. In Microeconomic theory: basic principles and extensions (2nd ed., pp. 139 140). Hinsdale, IL: Driden Press. Nicholson, W. (1995). Microeconomic theory: basic principles and extensions New York: The Dryden Press. Nicholson, W., & Snyder, C. (2008). Production Functions. In Microeconomic theory: basic principles and extension s (pp. 295 322). Mason, OH: Thompson South Western. Pearson, A., Pallas, L. O., Thompson, D., Doucette, E., Tucker, D., Wiechula, R.,...Jordan, Z. (2006). Systematic review of evidence on the impact of nursing workload and staffing on establishing healthy work environments. International Journal of Evidence Based Healthcare, 4, 337 384. doi:10.1111/j.1479 6988.2006.00055.x Polit, D. F., & Beck, C. T. (2006). Essentials of nursing research: methods, appraisal, and utilization (6th ed.). Philadelphia, PA: Lippincott, Williams & Wilkins.

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72 U. S. Department Of Health And Human Services (2001). Nursing workforce recruitment and es is a growing concern Washington, D.C: U.S. General Accounting Office testimony before the Committee on Health, Education, Labor and Pensions, U. S. Senate, May 17, 2001. Unruh, L. (2003). Licensed nurse staffing and adverse events in hospitals. Medi cal Care, 41 (1), 142 152. Unruh, L. (2008). Nurse staffing and patient, nurse and financial outcomes. American Journal of Nursing, 108 (1), 62 71. Unruh, L. Y., & Zhang, N. J. (2012). Nurse staffing and patient safety in hospitals. Nursing Research, 61 (1), 3 12. doi: 10.1097/NNR.0b013e3182358968 Yeung, S. M., Davis, A. M., & Soric, R. (2010). Factors influencing inpa tient rehabilitation length of stay following revision hip replacements: a retrospective study. BMC Musculoskeletal Disorders, 11, 252. Zhang, N. J., Unruh, L., Liu, R. & Wan, T. T. (2006). Minimum nurse staffing ratios for nursing homes. Nursing Economics, 24 (2), 78 85. Zhang, X., & Grabowski, D. (2004). Nursing home staffin g and quality under the Nursing Home Reform Act. The Gerontologist, 44 (1), 13 23.

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73 BIOGRAPHICAL SKETCH Mary Margaret Nason graduated from the University of Alabama, Huntsville with her Bachelor of Science in Nursing, with high honors in 1979. Upon graduation, she served as an officer in the United State s Naval Nurse Corps until 1984. She received her Master of Science in Nursing from the University of Florida in 2001. She received her Ph.D from the University of Florida in the spring of 2014. Her minor course of study for her doctorate was Health Services Research, Management, and Policy. During her Ph.D. program she earned a research grant from Sigma Theta Tau, Lambda Rho Chapter at larg e. Her nursing e xperience includes a broad range of progressive clinical, administrative, research, educational, and informatics roles She has served as a member University of Florida Institutional Review Board (2006 2008 ) Her research interests are n urs ing workforce, patient outcomes and exploration of organizational effectiveness.



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HEALTHSYSTEMS EvaluationofaPatientCareDeliveryModel:PatientOutcomes inAcuteCardiacCare RaquelM.Meyer,RN,BScN 1 ,SpingWang,PhD 2 ,XiaoqiangLi,PhD 3 ,DonnaThomson,RN,MBA 4 &LindaOBrien-Pallas,RN,PhD,FCAHS 5 1 LambdaPi, DoctoralFellow&ResearchOf“cer,NursingHealthServicesResearchUnit,LawrenceBloombergFacultyofNursing,UniversityofToronto, Toronto,Ontario,Canada 2ResearchAssociate,NursingHealthServicesResearchUnit,LawrenceBloombergFacultyofNursing,UniversityofToronto,Toronto,Ontario,Cana da 3ResearchAssociate,NursingHealthServicesResearchUnit,LawrenceBloombergFacultyofNursing,UniversityofToronto,Toronto,Ontario,Cana da 4SeniorVPClinicalOperations&ChiefNursingExecutive,St.PetersHealthSystem,Hamilton,Ontario,Canada 5 LambdaPi ,Professor&CHSRF/CIHRChairinNursingHumanResources,LawrenceBloombergFacultyofNursing,UniversityofToronto,Nursing HealthServicesResearchUnit,Toronto,Ontario,Canada Keywords Nursestaf“ng,workenvironments,patient outcomes Correspondence RaquelMeyer,155CollegeStreet,Room130, LawrenceBloombergFacultyofNursing, UniversityofToronto,Toronto,Ontario,Canada M5T1P8.E-mail:raquel.meyer@utoronto.ca Accepted:June13,2009 doi:10.1111/j.1547-5069.2009.01308.x Abstract Purpose :Toevaluatetheinuenceofnursestafngandworkenvironment variablesonpatientoutcomesbytestingaconceptualmodel. Design :Aprospective,correlationaldesignwithcross-sectionalandlongitudinalcomponentswasconductedinCanadiancardiacandcardiovascularcare inpatientunits. Methods :Datawerecollectedfrommultiplesources.Hierarchicallinearmodelingwasusedtoexaminerelationshipsamongvariables. Conclusions :Thendingsindicatethatpatientoutcomesareinuencednot onlybypatientandnursecharacteristics,butalsobyorganizationalstafng practices.Organizationsthatmanagethecomplexityofworkconditionsand targetstafngutilizationlevelsbetween80%and88%attheunitlevelcan optimizepatientoutcomes. ClinicalRelevance :Empiricalvalidationofthemodelprovidesevidenceto informmanagementdecisionsabouthospitalnursestafng. Ashealthsystemsevolve,theneedtoimprovehealthcareserviceoutcomesthroughthemanagementoforganizationalfactorsthatinuencenurses'workingconditionsandworklivesremainssalient(Rafferty,Maben, West,&Robinson,2005).Workenvironmentfactorsand nursestafngarecloselylinkedtooutcomesforpatients, nurses,andorganizations(Lankshear,Sheldon,&Maynard,2005).Agreaterunderstandingofthecomplexityof workconditionsandtheeffectsofhospitalnursestafng attheunitlevelareessentialtomeetincreaseddemand forcostandqualityaccountabilityinhealthcare. GuidedbythePatientCareDeliveryModel(PCDM), interrelationshipsbetweenvariablestheorizedtoinuencepatientoutcomeswereexamined.Aspartofalarger studybyO'Brien-Pallas,Thomson,etal.