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Linking the Functional Independence Measure (FIM) and the Minimum Data Set (MDS)

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1 LINKING THE FUNCTIONAL INDEPENDENCE MEASURE (FIM) AND THE MINIMUM DATA SET (MDS) By YING-CHIH (INGA) WANG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 Copyright 2007 by Ying-Chih (Inga) Wang

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3 To my parents Sang-Jyi and Ching-Hsian.

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4 ACKNOWLEDGMENTS Four years of wide goose chasing left me tr emendous unforgettable memories and learning experiences. I still vividly rememb er of my first question for my advisor was What is a grant? and my first statistics class was talking about normal distri bution and how to compute the standardized Z score. As time went by, along with the cheers of Gator football game, I had opportunities to expose myself to a variety of interesting topics in cluding neuroanatomy, outcome measurement, biomechanics, and assistive technology. Till now, I finally feel that I am equipped with certain tools for use and have some skills to enable me to continue to explore unknown territory. I would like to thank for many people who s upported me along the way. I would not have been able to go this far without support and gu idance from them. First, I would like to give thanks to my lovely advisor, Dr. Craig Velozo, a man with great vision an d who is fun to work with. Thanks go to him for his guidance, inspirati on, and most important of all, financial support of the past four years. I also would like to thank my committee members (Dr. Sherrilene Classen, Dr. John C. Rosenbek, and Dr. James Algina) for their invaluable contribution to make my dissertation better. I would like to share this joyfulness with my colleagues and friends who accompanied and cheered me forward all the time. I also wish to thank th e rehabilitation science doctoral program at the University of Florida an d the Rehabilitation Outcomes Research Center (RORC) for their support throughout this process. Finally, I would like to thank my parents who always gave me unconditional suppo rt and encouraged me to pur sue what I wanted to be.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .......10 ABSTRACT....................................................................................................................... ............11 CHAPTER 1 THE STATE OF THE ART OF TE ST EQUATING IN HEALTHCARE............................13 Introduction................................................................................................................... ..........13 The History and Concept of Equating in Education...............................................................14 Equating: Education versus Healthcare..................................................................................21 State of the Art of Equati ng Studies in Health Care...............................................................22 Expert Panel Equating.....................................................................................................22 Equating an Item Bank.................................................................................................... 24 Rasch Equating M ethod...................................................................................................25 Next Critical Studies for A dvancing Linking in Healthcare........................................... 28 Research Question.............................................................................................................. ....31 Research Question 1............................................................................................................ ...32 Research Question 2............................................................................................................ ...32 Research Question 3............................................................................................................ ...32 2 RASCH ANALYSIS OF THE MINIMUM DATA SET (MDS) ON THE PHYSICAL FUNCTIONING AND COGNITION DOMAINS................................................................39 Introduction................................................................................................................... ..........39 Methods........................................................................................................................ ..........41 Sample......................................................................................................................... ....41 Resident Assessment Instrument Minimum Data Set (RAI-MDS)..............................42 Administration of the MDS.............................................................................................43 Rasch Analysis................................................................................................................43 Sample Size Requirement for Rasch Analysis................................................................45 Analysis....................................................................................................................... ....45 Dimensionality.........................................................................................................45 How well the data fit the model...............................................................................46 Item difficulty hierarchy...........................................................................................46 Person-item match: targeting...................................................................................46 Separation index.......................................................................................................47 Rating scale structure...............................................................................................47 Differential item functioning (DIF)..........................................................................47 Results........................................................................................................................ .............48

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6 Dimensionality................................................................................................................48 Rasch Analysis................................................................................................................49 ADL/Physical functioning items..............................................................................49 Cognitive items........................................................................................................53 Discussion..................................................................................................................... ..........57 3 DIFFERENTIAL ITEM FUNCTIONING OF THE FUNCTIONAL INDEPENDENCE MEASURE ACROSS DIFFERENT DIAGNOSTIC GROUPS............................................73 Introduction................................................................................................................... ..........73 Method......................................................................................................................... ...........76 Participants......................................................................................................................76 Differential Item Functioning Ba sed on the Rasch Model.............................................. 77 Differential Item Functioning Based on Two-Parameter Logistic IRT M odel................ 79 Results........................................................................................................................ .............82 Subjects....................................................................................................................... .....82 DIF Analysis Based on Rasch M odel.............................................................................. 82 DIF Analysis Removing M isfit Items........................................................................... 84 The Impact of DIF Items on Person Ability M easures.................................................... 84 DIF Analysis Based on 2PL IRT M odel.......................................................................... 85 Discussion..................................................................................................................... ..........87 4 EVALUATING THE FIM-MDS CROSSW ALK CONVERSION ALGORITHM VIA FUNCTIONAL RELATED GROUP CLASSIFICATION..................................................101 Introduction................................................................................................................... ........101 Methods........................................................................................................................ ........104 Data Preparation............................................................................................................104 Analysis Procedure........................................................................................................ 105 Results........................................................................................................................ ...........108 Sample......................................................................................................................... ..108 Validation at the Individual Level................................................................................ 108 Score distribution...................................................................................................108 Point difference |FIMa-FIMc|................................................................................. 109 Validation at the Classification Level............................................................................ 110 Validation at the Facility Level..................................................................................... 111 Discussion..................................................................................................................... ........112 5 CONCLUSION: INTEGRATING THE FINDINGS...........................................................129 APPENDIX A DATA REQUEST: THE FUNCTIONAL STATUS AND OUTCOMES DATABASE (FSOD)......................................................................................................................... ........135 B DATA REQUEST: THE MINIMUM DATA SET (MDS)..................................................136 LIST OF REFERENCES.............................................................................................................137

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7 BIOGRAPHICAL SKETCH.......................................................................................................149