(2004),thispaperidentieskeyworkfactorsrelatedtopatients,nurses, andunitsthatinuencedpatientoutcomesandprovides evidence-basedstandardsforadjustedrangesofnurse stafngutilizationlevelsforpatientsreceivingcardiacand cardiovascularcareintertiarycarehospitals.Patientoutcomesincludedadversemedicalconsequences(e.g.,fall withinjury,mortality),physicalandmentalhealth,and patients'knowledge,behavior,andstatus.Thendings willassisthealthsystemandnursemanagersindevelopingstafngandworkenvironmentstrategiestooptimize productivityreturnsandminimizestafngcosts,while ensuringqualityoutcomes. ConceptualModel ThePCDMisbasedonOpenSystemTheory,anditsdevelopmentandtestinginhospital(O'Brien-Pallas,Irvine, Peereboom,&Murray,1997)andcommunity(O'BrienPallasetal.,2001,2002)settingshasbeendetailed JournalofNursingScholarship,2009;41:4,399…410. 399 c 2009SigmaThetaTauInternational

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PatientCareDeliveryModel Meyeretal.elsewhere(O'Brien-Pallas,Meyer,&Thomson,2004). TheoverallpurposeofthePCDMistounderstandtherelationshipsbetweenoutcomesandfactorsknowntoinuencevariabilityinnursingwork;namely,thecharacteristicsofpatientsandofnursingteams,aswellas factorsrelatedtothecaredeliveryenvironment(O'BrienPallasetal.,1997).InthePCDM,thehospitalisconceptualizedasanopensystem.Patientsarenestedhierarchicallywithinandacrossnursesandunits,andnurses arenestedwithinunits.Themodelemphasizesthatinputsfromthecaredeliverysystem(e.g.,characteristics ofpatients,nurses,andthesystem,aswellassystem behaviors)andthroughputfactors(e.g.,communication andcoordination,environmentalcomplexity,andnursingactivities)crossthepatientcaresubsystemboundaries.Atransformationoccursasaconsequenceofinteractionsandprocessesamongsystemsubstructuresthat resultinoutputsforthesystemandprovidefeedback fortheentiresystem.Akeyintermediateoutputisthe stafngutilizationleveloftheunit,whichrepresents therelationshipbetweenworkloadhoursandworked hours.Typically,utilizationlevelsdonotexceeddesign capacityandeffectivecapacity.Designcapacityisthe maximumoutputthatcanbeattainedunderidealconditions;thisusuallyconstitutesanunrealisticgoalinreallifeemploymentsettings(Stevenson,2009).Effectivecapacityisthemaximumpossibleoutputgiventhepatient mix,schedulingdifcultiesandbreaks,technologyin use,andqualityfactors(Stevenson).Effectivecapacityisexpectedtobelessthandesigncapacitybecause oftherealitiesoftheworkplace,whichmayinclude changingpatientmix,educationalneedsofstaff,techFigure1. PatientCareDeliveryModel.nologymaintenance,schedulinglimitationsrelatedto unioncontracts,andstaffavailabilityaswellasbalancingofoperations.DistaloutputsinthePCDMincludepatient,nurse,andsystemoutcomes. Figure1 depictsthePCDMasitwasconceptualizedinthisstudy toinvestigatepatientoutcomes. ThePCDMhighlightsthatpatient,nurse,workenvironment,andsystemfactorsinteractinterdependently anddynamicallytoinuenceoutputs.Areviewofthe researchsupportingtheserelationshipsissummarized elsewhere(Pearsonetal.,2006).Patientsenterthe healthcaresystemwithcharacteristicsthatcontributeto theirownoutcomes.Variabilityinpatientoutcomeshas beenassociatedwithdemographiccharacteristicssuch asage(Estabrooks,Midodzi,Cummings,Ricker,&Giovannetti,2005;Hu,Chow,Dao,Errett&Keith,2006; Titleretal.,2006),education(Huetal.),familysupport(Titleretal.),andincomeoremploymentlevels (Allareddy&Konety,2006;Huetal.),aswellaspatients'pre-existinghealthcharacteristics,includingincreasedcomorbidityorseverityofillness(Allareddy& Konety)andpoormentalhealthstatus(deJongeetal., 2001). Nursecharacteristicsarealsoknowntoinuencepatientoutcomes.Forexample,nurseexperienceandeducationhavebeenpositivelyrelatedtoclinicaloutcomes (McGillisHall,Doran,&Pink,2004;O'Brien-Pallasetal., 2002)andreduced30-daymortality(Aiken,Clarke,Cheung,Sloane&Silber,2003;Estabrooksetal.,2005; Tourangeauetal.,2007).Casualandtemporaryemploymenthasalsobeenassociatedwithpatientmortality (Estabrooksetal.).400

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Meyeretal. PatientCareDeliveryModel Table1. KeyMeasuresandDataSources MeasureWhenadministeredSource SF-12HealthStatusSurveya(physicaland mentalhealthstatus) Admissionorinpreoperativeclinic,dischargePatientself-report NANDANursingDiagnosesbandOmaha ProblemRatingScalecAdmission,discharge,dailytoidentifynewor resolveddiagnoses Datacollectorfrompatientchart/kardexand nurse PatientdataformOnceoverpatientstayDatacollectorfrompatient chart/kardex/interview ResourceintensityweightAfterdischargeElectronic“lesubmittedbyHeathRecords Department NursesurveyOnceatbeginningofdatacollectionNurseself-report Dailyunitstaf“ngformDailyDatacollectorfromunitassignmentsheetand wardclerk(e.g.,workload) aWare,Kosinski,andKeller(2000);bKim,McFarland,andMcLane(1991);cMartinandScheet(1992).Patientoutcomesmayalsoberelatedtoorganizationalcharacteristicsandbehaviors.Hospital-levelanalysesofworkenvironmentcharacteristicssuchasleadership,qualitymanagement,andcollegialrelationships havebeenassociatedwithlowerratesofpatientmortalityandfailuretorescue(Aiken,Clarke,Sloane,Lake,& Cheney,2008;Estabrooksetal.,2005;Kazanjian,Green, Wong,&Reid,2005).Reviewsofnursestafngstudiesin theacutesectorhavefoundmixedsupportfortheassociationsbetweenindicatorsofstafnglevels(e.g.,hoursper patientday,nurse-patientratios,full-timeequivalents) andpatientoutcomessuchasmortality,failuretorescue, urinarytractinfection,andpatientsatisfaction(Lang, Hodge,Olson,Romano,&Kravitz,2004;Lankshearetal., 2005).However,moststudiesexaminestafngindicators atthehospitallevel.Investigationsofunit-levelassociationsareneededtoincreasetheaccuracyoftheseestimatesandtoinformnursingservicedeliveryatthepoint ofcare. Understandingthefactorsthatinuencepatientoutcomesisimportantbecauseofrisinghealthcarecostsand thecommitmenttoquality,timely,andsafecare.Theobjectivesofthisstudyweretodetermineworkenvironmentandnursestafngvariablesthatinuencepatient outcomesandtoidentifytheappropriatestafnglevels forachievingpositivepatientoutcomes.MethodologyDesign,Sites,andParticipantsAprospective,correlationaldesignwithcross-sectional andlongitudinalcomponentswasusedtocollectdata ( Table1 ).OfsixparticipatingCanadianhospitalsinOntarioandNewBrunswickthatmettheinclusioncriteria(i.e.,highvolumesofpatientsinthecardiaccasemix groupsofinterest),fourwereteachinghospitals.Crosssectionaldatawerecollectedeitheratthebeginningof thestudyorwhenpatientsweredischarged;repeated data,eitherdailyorattwotimepointsbetweenadmissionanddischarge,werecollectedduringa6-month datacollectionperiodbetweenFebruaryandDecember 2002.EthicalapprovalwasreceivedfromtheUniversity ofTorontoandhospitalsites.Patientandnurseconsents wereobtainedonsite. Toachieveasignicancelevelof.001andamoderate combinedeffectsize,anestimatedsampleof145patients withineachoftheselectedcardiacandcardiovascular CaseMixGroupswasrequiredtoexamineproposedrelationshipswithhighpower(90%).Multipledatasources includedhospitalrecords,nursesurveys,dailyunitdata, andapatientdataformlledoutbynursesordatacollectors.TheShortFormHealthSurvey(SF-12)healthstatus wasreportedbypatientsatadmissionorinthepreoperativeclinicandatdischarge.Hospitalsizerangedfrom121 to1060beds.Intotal,1230patientsand727nursesfrom 24unitscompletedthedataforms.Inter-raterreliability ofallmeasuresremainedat90%duringorientationand throughoutthestudy.MeasuresAsshownin Table1 ,patientvariableswerecollected throughthepatientdataform,patientself-reportsurvey,patientinterview,andmedicalchart.Nursevariables werecollectedthroughaone-timenursesurvey.Unitleveldatawerecollectedthroughunitproles(e.g.,unit type,numberofbeds)ordailystafngforms.Tomeasuretheatmosphereormoraleofaunit,someofthe individualnursemeasurementswereaggregatedtothe unitlevel.Operationaldenitionsofthevariablesarepresentedin Table2 .401

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PatientCareDeliveryModel Meyeretal. Table2. OperationalDe“nitionsofPredictorsandOutcomes Variable Measure A.Predictors Patientcharacteristics GenderMale,female EmploymentstatusEmployed,notemployed,orretired EducationHighschooldiplomaorless,postsecondary HealthserviceutilizationFamilyphysiciancaregiverathome,referralstohomecare,attendanceatpreoperativeorpostoperative clinics MedicaldiagnosisMedicaldiagnosisresponsibleforthelargestproportionofthelengthofstay(assignedatdischargeusing CaseMixGroups(tm)methodology;CMG)aAgeYears KnowledgeAbilityofthepatienttorememberandinterpretinformationforeachnursingdiagnosison5-pointOmaha ProblemRatingScalebBehaviorObservableresponses,actions,oractivitiesofthepatient“ttingtheoccasionorpurposeforeachnursing diagnosison5-pointOmahaProblemRatingScalebStatusConditionofthepatientinrelationtosignsandsymptomsforeachnursingdiagnosison5-pointOmaha ProblemRatingScalebPhysicalandmentalhealthMedicalOutcomesStudyForm12Rc;a12-itemscaleofphysicalfunctioning,vitality,rolefunctioning, physicalproblems,socialfunctioning,bodilypain,mentalhealth,andgeneralhealthperceptions NursingdiagnosesNumberofNorthAmericanNursingDiagnosesAssociation(NANDA)ddiagnoses WorkedhoursperpatientAverageoftheunitdailyworkedhoursofallstaffdividedbythemidnightpatientcensusoverthepatients lengthofstay LengthofstayNumberofdayshospitalized ResourceintensityweightRelativevaluesdescribingtheexpectedresourceconsumptionofthe"average"patientwithincasemix, complexity,andagegroupsthatwereusedtocontrolforpatientacuitylevels Nursecharacteristics EducationHighestnursingeducationalcredential EmploymentstatusFull-time,part-time,orcasualstatus JobinstabilityAnyreportofforcedchangetounitinpastyear,anticipatedforcedchangeofunitsinnextyear,orexpected joblosswithinnextyear(yesvs.no) ShiftchangeReportofmorethanoneshiftchangeinthepast2weeks(vs.none) AgeYears ExperienceYearsworked PhysicalandmentalhealthMedicalOutcomesStudyForm12Rc;a12-itemscaleofphysicalfunctioning,vitality,rolefunctioning, physicalproblems,socialfunctioning,bodilypain,mentalhealth,andgeneralhealthperceptions Nurse-patientratioAveragedailynumberofpatientscaredforbyanurseondayshiftsoverthedatacollectionperiodas recordedonaDailyPatientAssignmentForm OvertimeNursereportsofovertimeworked AutonomySumscoreofsixautonomyitemsona4-pointscalefromtheRevisedNursingWorkIndex(R-NWI)eJobsatisfactionMeanscoreof“veitemsona5-pointscaleforsatisfactionwithsocialcontact,presentjob,interactionswith management,amountofresponsibility,andbeinganurse(dissatis“ed 3.5) InterventionsdelayedAnyreportofinterventionsdelayedonthelastshiftforvitalsigns/medications/dressings, mobilization/turns,responsetopatientbell,orPRNmedication(1ormorevs.none) InterventionsnotdoneAnyreportofinterventionsnotdoneonthelastshiftforvitalsigns/medications/dressings, mobilization/turns,patient/familyteaching,dischargeprep,comforting/talkingwithpatients, documentingnursingcare,backrubs/skincare,oralhygiene,orcareplan(1ormorevs.none) Unitcharacteristicsandbehaviors SkillmixProportionofnursinghourscontributedbyregisterednurses %offull-timenursesProportionofnursesemployedfull-time %ofnursesreportingshiftchangesProportionofnursesreportingmorethanonechangeofshiftintheprevious2weeks Staf“ngutilizationlevelAttheunitlevel,workloadhoursdividedbynurseworkedhoursmultipliedby100.Dailyunitworkload scoreswerecomputedusingGRASP c ,astandardtimemethodology,orMedicus c ,arelativevalue methodology.Workedhoursweremeasuredasthedailynumberofpaidhours(includingpaidbreaks) workedbyallnursingstaff. Continued.402