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8 LIST OF TABLES Table page 1-1 Educational Equating Methodologies................................................................................33 1-2 Education versus Healthcare Di fferences in Equating Procedures.................................35 1-3 Review of Linking Studies in Health Care........................................................................36 2-1 Demographic Characteristics.............................................................................................61 2-2 Minimum Data Set (MDS) Physic al Functioning and Cognition Items.........................62 2-3 Factor Analysis on MDS Items Factor Pattern...............................................................63 2-4 Physical Functioning Item Statistics (Listed by Item Difficulty Order)............................64 2-5 Cognition/Communication Item Statistics.........................................................................65 3-1 FIM Instrument............................................................................................................. .....92 3-2 Participants Descriptive Statis tics for Each Diagnostic Group..........................................93 3-3 Difficulty Calibrations for FIM Motor Items.....................................................................94 3-4 Item Difficulty Calibrations for FIM Cognition Items......................................................94 3-5 Item Parameter Calibrations for FIM Motor Items............................................................95 3-6 DIF Analysis for FIM Motor Items...................................................................................95 3-7 Item Parameter Calibrations for FIM Cognitive Items......................................................96 3-8 Item Parameter Calibrations for FIM Cognitive Items......................................................96 4-1 FIM-MDS Crosswalk Conversi on Table ADL/Motor Scale........................................118 4-2 FIM-MDS Crosswalk Conversion Ta ble Cognition/Communication Scale................119 4-3 Demographic Baseline Characteristics............................................................................120 4-4 Summary of the Validation Results at Individual Level..................................................121 4-5 FRG Classification for Stroke Sample.............................................................................122 4-6 FRG Classification for Amputation Sample....................................................................122 4-7 FRG Classification for Or thopedic Impairment Sample.................................................122

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9 4-8 Validation Results at the Facility Level...........................................................................123

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10 LIST OF FIGURES Figure page 2-1 Person Score Distribution Item Diffic ulty Hierarchy Map Physical Functioning........66 2-2 Frequency Count of Item Rating Scale Physical Functioning Items (A) Rating scale category from 0 to 2 (B) Rating scale category 3, 4, and 8...............................................67 2-3 Rating Scale Structure of th e Physical Functioning Items.................................................68 2-4 General Keyform Structure of the Physical Functioning Items.........................................69 2-5 Person Score Distribution Item Di fficulty Hierarchy Map Cognition.........................70 2-6 Rating Scale Structure of th e Cognition/Commun ication Items........................................71 2-7 General Keyform Structure of the Cognition/Communication Items................................72 3-1 Examples of DIF A) Unifor m DIF and B) Non-uniform DIF...........................................97 3-2 Differential Item Functioning Plots fo r A) Motor and B) Cognition items across differential impairment groups (Stroke, Amputation, and Orthopedic Impairment).........98 3-3 Differential Item Functioning Plots fo r A) Motor and B) Cognition items across differential impairment groups after removing misfit items..............................................99 3-4 Differential Item Functioning Plots for FI M-walking (A, B, C) and FIM-stair (D, E, F) items based on the ICC DIF method...........................................................................100 4-1 FIMFunction Related Groups predic ting model for the Stroke population (Impairment code= 1.1 to 1.9).........................................................................................124 4-2 FIMFunction Related Groups predicting m odel for the individuals with lower limb amputation (Impairment code= 5.3 to 5.9)......................................................................124 4-3 FIMFunction Related Groups predicting model for the individuals with lower extremity fracture (Impairment code= 8.1 to 8.4)...........................................................125 4-4 FIMFunction Related Groups predicti ng model for the individuals with hip replacement (Impairme nt code= 8.5 to 8.52)...................................................................125 4-5 FIMFunction Related Groups predicti ng model for the individuals with knee replacement (Impairme nt code= 8.6 to 8.62)...................................................................126 4-6 FIM and MDS Score Distribution....................................................................................127 4-7 Point Difference Between the Actual and Converted FIM Score Distribution...............128

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11 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy LINKING THE FUNCTIONAL INDEPENDENCE MEASURE (FIM) AND THE MINIMUM DATA SET (MDS) By Ying-Chih Wang May 2007 Chair: Craig A. Velozo Major Department: Rehabilitation Science To develop an effective and efficient mechan ism for evaluating and tracking changes of functional status across the continuum of care, it is necessary to integrate information and achieve score comparability across acute and post-acu te healthcare facilities. While utilizing a single and comprehensive outcome assessment inst rument across all facilit ies would provide the best mechanism for the synchronized and seamless monitoring of patient outcomes, the fact that different instruments are firmly entrenched in diffe rent types of post-acute healthcare settings has made large-scale reformation extremely difficult. One solution for integrating functional status that requires minimum cost and effo rt would be the development of crosswalks or statistical links between functional status subscales from di fferent instruments. While the Functional Independence Measure (FIM) is widely used in inpatient rehabilitation facilities, the Minimum Data Set (MDS) is federally mandated for all reside nts in skilled nursing faci lities. To investigate the feasibility of creating measurement links be tween these two functional outcome instruments, this study consisted of four steps: 1) a concep tual paper reviewing linki ng methodologies and the state of the art of existing linking studies in healthcare; 2) a insp ection of the MDS item characteristics using the Rasch model; 3) an i nvestigation of whether the FIM items function similarly across different impairment groups us ing differential item f unctioning analysis (b-

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12 difference and item characteristic curve methods); and 4) an evaluation of the accuracy of the crosswalk conversion algorithm by applying Func tional Related Groups (F RGs) classification system. The item difficulty hierarchical orde r of MDS physical functioning and cognitive domains demonstrated similar patt ern to those in previous studie s related to the FIM. Several FIM motor and cognitive items were found to ha ve significant DIF across three impairment groups (stroke, amputation, and orthopedic impa irment). These incons istencies in item calibrations led to the development of separate crosswalk conversion tables for each impairment group. The validity testing the FIM-MDS conversi on algorithm resulted in mixed findings. The similarity between the actual and converted scor e distributions, relativel y strong correlations across the FIM and the MDS raw scores, and a fair to substantial strengt h of agreement when using the actual FIM scores and th e MDS derived FIM scores to cl assify individuals into FRGs, all supported the development of FIM-MDS crosswalk conver sion algorithm. However, the average of point differences betw een the actual and converted scor es were large and results from Wilcoxon signed ranks test do not support the eq uivalence of actual and converted score distributions at both individual and facility level. To improve the application of FIM-MDS crosswalk conversion algorithm in the clinical si tes, rigorous explorati on of the optimal linking methodologies, the needs for quality of test admi nistration, and rater trai ning are recommended.

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13 CHAPTER 1 THE STATE OF THE ART OF TE ST EQUATING IN HEALTHCARE Introduction A myriad of rehabilitation outcome measures have been developed over the past 50 years. These assessments typically cover such health domains as physical functioning, cognition, basic and/or instrumental activ ity of daily living, depression, pain, a nd quality of life [1]. Despite the proliferation of measurement tools, many instrume nts evaluate similar attributes. For example, more than 85 instruments currently evaluate ba sic and instrumental activ ity of daily living and more than 75 measures are available to measure quality of life [2]. While these assessments are designed to measure the same construct, scores from one instrument cannot be compared to similar scores gathered by another instrument [3]. This lack of communication across assessments seriously hampers healthcare outcomes measurement. As patients transfer from one setting to another, their information is disc ontinuous since different instruments are often specific to particular healthcare settings. The incompatibility of assessment data prohibits postacute healthcare services in monitoring and eval uating the effectiveness of intervention through the continuum of care. Furthermor e, facilities that use different instruments cannot be compared relative to their outcomes locally or nationally. Recently, several healthcare studies have at tempted to confront this measurement challenge by attempting to achieve score co mparability using test equating methodologies. Equating is a procedure used to adjust scores on test forms so that the score on each form can be used interchangeably [4]. Despite the availabil ity of numerous, well-de veloped equating methods in the field of education, few of these methods ha ve been applied in healthcare. This may be a function of lack of familiarity with the education literature, and/or the belief that educational equating methods are not applicable to equate healthcare assessmen ts. To better understand

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14 equating, a literature review co mparing the equating techniques used in education to those presently used in healthcare would provide th e critical background for future equating studies. Therefore, the purpose of this project was to 1) review equating concepts and existing methodologies in education, 2) discuss the challeng es in using these methodologies in healthcare, 3) review the state of the art of equating in h ealthcare, and 4) propose th e next critical studies necessary to advance eq uating in healthcare. The History and Concept of Equating in Education The history of equating can be traced back to the education field in the 1950s, when the excessive testing in the schools rendered the need for comparable scores between test batteries. The College Entrance Examination Board and the American College Testing Program provide an example in which many colleges have to make deci sions to enroll students, some of whom have taken one of the standard tests and some the ot her (e.g., the Scholastic Aptitude Test (SAT) or the American College Test (ACT) test batter y) [5]. For purposes of fairness in admission selection, many colleges would like to use the scores from these test batteries interchangeably. Hence, tables were developed which allow the co nversion of scores between tests from different publishers. As a result, students can take different admission tests. Using conversion tables, each colleges admissions office can be converted to a score that is considered acceptable by that college [6]. As the development and administration of na tional-wide test in education became more and more popular, standardized tests were used and administer ed throughout the United States several times throughout the year. This led to anot her challenge. Students were potentially taking the same test on multiple occasions and therefore memorizing the answers to test items. In order to guarantee the fairness of the te st and control the expos ure rate of test items, sets of test questions were built according to certain content a nd statistical test specif ications to replace test

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15 items on old forms [7]. Although multiple forms of a test are ideally constructed according to strict statistical specifications, it is still possible for these different test forms to vary in difficulty. Therefore, the equating was applied to adjust scores on different vers ions of test forms such that scores from these test forms were put onto a common metric and became comparable [7]. In 1964, some of the first stud ies on equating appeared at the Annual Meeting of the National Council on Measurement in Education in Chicago and later were published in the first volume of the Journal of Educational Measurement [5, 6, 8, 9]. Over the past few decades, as the number and variety of testing programs that used multiple test forms increased, the topic of equating became more and more popular and vita l. In 1985, the Standards for Educational and Psychological Testing, developed jointly by the American Educational Research Association (AERA), American Psychological Association (A PA), and National Council on Measurement in Education (NCME), listed equating into its index and dedicated a substantial portion of the standards to equating issues [7]. To date, various equating issues have emerged in the literature, such as different equating concepts [10-14], pr operties of equating [15], comparing different equating methods [16-18], guidance for evaluating the accuracy of equating [19], investigating test equating in the presence of differential it em functioning [20], and evaluating the effects of multidimensionality on equating [21, 22]. In 1982, Holland and Rubin published the book Test Equating [23], which included several important studi es from the Educational Testing Services (ETS). In 1995, Kolen and Brennan published Test Equating Methods and Practices [7], which provides comprehensive summaries of equating concepts, methodol ogies, research designs, and practical issues in conducting equating. As diverse equating concepts co ntinue to emerge and various equating methods continue to evolve, the subject of equating ha s become a well-defined analytical procedure. The properties of

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16 equating proposed by Lord (1980) [15] have b ecome an essential key concept in conducting equating. These properties include the following: 1) the tests to be equated should measure the same construct; 2) conditional distribution of scor es given a true score should be equal (equity property); 3) the equating relationship should be the same regardless of the group of examinees (group invariance property); and 4) the equating transformation should be symmetric (symmetry property) [15]. Based on Lords equating proper ties, equating is the processes adjusting the difficulty of the test forms that measure the same construct. The equating results should be invariant no matter which sub-samples are used to create the conversion algorithm. The equating function used to transform a score on Form X to Form Y should be the inverse from Form Y to Form X (i.e., score 35 on Form X equals to 42 on Form Y and vice versa). This property ruled out the use of regression to pr edict scores from another test scores for equating since the regression of y on x usually differs from the regression of x on y [4]. Equating methods can generally be classified ac cording to the test theory on which they are based: classic test theory (CTT) and item res ponse theory (IRT). Table 1-1 introduces the most commonly used statistical equati ng methods and related data colle ction designs that usually go with the equating methods. In CTT, equating methods usually are achieved by making assumptions about statistical properties of scor e distribution. Mean equa ting, linear equating, and equipercentile equating form the basic equating met hods in this category. In mean equating, Test X is considered to differ in difficulty from Te st Y by a constant amount. For example, if the mean of Test X was 50 and the mean of Test Y was 52, 2 points would need to be added to a Test X score to transform a score on Test X to the Test Y scale. In linear equating, the linear conversion is based on the rationa le that the same person should occupy identical standardized deviation scores on the two tests such that ) ( ) ( ) ( ) ( y y u y x x u x (where x is the scores