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Meyeretal. PatientCareDeliveryModel Table2. Continued Variable Measure B.Outcomes Knowledge,behavior,andstatus changescores Differencescoresbetweenadmission/onsetanddischarge/resolution(improvedoverhospitalstayversus nochangeordeteriorated) Physicalandmentalhealthchange scores Differencescoresbetweenadmissionanddischarge(improvedatdischargevs.nochangeordeteriorated) MedicalconsequencesAnyreportofdeath,medicalerrorswithconsequences,urinarytractinfections,woundinfections, pneumonia,fallswithinjury,bedsores,orthrombosisduringhospitalstay(1ormorevs.none) aCanadianInstituteforHealthInformation(2008);bMartinandScheet(1992);cWare,Kosinski,andKeller(2002);dKim,McFarland,andMcLane(1991);eAikenandPatrician(2000).Asmeasuredinthisstudy,stafngutilizationlevels provideanindexofhowwelltheunitwasstaffedrelativetopatientneedsfornursingcare.Thedesigncapacityofanursingunitwas100%(i.e.,workloadhours wereequivalenttoworkedhours).Effectivecapacitywas designcapacityminusbreaksandunanticipatedevents. Inthisstudy,7%oftheshiftsconsistedofpaidmandatorybreaks.Thus,theeffectivecapacityvaluewas93%. Underidealconditions,withnounanticipatedeventsrelatedtoeitherthesupplyofnursesorthedemandfor care,stafngutilizationlevelsof93%wouldmeetpatientneeds.However,underrealconditions,bothsupplyanddemandconditionscanchangequickly.Inthis study,stafngutilizationlevelsbelow93%allowedsufcientexibilitytorespondtochangingsituationsandto deliverrequiredcare.AnalysisDescriptivedatawereanalyzedusingSPSSversion15. HierarchicallinearmodelingwasconductedusingMLwiNbetaversion2.0(CenterforMultilevelModelling, UniversityofBristol,Bristol,UK).Subscalescoreswere generatedafterexploratoryfactoranalyseswereperformedandifalphareliabilitiesforthesubscalesreached acceptablecriteria(greaterthan0.7).Becausethedata werehierarchicalinnature,withpatientsmostlynested withinunits,andunitsnestedwithinhospitals,hierarchicallinearmodelingwasconductedtobetteraccountfor thepossibleclusteringofeffectswithinunitsbecausesurveyresponsesfrompatientswithinunitswerelikelyto beaffectedbyfactorsthatare"xed"forallstaffinthat unit(e.g.,sizeandtypeofunit);thatis,patientsshare atreatmentenvironment.Butsomepatientswerecrossclassiedbynursesandunits;thatis,patientscouldbe caredforbymultiplenursesinthesameunitorpatients couldchangeunitsduringtheirhospitalstay.Tohandle patientscaredforbymultiplenurses,thecharacteristics ofallcare-givingnursesforeachpatientweredisaggregatedtothepatientlevelaspartofpatientvariablesby weightingthenursevariablesbasedonthenumberof daystheyprovidedcaretothepatient.Tohandlepatientsbelongingtomultipleunits,theproportionofdays intheunitoutoftheirtotallengthofstaywasassigned asweightstoeachunitoftheirstay.Hospitalcouldnot betreatedasaseparatelevelinthemodelingduetothe smallnumberofstudyhospitals( N = 6).Thepredictorsfor thesixpatientoutcomesweremodeledwithtwo-levelhierarchicallogisticregressions:patientandunitlevels. TheeffectsofthePCDMvariablesthatweretheoreticallyimportanttotheoutcomeswereassumedtobeadditiveandweretestedinhierarchicallinearregression models.Patientcharacteristics(e.g.,comorbidity,mental healthstatusonadmission)wereincludedtocontrolfor theacuityorbaselinestatusofpatients.RevisedNursingWorkIndexsubscalesandunitvariablesaggregated fromindividualnurseswereincludedinthenalmodelsiftheyweresignicantlyassociatedwiththeoutcome variables.VariablesofimportanceinthePCDMwereremovedfromthenalmodeliffoundtobenotsignicant inthepreliminaryanalysisacrosspatientmodels.Missing valueswereimputedusingeitherregressionimputation, cellmeanimputation,ormeanofnearbypoints(fordaily data).Intheend,1198of1230patientswereincludedin themodeling. Therelationshipsbetweenstafngutilizationlevels andpatientoutcomeswerehypothesizedtobenonlinear,withpositiveoutcomesobservedwhenunitstafng isadequaterelativetopatientneedsfornursingcare, butturningnegativewhenunitsareunderstaffed.We hypothesizedthatasunitsbecomeincreasinglyunderstaffed,nursesdonothaveadequatetimetoprovidethe nursingcarepatientsrequire,therebycompromisingpatientoutcomes.Severalmodelingstrategieswereusedto examinethenonlinearrelationshipandtodeterminethe stafngutilizationlevelsatwhichpatientoutcomesbegin403