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17 on form X, and u(x) and ) ( x are the mean and standard deviat ion of score distribution on form X). While mean and linear equating only allow linear function, the equipercentile equating method permits a curvilinear relationship betw een two test scores and is developed by identifying scores on Test X that have the same pe rcentile ranks as scores on Test Y. It should be noted that when two test forms have different psychometric characteristics (e.g., different reliability) or when data are collected from two non-equivalent groups more sophisticated equating methods should be considered such as the Tucker method [24], the Levine method [25], frequency estimation equipercentile equating [26], Braun-Holland Linear method [26], and chained equipercentile equating method [27, 28] Angoff (1982) [29] identified more than 12 scenarios used by the Educational Testing Service, including equating formulas for equal reliable tests, unequal reliable tests as well as under di fferent research designs. Petersen and colleagues (1982) [30] summarized 22 equating models incl uding linear and non-linear models, true-score and observed score models, and described major assumptions in each scenario. Three data collection designs are frequently used with the CTT statistical equating methods to collect data for equating purpose [29]. In Table 1-1, Text X and Test Y represent two test forms of a test. Subgroup 1 and 2 represen t two samples from one population formed by random assignment, whereas Group 1 and 2 represen t two samples recruited from two different populations. Dashes (---) within the cells indica te that a specific test form was taken by a particular group. In Design a (Random Groups, One Form Admini stered to Each Group), the entire examinees are randomly assigned into two subgroups and each subgroup takes one of the test forms. In Design b (Random Groups, Both Forms Ad ministered to Each Group, Counterbalanced), the same tests are administered to all examinees If fatigue or practice effects exist, the tests are given in different order to counterbalan ce the effect. Lastly, in Design c

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18 (Nonrandom Groups, One Test Administered to Each Group; Co mmon Equating Test Administered to Both Group), diffe rent tests are given to a different group of examinees with an additional set of items (anchor tests or common it ems) administered to all examinees. The score on the set of common items could e ither contribute to the examin ees score on the test (internal anchor test) or do not contribute to the examinees score on the test form (external anchor test). To avoid different response behavior, common ite ms are supposed to be a mini version of the total test form, proportionally repr esentative of the total test fo rms in content and statistical characteristics, and occupy a similar location in the two forms [4]. For the minimum length of the anchor test, a rule-of-thumb is either more than 20 items or 20% of the number of items on any of the tests [13]. Item response theory (IRT) comprises a family of models. Each designed to describe a functional relationship between person ability measures and ite m characteristic parameters. While most CTT methods emphasize equating parallel or alternative test forms, the IRT models along with the implementation of computerized ad aptive testing have fac ilitated and extended the implementation of equating proce ss with the ability to equate an item bank (a composition of questions that develop for an operational definition of a variable/construct [31]). Because of the invariant property of IRT that the examinees abil ity is invariant with respect to the items used to determine it and item statistics under differe nt groups of examinees remain unchanged [32], IRT equating methods make it possible to ensure th at person performances are comparable even when each person responds to a unique set of item s [31]. Different test forms can be linked as long as there are common persons (who take bot h test forms), or common items (which exist across different test forms) in the dataset. This feature extends the poten tial of applying linking beyond equating parallel test forms.

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19 Prior to using IRT for equating, one needs to decide which IRT model to use. Overall, IRT models can be classified into 1-, 2-, and 3-parameter model based on the number of item parameters included in the model. The general form of 3-parameter logistic model, which includes all three parameters, can be expressed in the logistic formula: ) ( ) (1 ) 1 ( ) (i i i i i ib Da b Da i i ie e c c P where a is a discrimination parameter (a), which determines how well the item can discriminate persons with different level of abilities; b is an item difficulty parameter, which determines the difficulty of the item; and c is a lower asymptote parameter (c), which is also called the guessing parameter. The higher the a value, the more sharply the item discriminates between high and low ability examinees. The higher the b value, the more challenging the item is. The higher the c value, the greater the probability that a person can get an item correct without any knowle dge (e.g., multiple choice). In the 2-parameter IRT model, the guessing parameter (c) is set to be zero such that there is no guessing factor when a person takes a test (e.g., Likert scale from disa gree to agree). In the 1-parameter IRT model, the item discrimination (a) is assumed to be equal across all items and ther e is no guessing factor within a test. Furthermore, if the unidimensi onality assumption is violated, multi-dimensional IRT models that can handle more than one dominant person trait ( ) can be considered. The equating methods based on the IRT model require it erated computation that is usually achieved via computer software. After a person responds to a set of items, the persons ability and item parameters are estimated via an IRT mathematical model. The IRT true score equating method is one of the most commonly used equating methods under the IRT model. For the IRT tr ue score equating, the true sc ore from one test associated with a given persons latent trait is considered to be equi valent to the true sc ore from another test related to that latent trait. The equating method comprises th e following steps: a) specify a true