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PatientCareDeliveryModel Meyeretal.todeteriorate,includingacurvilinearrelationshipand piece-wiseregression.ResultsSampleDescriptionSamplecharacteristicsaregivenin Table3 .Patients werehousedin24cardiacandcardiovascularcareunits. Oftheseunits,11werecriticalcare,2werestep-down units,2weredaysurgeryunits,and9wereinpatient units;20werepurecardiologyand4wereeithermixed unitsorintensivecareunits.Acrossunits,theoverallaveragestafngutilizationlevelwas90%( SD = 27.1%)for thestudyperiod.On60.4%ofstudydays,stafngutilizationlevelsreached85%.On46.2%ofstudydays,the stafngutilizationlevelsexceeded93%,indicatingthat patientneedsfornursingcareexceededthehoursworked bynurses(i.e.,effectivecapacitywassurpassed).Theproportionoffull-timestaffwas62%( SD = 18%),and97% ofnursingworkedhourswerecontributedRNs. Patientswererelativelyolderandmostlymale.Length ofstayaveraged6.4days,withameanresourceintensityweight(RIW)of2.8( 2.66)thatwashigherthan theOntarioacutecareinpatientaverageof1.38(MinistryofHealthandLong-TermCare,2002).Thenumber ofnursingdiagnosesaveraged4.5,withthehighestvaluesobservedincriticalcareunits.Medicalconsequences occurredinfrequently(6.1%ofpatients).Patienthealth waspooratadmission,with87%and49.2%ofpatients scoringbelowtheU.S.populationaverageforphysical andmentalhealth,respectively.However,nearlyhalfof patientshadimprovedphysicalandmentalhealthscores atdischarge.GeneralimprovementofpatientsinOmaha Scaleknowledge(55.7%),behavior(43.1%),andstatus (78%)scoreswasalsoobservedatdischarge. Nursesinthestudywerepredominantlyfemale (93.9%)andRNs(96.6%);relativetothegeneralnursingworkforceinOntario,theywereyounger(40.7 8.21) withsimilaryearsofexperience(16.5 8.87;Ontarioaverageof44yearsinageand17yearsofexperiencein 2002;CollegeofNursesofOntario,2002).Fourtenths ofnursesheldabachelor'sorhigherdegreeandwere inrelativegoodhealth.Onaverage,nursescaredfor 2.3patientsaday.Theworkconditionswerestressful,asreectedbyovertimehours,anticipatedorforced changeintheirworkunit,frequentchangeofshift, andnumberoftasksnotdoneordelayed.Onaverage,morethanhalfofnursesweredissatisedwith work,primarilywithopportunitiestointeractwithmanagement(45.5%),followedbyamountofresponsibility (23.6%).MultivariateResultsRegressioncoefcientestimatesandoddsratiosfrom thehierarchicallogisticregressionmodelsforthepatient outcomesarepresentedin Tables4 and 5 MedicalConsequences. Medicalconsequences weremorelikelytobeexperiencedbyacutecarecardiacpatientswithhighernumbersofnursingdiagnoses andlowermentalhealthscores.Medicalconsequences were52%morelikelytooccurforeachadditionalnursingdiagnosisand13%morelikelyforeachadditional hourofcaregiven.ForeachoneunitincreaseinSF-12 mentalhealthscoresatadmission,patientswere2%less likelytosufferamedicalconsequence.Patientswithpoor healthwereatincreasedriskforadversemedicalconsequences.Increasedhoursofcaremayhavereectedthe timeneededtocareforpatientssufferingmedicalconsequences.Stafngvariables,includingstafngutilization level,werenotstatisticallysignicant. Physicalhealth. Foreveryadditionalnursingdiagnosis,theoddsofimprovementinpatientphysicalhealth atdischargedecreasedby11%.Physicalhealthwasalso lesslikelytoimproveifpatientsconsumedrelatively higherresources,thatis,amongpatientswithhigheracuitylevels.Asstafngutilizationlevelsexceeded80%, theoddsofimprovementinphysicalhealthdecreasedby 45%.Therelationshipbetweenstafngutilizationlevels andphysicalhealthisillustratedin Figure2 .Nurseovertimealsonegativelyimpactedphysicalhealth.Improvementsinphysicalhealthatdischargewere7%lesslikely foreachadditionalhourofnurseovertime. Mentalhealth. Improvementsinpatientmental healthatdischargeweremorelikelywhenpatients scoredhigherinphysicalhealthstatusatadmission,but werelesslikelywhenpatientsstayedlongerinthehospital.Patientmentalhealthwasalsolesslikelytoimprove ifpatientshadbettermentalstatusatbaseline,suggestingthatpatientswithhigherscoresatadmissionwere lesslikelytoshowimprovementsatdischarge.There wasanegativerelationshipbetweenincreasedworked hoursperpatientandimprovedmentalhealth,probablybecausepatientswithdeterioratedmentalhealthconsumedmorehoursofnursingcare.Stafngvariables,includingstafngutilizationlevels,werenotstatistically signicant. Omahascaleknowledge,behavior,andstatus. Again,ceilingeffectsweresuggestedwherebypatients withhigherOmahascoresatadmissionwerelesslikely toshowimprovementsatdischarge.Aftercontrollingfor baselinepatientphysicalandmentalhealthandOmahascores,patientsweremorelikelytohavegained knowledgeabouttheirhealthconditionswhencaredfor bynurseswhoreportedhigherautonomyintheirjobs.404

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Meyeretal. PatientCareDeliveryModel Table3. SampleCharacteristics A.Predictorsinhierarchicallinearmodels%Mean SD Patientcharacteristics( N = 1230) Gender:male 66.7 Employmentstatus Employed 48.9 Notemployed11.7 Retired 39.4 Postsecondaryeducation41.9 Haveafamilyphysician95.2 Withapotentialcaregiverathome82.0 Wasaplannedadmission44.5 MostcommonCMG:percutaneoustransluminalcoronaryangioplasty13.5 Surgicalpatientsattendedpreoperativeclinic33.0 Surgicalpatientsreceivedpostoperativeeducation57.5 Age(years) 63.513.01 Omahascoreattime1:knowledge(range1…5)3.40.75 Omahascoreattime1:behavior(range1…5)4.00.58 Omahascoreattime1:status(range1…5) 3.30.62 Physicalhealthatadmission(%aboveU.S.generalpopulation/mean/SD)13.035.211.20 Mentalhealthatadmission(%aboveU.S.generalpopulation/mean/SD)50.848.211.00 Numberofnursingdiagnoses(range1…18)4.52.37 Workedhoursperpatient 9.24.18 Lengthofstay 6.47.88 Resourceintensityweight 2.82.66 Nursecharacteristics( N = 727) Education:Bachelorsdegreeorhigher42.3 Employment:full-time59.8 Unitinstability(forced/anticipatedunitchangeorexpectedjobloss)20.9 Changeshiftmorethanonceina2-weekperiod32.4 Age(years) 40.78.21 Yearsofworkingexperienceinnursing 16.58.78 Physicalhealth(%aboveU.S.femalepopulation/mean/SD)65.250.18.50 Mentalhealth(%aboveU.S.femalepopulation/mean/SD)50.847.310.40 Nurse-patientratio 2.31.43 Overtimehoursperweek 2.86.11 Autonomy(range8…24) 16.13.18 Dissatisfactionwithcurrentjob57.5 No.ofinterventiontasksnotdone(range0…9)%atleastone/mean/SD74.62.11.84 No.ofinterventionstasksdelayed(range0…4)%atleastone/mean/SD60.41.11.13 Unitcharacteristics( N = 24) Skillmix(%ofRNworkedhours) 96.97.90 Proportionoffull-timenurses 0.620.18 Proportionofnursesreportingshiftchanges0.580.12 Staf“ngutilizationlevel(%) 86.616.78 B.Patientoutcomesn = 1230 ImprovedOmahascoresfromadmissiontodischarge Knowledgescores55.7 Behaviorscores43.1 Statusscores 78.0 Improvedhealthscorefromadmissiontodischarge Physicalhealth41.1 Mentalhealth 42.3 Medicalconsequences6.1 405