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20 score (X ) on Form X, b) find the latent trait (i) that corresponds to that true score, and c) find the true score on Form Y, (Y ), that corresponds to that true score (i), where X j i i i i ij i Xc b a p: , ,) ; ( ) ( the test performance on Form X and Y j i i i i ij i Yc b a p: , ,) ; ( ) ( the test performance on Form Y; p is the probability of passing an item based on a persons ability level ( ) and item parameters ( a is the item discrimination parameter; b is the item difficulty parameter; c is the guessing parameter); and j is a particular item on the test form [4]. An alternative IRT equating method is th e IRT observed score equating. After the probability of a number of correct scores for exam inees of a given ability level are computed, the observed score distributions then are cumulated over a population of examinees across the entire person ability spectrum. This can be achieved by an integration function to obtain the cumulated observed score distributions, while some co mputer programs (e.g., BILOG [33]) output a discrete distribution on a finite number of equa lly spaced points. After generating an estimated distribution of observed score di stribution for each form (e.g., Fo rm X and Form Y), both score distributions then are rescaled and equated using conversiona l CTT equipercentile equating methods. Kolen and Brennan (2004) have provided detailed exam ples for conducting true score and IRT observed score equating [4]. Two data collection designs commonly use with IRT equating me thods include the common-item equating and the common-person equa ting (Table 1-1) [34]. In common-item equating, the two tests share items in common where individuals take tests that include additional common items to all test forms. For example, McHorney and Cohen (2000) [35] used common-item equating to equate a survey of func tional status items where a set of unique items was included on each of three forms and a set of common items was administered to all groups. As for common-person e quating, common persons take both tests of different items that are

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21 designed to measure the same construct. For in stance, Fisher et al. (1995) [43] created a statistical link between the Functional I ndependence Measure (FIM) and the Patient Evaluation Conference System (PECS) ) where pa ired assessments (both FIM and PECS) were collected within a certain period of time. Sin ce the common items or persons are the only link between different test forms, choosing of the linking items/persons becomes a critical issue. Smith (1992) [38] suggested to select items th at are around average person ability level (i.e., avoid too challenging or extremely easy items) and the linking items should spread across a range of person ability spectrum. Meanwhile, th e common items/persons between different test forms should be evaluated for their response pattern Misfit items/persons that misrepresent the response pattern may lead to inappropriate shifti ng constant for equati ng and should be removed from the linking process [38]. Equating: Education versus Healthcare There are major differences between equati ng studies in education versus that in healthcare. In education, the common purpose of equating is to devel op conversions between different versions of an examination. At pres ent, many tests administ ered by ETS today use a new version of a test at each major administration (such as th e Graduate Record Examination (GRE), Test of English as a Foreign Language (TOEFL), and the Scholastic Aptitude Test (SAT). The alternative forms or different versio ns of a test are usually developed with the guidelines to ensure common content and consistent statistical characteristics. These alternate forms are embedded within the national exams and implemented while students or applicants are taking the tests. Nation-wide administrations readily provide large sample sizes as well as sample randomization (which is needed in some equating methods). Lastly, there ar e follow up studies to monitor and check the accuracy and stabi lity of the equating algorithm longitudinally.

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22 In contrast to educational tests, healthcar e equating has a quite different purpose. In health care, many functional measures have been developed or are used in healthcare settings. While those assessment tools are developed to measure the same construct, they are built differently in many aspects, including the num ber of items, rating scale categories, item definitions, or item formats (such as self-report or performance test). Since decisions to equate or link instruments in healthcare occur after individual instruments have been developed, psychometricians have to confront the inherent differences that exist between instruments. Several healthcare studies ther efore created item-to-item c onversions based on instrument manuals and subjectively decided upon by expert panels. Moreover, while equating is a specific term referring to linking scores on alte rnate forms of an assessment that are built according to similar content and statistical specif ications [11, 12], most of the test equating studies in healthcare do not belong to this category. Linking which is defined more broadly as a scaling method used to achieve comparability of scores from two different tests, may be considered a better term equating for existing as sessments in healthcare. Table 1-2 compares equating procedures in e ducation and healthcare. State of the Art of Equati ng Studies in Health Care Expert Panel Equating Linking instruments in healthcare have genera lly focused on creating a translation between each item on the instrument. Studies by Williams et al. (1997), Nyein et al. (1999) and Buchanan et al. (2003) represent examples where the e quating of two scales wa s attempted by matching and rescaling each item across the two instru ments [36, 39, 40]. In 1997, Williams and his colleague [36] created the cr osswalk between the Functional Independence Measure (FIM) and the Minimum Data Set (MDS) using an expert pane l. MDS items were first chosen and rescaled into pseudo-FIM items to correspond to similar FIM items (e.g., eating-FIM to eating-MDS,

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23 bathing-FIM to bathing-MDS). Since pseudo-FIM items could only be defined for 12 of the 18 FIM items, this procedure resulted in 8 motor and 4 cognitive items (out of the original 13 motor items and 5 cognition items) included in the anal ysis. Furthermore, the conversion algorithm was based on item-to-item rating scale category comp arison. For example, if the expert panel suggested that rating 3 (limited assistance) of a 5-level MDS ite m plausibly corresponded to FIM rating 4 (minimum assistance) of a 7-level FIM item, the MDS rating 3 was rescored as 4. The final rating scale was determined by agreement between two or more (out of seven) panel members. With the criteria of FIM and MDS assessments occurring within 2 weeks, 173 rehabilitation patients with paired FIM and MDS scores were recr uited from nursing home rehabilitation by therapists and nurses. Intraclass correlation coefficients between the FIM and Pseudo-FIM motor and cognitive subscales were bot h .81. The reported correlation coefficients provide an indication of how well scores of one instrument can be predicted from scores of the other instrument and indire ctly imply how well the conve rsion algorithm may work. Using similar strategies, Nyein et al. (1999) [39] investigated the feasibility of whether a Barthel score can be derived from the motor ite ms of the FIM. Based on examination of both manuals, conversion criteria were developed by researchers via item-to-item rating scale conversion. As a result, 7-point rating scale FIM items were c onverted to corresponding 4-point rating scale Barthel Index items. Following the development of the conversion algorithm, a sample of 40 patients was assessed for Barthel and FIM by a multidisciplinary team. The FIMbased derived Barthel score was compared with the actual Barthel score. Absolute agreement between the converted and actual sc ores ranged from 75 to 100% a nd the kappa statistical values ranged from 0.53 to 1.0 (moderate to s ubstantial strength of agreement).

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24 Another study using expert panel to crea te the conversion system item by item is by Buchanan and colleagues in 2003 [40]. These inve stigators attempted to develop a translation between the FIM and the Minimum Data Set for Post-Acute Care (MDS-PAC). The development of translation began with comparing the mean FIM and MDS-PAC motor scale score differences and mean FIM and MDS-PAC item score differences To improve the comp arability between the FIM and the MDS-PAC, the scoring for MDS-PA C ADL items was changed (six-point rating scale was rescaled to eight-point rating scale) and FIM-like items were created. Over 3,200 FIM and MDS-PAC pairs of data were collected from fifty certified rehabilitation facilities by trained clinicians. While these initial attempts at linking are en couraging, the methodological and statistical approaches used had considerable limitations. For example, a draw back of using the expert panel or reviewing the manual instructions to deve lop the conversion algorith m is that such an approach is not statistically base d. Although the approach is intuitiv e, it is subjective. Different algorithms could be developed based on the di fferent experts bac kground and experience. Furthermore, it is rare to find an exact one-t o-one relationship across items from different instruments. Consequently, rese archers must revise, combine or develop supplement items to equating instruments. These modi fications not only invalidate th e psychometric properties of the original instruments but also interfere with the in tegrity of the instruments. As evidenced in the educational literature, equati ng does not require item-to-item relationship but based on the rationale that both set of items ar e measuring the same construct. Equating an Item Bank Several healthcare studie s have used IRT methods to link different test forms [3, 35, 41, 42]. This methodology is founded on the basis that it ems from different instruments that measure the same construct can be placed on a common scal e. Instead of viewing each instrument as an

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25 independent measure, items from similar questionnaires can be c onsidered part of an item bank intended to measure the same construct [35]. In 2000, McHorney & Cohen [35] sampled 1, 588 items from different functional status instruments to assure sufficient items allocated across the continuum of hypothesized construct. Two hundred and six items were selected and re vised to meet standard criteria for question design. Common-item equating was used with a se t of common items admini stered to all groups and a set of unique items was embedded in each of the 3 forms. After obtaining item parameter estimations from a concurrent run (estimating a ll item parameter simultane ously in a single run) using a 2-parameter IRT model, a functional status item bank was established with all the items placing on a common scale. The result was a functiona l status item bank with items scaled onto a common metric. The authors provided no conversi on tables or evaluati on of the accuracy of equating. Rasch Equating Method Currently, there are only few equating studies in the healthcare field that developed the instrument-to-instrument crosswalks. These e quating studies all used the Rasch model (1parameter IRT model) to perform the equating procedure [43-45]. Emerged in the early 1960s through George Raschs work [46], the Rasch mode l is a probabilistic mathematical model that assumes the probability of passing an item depends on the relationship between a persons ability and an items difficulty. Being the most parsim onious model in the IRT family (compared to more complicated 2and 3-parameter IRT models), early studies in healthcare have tended to employ the Rasch model rather than other higherorder IRT models (2a nd 3-parameter) [47]. Fisher and colleagues (1995) [43] were the firs t to use Rasch true score equating method to create a crosswalk between 13 FIM motor items and 22 motor skill items from the PECS. Fiftyfour consecutive patients admitted as inpatients were rated on both the FIM and the PECS by

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26 trained rehabilitation professionals. Items from both instruments were initially co-calibrated, analytically treating the 35 physical functioning items as one instrument. The co-calibration placed the items from both instruments onto a common metric with a common origin. Then, each instrument was analyzed separately, anchoring the item and rating scale calibrations to those obtained from the co-calibrated analysis. Follo wed by the separate analyses, converting from FIM to PECS and vice versa was achieved by conn ecting FIM raw scores and PECS raw scores to corresponding person ability measures. A PECS/FIM rehabits crosswalk table was presented. The Pearson correlation of the personal measures produced by the separately anchored FIM and PECS items was 0.91. To enhance and further inve stigate the equating results, Smith & Taylor (2004) [45] replicated the Fishers study with larger sample size and modified research design. Approximately 500 subjects were recruited in this study (comparing to 54 subjects in the Fishers study) with diagnostic groups more representative of the rehabili tation population. Rehabilitation professionals were trained prior to data coll ection. To prevent ambiguity, FIM walking and wheelchair mobility items were calibrated separate ly as two separate items. Similar to Fishers study, the conversion crosswalk was achieved using Rasch true score equating with both FIM and PECS items co-calibrated and anchored in separate analyses. Similar to the findings of Fisher and colleagues, person ability measures estimated by separate FIM and PECS items correlated at 0.92. Fisher and his colleagues further used Rasch true score equating to link other healthcare instruments. In 1997, Fisher and his colleagues [44] equated 10 items of physical functioning (PF-10) and 29 items from the Louisiana State Un iversity Health Status Instruments (LSU-HSI) based on a convenience sample of 285 patients. The person ability measures estimated from

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27 these two instruments correlate d 0.80. Conversion tables were provided for tr anslating raw scores from one instrument to the other via a common metric. Furthermor e, Fisher (1997) [48] published a theoretical article which provide d a framework for linking physical function measures by reviewing more than 30 Rasch st udies of physical func tion measures. Fisher suggested that the difficulty hier archy of physical func tioning tasks was affected by two factors: 1) the extent of involvement of upper and lowe r extremities in coordinated activity and 2) the amount of strength needed. Items that require extensiv e coordination and strength of upper and lower body, such as walking, usually appear to be the most challenging items. Feeding and grooming, which only require strictly upper extr emity functions, were usually found the easiest tasks. Transfer activities, involving moderately coordinating both upper and lower extremities, are of medium difficulty. Besides, bowel and bladder management, which involves an involuntary muscle control com ponent, usually will fail to fit the Rasch measurement model. Based on the above consistencies across instrume nts designed to measure physical functioning, Fisher further supported that the development a nd deployment of a universal rehabits metric was a realizable goal. As for measuring cognitive functioning, Cost er and colleague (2004) [42] also supported the feasibility of constructing a meaningful outcome measure to assess cognitive functioning in daily life. They found the majority of items ( 46/59) could be located along a single continuum when performing a Rasch analysis across cognition items from several widely used instruments including the Activity Measure fo r Post-Acute Care, the Medical Outcomes Study 8-Item ShortForm Health Survey, the FIM instrument, the MDS, the MDSPAC, and the Outcome Assessment and Information Set (OASIS). Mean while, they found about 25% of the convenience sample (out of 477 patients receiv ing rehabilitation serv ices) were at ceiling and relatively few