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PatientCareDeliveryModel Meyeretal. Table4.ResultsofHierarchicalLinearModelsforMedicalConsequencesandforPhysicalandMentalHealth MedicalconsequencesPhysicalhealthMentalhealth RegressionOddsRegressionOddsRegressionOdds Predictorcoef“cientratiocoef“cientratiocoef“cientratio Patientlevel Patientcharacteristics Physicalhealthatadmission Š 0 010 99 Š 0 130 880 011 01Mentalhealthatadmission Š 0 030 980 001 00 Š 0 090 92Numberofnursingdiagnoses 0 421 52Š 0 120 89Š 0 060 94 Workedhoursperpatient 0 101 110 001 00 Š 0 060 94Lengthofstay 0 021 020 011 01 Š 0 040 96Resourceintensityweight 0 031 03 Š 0 100 90Š 0 010 99 Nursecharacteristics Education(ref:diploma) 0 221 250 111 110 051 05 Physicalhealth 0 031 03 Š 0 011 000 011 01 Mentalhealth Š 0 050 95 Š 0 010 990 011 01 Interventionsnotdone Š 0 540 580 081 080 271 32 Interventionsdelayed Š 0 730 48 Š 0 020 98 Š 0 100 91 Nurse-patientratio 0 301 350 051 05 Š 0 .140 87 Overtimehours Š 0 020 98 Š 0 080 930 041 04 Unitlevel ProportionofRNworkedhoursa4 691 60 Š 0 940 910 531 05 Staf“ngutilizationlevels(beyond80%)b cŠ 0 600 55Staf“ngutilizationlevels(beyond85%)b cŠ 0 480 620 301 35 Staf“ngutilizationlevels(beyond88%)b c Note .p .05.aOddsratiosbasedona10%increase.bUsedproportiontomodel.cAcurvilinearrelationshipwastestedbyincludingbothlinearand quadratictermsforstaf“ngutilizationlevels.Ifbothtermsweresigni“cantat5%level,theeffectofstaf“ngutilizationlevelsontheoutcomevar iablereversedafterreachingthecutpoint.IftheU-shapeeffectwasnotsupported,piecewiselinearregressionwasmodelednextusingalineartermanddumm y variablewithapredeterminedcut-offpointvalue(e.g.,80%,85%).Astatisticallysigni“cantdummytermindicatedthatthedirectionoftherelati onship betweenstaf“ngutilizationlevelsandthepatientoutcomechangedandthetermwasthereforeretainedinthe“nalmodel.Ifbothstrategiesfailed,a dichotomizedstaf“ngutilizationlevelatvariouscutpointswastested.Ifallthesefailed,adichotomizedstaf“ngutilizationlevelat85%wasinc ludedinthe model.Wetestedthestatisticalsigni“canceofdichotomizedstaf“ngutilizationlevelsat80%,85%,or88%forthreerespectivemodelspresentedin thistable.Severalotherunitattributesweresignicantlyassociated withpatientknowledge.ImprovedOmahaScaleknowledgescoresatdischargewere74%morelikelyforevery 10%increaseinRNworkedhoursontheunitand24% morelikelyforevery10%increaseinfull-timenurses ontheunit.Knowledgescoreswere44%lesslikelyto improveforevery10%increaseinnursesontheunit withmorethanoneshiftchangeinthepast2weeks. ImprovementsinpatientOmahaScalebehaviorscoresat dischargerelatedtotheirnursingdiagnoseswerepositivelyrelatedtonurses'jobsatisfactionandjobsecurity. Patientswere176%morelikelytohaveimprovedbehaviorscoreswhennursesweresatisedwiththeirwork.Patientswere53%lesslikelytoexhibitimprovedbehavior whennursesexperiencedoranticipatedaforcedchange inworkunits. RelationshipswerealsoobservedbetweenstafngutilizationlevelsandtheOmahaScaleoutcomes.Inpiecewiseregression,thelinearrelationshipbetweenstafng utilizationlevelsandimprovedOmahaScaleknowledge andstatuschangeddirectionatavalueof88%.Acurvilinearrelationshipwithacut-pointof88%wasalso observedbetweenstafngutilizationlevelsandOmaha Scalebehaviorscores.Theseresultsindicatedthatpatient knowledge,status,andbehaviorscoresweremorelikely todecreaseasstafngutilizationlevelsexceeded88%.DiscussionThisstudytestedthePCDMusingadditiveregression models.Consistentwithpreviousresearch(McGillisHall etal.,2004),patientcharacteristicsinuencednursing carerequirementsandtheextenttowhichpositiveclinicaloutcomeswereachieved.Inourstudy,patients'preexistinglevelsofphysicalandmentalhealthandtheir nursingcomplexity(asreectedbynursingdiagnoses) inuencedtheextenttowhichmedicalconsequences wereexperiencedandphysicalandmentalhealthwere406

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Meyeretal. PatientCareDeliveryModel Table5.ResultsofHierarchicalLinearModelsforKnowledge,Behavior,andStatus OmahaknowledgeOmahabehaviorOmahastatus RegressionOddsRegressionOddsRegressionOdds Predictorcoef“cientratiocoef“cientratiocoef“cientratio Patientlevel Patientcharacteristics Physicalhealthatadmission 0 011 010 011 010 011 01 Mentalhealthatadmission 0 001 000 001 000 001 00 Numberofnursingdiagnoses 0 051 050 061 070 081 08 Knowledgeatadmission Š 1 330 26Behavioratadmission Š 2 140 12Statusatadmission Š 1 480 23Workedhoursperpatient 0 041 04 Š 0 020 980 001 00 Lengthofstay 0 011 01 Š 0 010 990 001 00 Resourceintensityweight 0 011 010 081 080 051 05 Nursecharacteristics Education(ref:diploma) Š 0 290 75 Š 0 080 920 101 10 Physicalhealth Š 0 020 98 Š 0 010 99 Š 0 020 98 Mentalhealth Š 0 010 99 Š 0 010 990 021 02 InterventionsnotdoneŠ 0 470 620 031 03 Š 0 270 76 Interventionsdelayed 0 101 11 Š 0 010 99 Š 0 420 66 Nurse-patientratio 0 111 11 Š 0 030 970 161 17 Overtimehours 0 021 02 Š 0 030 970 021 02 Unitinstability Š 0 750 47Autonomy 0 171 19Satisfactionwithcurrentjob(ref:dissatis“ed) 1 022 76Unitlevel ProportionofRNworkedhoursa5 551 740 421 042 061 23 Proportionoffull-timeemploymenta2 131 24ProportionofnursesreportingshiftchangesaŠ 5 750 56Staf“ngutilizationlevelsb7 40 cn/a17 83 dn/a4 94 cn/aStaf“ngutilizationlevels(Quadratic)bŠ 10 11 dn/aStaf“ngutilizationlevels(beyond88%)bŠ 1 49 cn/aŠ 80 cn/a Note .p .05.aOddsratiosbasedona10%increase.bUsedproportiontomodelandsamemodelingstrategiesasoutlinedinnotesinTable4.cPiecewiseregressionwasmodeledforOmahaKnowledgeandStatusmodels(withbothlinearanddummyterms).dAcurvilinearrelationshipwastested forOmahaBehaviormodelbyincludingbothlinearandquadraticstaf“ngutilizationlevelterms.Cutpointwas88.2%. 40%60%80%100%120% Figure2. Exampleofcurvilinearrelationshipbetweenstaf“ngutilization levelsandphysicalhealth.improvedatdischarge.Althoughhospitalshavelimited controloverthecharacteristicsandhealthneedsofadmittedpatients,administratorsareabletoaddressstafng issuesthatareassociatedwithclinicaloutcomes.Forexample,giventhatmedicalconsequencesrequiredadditionalhoursofnursingcare,organizationsthatinvestin structuresandstafngtominimizeadverseeventsmay notonlyimprovepatientsafety,butmayalsodecrease costs(Thungjaroenkul,Cummings,&Embleton,2007). Reducingovertimehoursworkedbynursesandadequatelystafngnursingunitsarekeystrategiesfor improvingclinicaloutcomes.Asnursesworkedmore overtime,patienthealthwaslesslikelytoimprove. Ourndingisconsistentwithhospitallevelstudiesthat haveobservedthedetrimentalinuenceofovertimeon407

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PatientCareDeliveryModel Meyeretal.mortality(Berney&Needleman,2006),infections,decubitusulcers(Stoneetal.,2007),errorsandnear errors(Rogersetal.,2004),andmedicalincidents (O'Brien-Pallas,TomblinMurphy,etal.,2004).Although economistshavetheorizedtheeffectsofovertimeonproductivityandscheduling,conceptualmodelsareneeded tounderstandhowmechanismssuchasfatiguelinkovertimetopatientoutcomes(Thomson,2004). Patientscaredforonunitsthatwereunderstaffedrelativetopatients'needsfornursingcareweremorelikely toexperiencedeclinesintheirphysicalhealthandtheir knowledge,status,andbehaviorsrelatedtotheirhealth condition.Stafngutilizationlevelsof80%forphysical healthand88%forknowledge,status,andhealthbehaviorswerebelowtheeffectivecapacityvalueof93%. Thissuggeststhatnursingunitsrequiresurgecapacityin theirstafnglevelstointerveneinpatients'caretrajectoriesandtocoachpatientsinunderstandingandmanagingtheirhealthconditions.Forexample,ifacardiac patientexhibitedactivityintolerancerelatedtoinsufcientoxygenationforactivitiesofdailyliving,thenurse wouldassistthepatientinmodifyinghisbehaviorsto progressanactivitygradually,toengageinenergyconservationmethods,andtostopanactivityiffatigueor signsofcardiachypoxiawerepresent.Asourstudyunits becameincreasinglyunderstaffed,nurseshadinadequate timeforthistypeofcareorwereunabletospeeduptheir workandstillmaintaintheeffectivenessofnursinginterventions.Thisstudyextendsresearchonhospitallevel stafngindicatorstotheunitlevelandisconsistentwith previousstudies.Forinstance,higherproportionsofregulatednursingstaffattheunitlevelwereassociatedwith improvedphysicalfunctioningofpatients(McGillisHall etal.,2003). Organizationalhiringandstafngpracticesattheunit levelcanalsoinuenceoutcomes.Byemployinghigher proportionsofnursesinfull-timepositions,byreducing thefrequencyofshiftchanges,andbyincreasingtherelativeproportionofRNworkedhours,organizationscan improvepatients'knowledgeabouttheirconditionsat discharge.Continuityofthecaregiverispositedtoenhanceclinicaloutcomesbyfosteringnurses'knowledge aboutpatientsaswellasnurses'inuenceonclinical andworkplacedecisions(Grinspun,2002).Whenmore nursesonaunitworkfulltimeandchangeshiftslessoften,patientsmayexperiencegreatercontinuityofcare providerandhencemoreplannedandresponsiveteachingbynurses.Lessfatigueandgreateropportunityto establishtherapeuticrelationshipswithpatientsmayallownursestobetterassesspatientreadinessforlearning andtoprovidemoreindividualizedteachinginterventions.Carefragmentation,intheformofpatientmovementacrossmultipleunits,hasbeenassociatedwithreducedratesofteachinganddischargeplanningbynurses (Kanaketal.,2008).Ourndingssuggestthatcarefragmentationwithinunits(i.e.,lowerlevelsoffull-time nurses,frequentshiftchanges)mayalsohaveadetrimentalinuenceonpatients'knowledgeoftheirhealth conditions.Consistentwithpreviousresearch(Thungjaroenkuletal.,2007),stafngwithgreaterRNworked hoursensuredthatpatientsreceivedcareskilledintherapeuticrelationshipsandteachingmethods. Inconsistentassociationsbetweennurseautonomyand patientoutcomessuchasreducedmortality,failureto rescue,urinarytractinfections,andpressureulcershave beendocumented(Boyle,2004;Kazanjianetal.,2005). Ourstudyshowedthatenhancingnurses'jobautonomycanimproveclinicaloutcomesrelatedtopatient knowledgeoftheirmedicalandnursingconditions.Betterconceptualizationoftheclinical,organizational,and professionaldimensionsofnurseautonomyisneededto theorizetheassociatedinuencesonpatientoutcomes (Tranmer,2004)andtoreconcileconictingndings. Offeringsecureemploymentandmanagerialsupport arestrategiesemployerscanconsidertofosterimproved clinicaloutcomes.Althoughjobinsecurityandinsufcientsupervisorysupporthavebeenfrequentlylinkedto poornurseoutcomes(e.g.,Hall,2007;Verhaeghe,Vlerick,Gemmel,VanMaele,&DeBacker,2006),this studyextendstheassociationtoclinicaloutcomes.Improvementinpatienthealthbehaviorswaslesslikely