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28 people performing at the low end of the difficulty scale. Table 3 summarizes the equating studies in healthcare field. Next Critical Studies for Advan cing Linking in Healthcare To achieve more accurate and consistent e quating results and thereby advancing linking studies in healthcare, more rigorous research designs are needed. Su ccessful linking involves equating methods selection, and the conversion cr osswalk validation. Researchers who intend to conduct linking studies should examine the psychome trics of the instruments to be linked and be cognizant of the different test administration pr ocedures. Different equa ting methods including CTT and IRT should be examined to obtain optima l equating. Moreover, current linking studies in healthcare have attempted to develop a sing le conversion algorithm for all patients. Since health care includes diverse dia gnostic groups, group invariance shoul d be investigated. That is, a critical question is whether separate conve rsion tables/algorithms should be created for different diagnostic groups or wh ether a universal conversion tabl e/algorithm is adequate. This could be achieved by investigating whether items function similarly acro ss different diagnostic groups or by comparing the conversion algorithms created based on each diagnostic group. A major limitation of existing linki ng studies in healthcare is th e lack of inve stigation of the accuracy of the linking results and insufficien t reporting on how to interpret the converted scores. Follow-up validation studies would provi de valuable information for researchers, clinicians, administrators (conversion accuracy), and policy-makers (cost-efficiency) an insight to evaluate the application of linking in clinical sites. Without validation analyses, applications of the conversion algorithm can be challenged. To date, only tw o equating studies in healthcare have investigated the validity of their convers ion tables. Nyein and his colleagues (1999) [39] evaluated their Barthel-FIM conversion syst em in a prospective study of 40 subjects. Nonparametric statistical techniqu es were used to evaluate th e correlation between the derived

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29 Barthel score and the actual Barthel score (S pearman rank correlation) and percentage of absolute agreement (Wilcoxon signed rank test). A high correlation (Spearmans rho= 0.99) and absolute agreement ranging from 75 to 100% we re found to confirm the conversion criteria. Buchanan et al. (2003) [49] evaluated their FI M-(MDS-PAC) conversion system by using actual FIM score and converted FIM score from MDS-PA C to classify approximately 3,200 subjects into case-mix groups (CMG), a pr ocedure to compute th e medical payment. Percentage of cases that mapped into the same CMGs by actual FI M score and converted FIM score from MDS-PAC were computed. The FIM and PAC-to-FIM scales mapped 53% of cases into the same CMG; approximate 84% were classified wi thin 1 CMG and 93% within 2 CMG. Equating studies in healthcare requires rigo rous and systematic follow-up studies to validate the conversion crosswal ks. We propose that crosswalk validation phase should be investigated at two levels. First, the conversion crosswalk should be validated at the patient level. For example, one may ask how accurate is the conversion algorithm in terms of predicting a patients score from the other in strument. That is, do the conver ted and actual scores classify patients similarly? If the converted scores ar e found to be accurate within reasonable error, which require further definition, the conversi on algorithm may be used to track and monitor patients status through different healthcare settings. Second, th e conversion algorithm could also be validated at the sample level. For example, how accurate is the conversion algorithm in terms of group equivalence? Is the mean of the converted score distribu tion equivalent to the mean of the actual score distribution? If the conversi on crosswalk could reach group equivalence, the conversion algorithm may be valuable in comparing facility-level outcomes. Lastly, a limitation in present healthcare linking studies is small sample sizes. Kolen (1990) notes that less equating erro r can be anticipated with large sample size (e.g., sample sizes

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30 greater than ***) [50]. Large sa mples would also imply better re presentations of the population. Equating studies in education co mmonly involve large samples. For example, Kingston et al. (1986) [51] used 4,000 subjects to equate the Graduate Record Examination (GRE) via both CTT and IRT methods; Yin et al. (2004) [52] used 8,600 to link the American College Test (ACT) and ITED (the Iowa Tests of Educational Develo pment) via linear and equipercentile methods; and Dorans et al. (1997) [53] and Pommerich et al. (2004) [54] used approximately 100,000 subjects to the equate the ACT and the Scholastic Aptitude Test (SAT)). Sample sizes of 400 are suggested for Rasch model equating and 1,500 for 3-parameter IRT equipercentile equating [4, 19]. However, a sample size of less than 500 subjects is common for equating studies in healthcare [36, 43, 44]. Researchers who intend to conduct equating st udies may take advantages of existing healthcare databases. Several instruments related to functional outcomes are either extensively used or federally mandated across the post-acute healthcare settings, for example, the FIM for inpatient and sub-acute rehabilitation facilities, the MDS for skilled nursing facilities, and the OASIS for home health care. Using existing databa ses, researchers may be able to obtain large sample sizes across diverse diagnostic patients Moreover, a critical question is whether prospective studies are the best means of creating and validating crosswalks. Prospective studies may not produce the type of data that will be us ed in real-world applications of equating in healthcare. That is, the quality of healthcare data is likely to be influenced by the context of the demands and challenges of day-to-day reha bilitation services. Existing clinical and administrative databases may provide the data that are most relevant to everyday applications of crosswalks in healthcare.