whennurseswerepreoccupiedwithforcedoranticipated changesinworkgroupmembershiporwhennurses weredissatisedwiththeirjob,primarilybecauseof inadequateinteractionwithmanagers.Healthworkers whoperceiveunstableworkenvironmentshavereported higherexhaustionandlowerjobsatisfactionandwork engagement(Mauno,Kinnunen,Makikangas,&Natti, 2005).Wesurmisethatwhenunitstabilitywasthreatenedorjobdissatisfactionwashigh,nursesinthisstudy mayhavebecomelessengagedintheirwork.ConclusionsThisstudyaddstoagrowingbodyofevidencethatimprovementsinpatientoutcomesareinuencedbymultipleandinterrelatedstafngandworkenvironmentfactors.Theresultsofthisstudysuggestthatnurses'work performanceisenhancedwhenstafngpracticesrelated tojobsecurityandsatisfaction,nurseautonomy,overtime,shiftchanges,andRNandfull-timestafngcomplementsareappropriate.Further,adequatestafngof unitstoachievestafngutilizationlevelsof80%to88% alsoleadstobetteroutcomesforcardiacpatients.Units staffedatorbeyondeffectivecapacitymusturgently408

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Meyeretal. PatientCareDeliveryModeladdressstafnglevelstoimplementacceptablestandards. Patientoutcomesareakeymeasureoftheeffectivenessofnursingcare;however,nursesneedsupportiveworkingconditionstoenablehighqualitypatient care.AcknowledgmentsThestudywasfundedprimarilybytheCanadian HealthServicesResearchFoundation(#RC10621 06)andsecondarilybytheOntarioHospitalAssociation ChangeFoundationandtheNursingEffectiveness,Utilization,andOutcomesResearchUnit. ClinicalResourcesTheOmahaSystem.http://www.omahasystem.orgShortFormHealthSurvey(SF-12).http://www.sf36.org/tools/sf12.shtml ReferencesAiken,L.H.,Clarke,S.P.,Cheung,R.B.,Sloane,D.M.,& Silber,J.H.(2003).Educationallevelsofhospitalnurses andsurgicalpatientmortality. JournaloftheAmerican MedicalAssociation,290 (12),16171623. Aiken,L.H.,Clarke,S.P.,Sloane,D.M.,Lake,E.T.,&Cheney, T.(2008).Effectsofhospitalcareenvironmentonpatient mortalityandnurseoutcomes. JournalofNursing Administration,38 (5),223229. Aiken,L.H.,&Patrician,P.(2000).Measuringorganizational traitsofhospitals:TheRevisedNursingWorkIndex. NursingResearch,49 (3),146153. Allareddy,V.,&Konety,B.R.(2006).Characteristicsof patientsandpredictorsofin-hospitalmortalityafter hospitalizationforheadandneckcancers. Cancer,106 (11), 23822388. Berney,B.,&Needleman,J.(2006).Impactofnursing overtimeonnurse-sensitivepatientoutcomesinNewYork hospitals,19952000. Policy,Politics,&NursingPractice,7 (2), 87100. Boyle,S.M.(2004).Nursingunitcharacteristicsandpatient outcomes. NursingEconomics,22 (3),111123. CanadianInstituteforHealthInformation.(2008). Casemix groups(CMG + )directory2008 .Ottawa,Ontario,Canada: Author. CollegeofNursesofOntario.(2002). Membershipdatabases Toronto,Ontario,Canada:Author. deJonge,P.,Huyse,F.J.,Slaets,J.P.J.,Herzog,T.,Lobo,A., Lyons,J.S.,etal.(2001).Carecomplexityinthegeneral hospital:ResultsfromaEuropeanstudy. Psychosomatics,42 204212. Estabrooks,C.A.,Midodzi,W.K.,Cummings,G.G.,Ricker, K.L.,&Giovannetti,P.(2005).Theimpactofhospital nursingcharacteristicson30-daymortality. Nursing Research,54 (2),7484. Grinspun,D.(2002).Aexiblenursingworkforce:Realities andfallouts. HospitalQuarterly,6 (1),7984. Hall,D.S.(2007).Therelationshipbetweensupervisor supportandregisterednurseoutcomesinnursingcare units. NursingAdministrationQuarterly,31 (1),6880. Hu,A.,Chow,C.,Dao,D.,Errett,L.,&Keith,M.(2006). Factorsinuencingpatientknowledgeofwarfarintherapy aftermechanicalheartvalvereplacement. Journalof CardiovascularNursing,21 (3),169175. Kanak,M.F.,Titler,M.,Shever,L.,Fei,Q.,Dochterman,J.,& Picone,D.M.(2008).Theeffectsofhospitalizationon multipleunits. AppliedNursingResearch,21 ,1522. Kazanjian,A.,Green,C.,Wong,J.,&Reid,R.(2005).Effect ofthehospitalnursingenvironmentonpatientmortality: Asystematicreview. JournalofHealthServices&Policy Research,10 (2),111g117g. Kim,M.J.,McFarland,G.K.,&McLane,A.M.(1991).Pocket guidetonursingdiagnoses(4thed.).St.Louis,MO:Mosby. Lang,T.A.,Hodge,M.,Olson,V.,Romano,P.S.,&Kravitz, R.L.(2004).Nurse-patientratios:Asystematicreviewon theeffectsofnursestafngonpatient,nurseemployeeand hospitaloutcomes. JournalofNursingAdministration, 34 (7/8),326337. Lankshear,A.J.,Sheldon,T.A.,&Maynard,A.(2005).Nurse stafngandhealthcareoutcomes:Asystematicreviewof theinternationalresearchevidence. AdvancesinNursing Science,28 (2),163174. Martin,K.S.,&Scheet,N.J.(1992). TheOmahasystem: Applicationforcommunityhealthnursing .Philadelphia,PA: W.B.Saunders. Mauno,S.,Kinnunen,U.,Makikangas,A.,&Natti,J.(2005). Psychologicalconsequencesofxed-termemploymentand perceivedjobinsecurityamonghealthcarestaff. European JournalofWorkandOrganizationalPsychology,14 (3), 209237. McGillisHall,L.M.,Doran,D.,Baker,G.R.,Pink,G.H.,Sidani, S.,O'Brien-Pallas,L.,etal.(2003).Nursestafngmodelsas predictorsofpatientoutcomes. MedicalCare,41 (9), 10961109. McGillisHall,L.M.,Doran,D.,&Pink,G.H.(2004).Nurse stafngmodels,nursinghours,andpatientsafety outcomes. JournalofNursingAdministration,34(1),4145. MinistryofHealthandLong-TermCare.(2002).Discharge abstractdatabase.Toronto,Ontario,Canada:Author. O'Brien-Pallas,L.,IrvineDoran,D.,Murray,M.,Cockerill,R., Sidani,S.,Laurie-Shaw,B.,etal.(2001).Evaluationofa clientcaredeliverymodel,part1:Variabilityinnursing utilizationincommunityhomenursing. NursingEconomics, 19 (6),267276. O'Brien-Pallas,L.,IrvineDoran,D.,Murray,M.,Cockerill,R., Sidani,S.,Laurie-Shaw,B.,etal.(2002).Evaluationofa409

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