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31 A key to improve clinical care in healthcare is to develop an effective and efficient mechanism to evaluate and track changes of patients status acro ss the continuum of care. While utilizing a single outcome assessment instrument would provide the optimal mechanism for the synchronized and seamless monitoring of patient out comes, the use of different instruments is already firmly entrenched across these reha bilitation settings. Us ing rigorous equating methodologies, researchers may overcome the cha llenges inherent in comparing patients and facilities that use different outcomes measures. The establishment of th e crosswalk conversion algorithms may provide an economical means of monitoring patient progress and comparing facility outcomes across the continuum of care. Research Question The proposed study was funded by Dr. Velo zos VA Rehabilitation Research and Development Project, 03282R, Linking Measures across the C ontinuum of Care (October 2003 to March 2006). The main purpose of the project wa s to develop crosswalk tables/algorithms that link scores and measures from the FIM and th e MDS. It is based on the hypothesis that the functional status items of the FIM and the MDS are subsets of items along two constructs: an ADL/motor construct and a cogni tion/communication construct. Many studies have provided evidence that FIM has good psychometric properties in terms of reliability [55-64] and validity [65-69]. While not as extensively studied as FIM, evidence suggests that the MDS has adequate psychometric properties for use in re search purposes [7074]. Several studies have used Rasch analysis to investigate the FIM at the item level [48, 7578]. However, MDS instrument lacks such studie s. To the authors knowledge, there has been only one published study, by Williams and his colleagues [36], that has attempted to create the FIM and MDS crosswalk by expert panel. Instea d of using non-statistical based expert panel method to build the FIM-MDS crosswalk, Dr. Velo zo applied the Rasch tr ue score equating to

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32 develop the crosswalk conversi on algorithm between these two instruments. Two conversion tables, each for one construct (ADL/motor and c ognition/communication), were created. In 2004, Dr. Byers, a former student of Dr. Velozo, pe rformed a cross-validation study to evaluate the accuracy of the conversion tables at the patient level. Point di fferences between the actual and converted FIM/MDS scores were computed and the score distributions between the actual and converted scores were compared. In this chapter, several equa ting/linking methodologies commonly used to conduct equati ng/linking and the state of the art of existing test equating studies in healthcare were reviewed. The proposed studies are a logical exte nsion of this review and Dr. Velozo and Byers FIM-MDS linking research. Research Question 1 What are the item-level psychometrics of th e MDS in terms of physical functioning and cognitive domains (e.g., dimensionality, item difficul ty hierarchical order, rating scale structure, item-person targeting, and other item statistical properties)? Research Question 2 Do the items statistically function consisten tly across different diagnostic groups so that only one crosswalk is required or do inconsistencies in item calibrations mandate developing separate crosswalks (e.g., one for each impairment group)? Research Question 3 What is the accuracy of the crosswalk? How accurate is the crosswal k at individual level in measuring individual patients, at classification level in clas sifying patients into the same classification system, and at sample leve l in comparing the f acility outcomes?

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33Table 1-1. Educationa l Equating Methodologies A-1 Common Equating Me thods Based on CTT Equating Methods Descript ion of Equating Methods I. Mean Equating Under the mean equating, Test X is considered to differ in difficulty from Test Y by a constant amount along the score scale. Under equal reliable tests: ) ( ) ( y u y x u x II. Linear Equating In linear equati ng, the linear conversion is define d by setting standardized deviation scores (z-scores) on the two forms to be equal. ) ( ) ( ) ( ) ( y y u y x x u x III. Equipercentile Equating For the equipercentile equa ting, the equating function is developed by identifying scores on Test X that have the same percentile ranks as scores on Test Y. A-2 Common Data Collection De sign Usually Accompany with CTT Equating Methods (a) Random Groups, One Form Administered to Each Group (b) Random Groups, Both Forms Administered to Each Group, Counterbalanced (c) Nonrandom Groups, One Test to Each Group; Common Equating Test Administered to Both Groups Design A Test X Test Y Subgroup1 ------------------Subgroup2 ------------------Design B Test Test Subgroup1 ------------------------------------Subgroup2 ------------------------------------Design C Test X Test Y Test V Nonrandom Group1 ------------------------------------Nonrandom Group2 ------------------------------------Test X Test X Test Y Test Y

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34Table 1-1. Continued B-1 Common Equating Methods Based on IRT Equating Methods Descript ion of Equating Methods I. True Score Equating Under the true score equati ng, the true score on one form associated with a given person latent trait ( ) is considered to be equi valent to the true score on another form correspond to that latent trait. The equating procedure involves specifying a persons true sc ore on Test X, finding the corresponding to that true score, and finding the tr ue score on Test Y via the same II. Observed Score Equating IRT observed score eq uating uses the IRT model to produce an estimated distribution of observed nu mber-correct scores on each form, which then are equated using equipercentile methods. B-2 Common Data Collection Design Usua lly Accompany with IRT Equating Methods ( a ) Common Items Design ( b ) Common Person Design Test items Test items Persons1 Persons2 Persons3 Persons4 Persons5 Persons n |-------------------------| |-------------------------| |-------------------------||--------------------------| Common Item |-------------------------||--------------------------| Common Item |-------------------------| |-------------------------||--------------------------| Common Item |-------------------------| |-------------------------||--------------------------| Common Item |-------------------------| |-------------------------| |-------------------------| |-------------------------| |-------------------------| |-------------------------| |-------------------------| | |-------------------------| |-----------------------------| |-----------------------------| |-----------------------------||-----------------------------| Common Person |-----------------------------||-----------------------------| Common Person |-----------------------------| |-----------------------------||-----------------------------| Common Person |-----------------------------| |-----------------------------||-----------------------------| Common Person |-----------------------------| |-----------------------------| |-----------------------------| |-----------------------------| |-----------------------------| |-----------------------------| |-----------------------------| Test B Items Test A Items Test A Items Test B Items

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35 Table 1-2. Education versus Healthcar e Differences in Equating Procedures Education Healthcare 1) The decision of equating or linking usually occurred before developing different test forms 2) Tests being equated had the same question format, length, and rating scale (usually multiple choice) 3) Data collection is embedded in national-wised exam while applicants take the real test 4) Conduct one or more statistical equating methods and compared the results 5) Evaluate the results of equating including the accuracy and stability 1) The decision of equating or linking occurred after individual instruments were developed and implemented in clinical settings 2) Assessments being equated often have different question format, length, and rating scales (such as Likert scale) 3) Data collection usually is conducted via perspective studies from a convenient sample 4) Many studies use subjective expert panel for item-to-item conversion and usually only one equating method is used 5) Often no follow up studies evaluating the accuracy and/or stability of equating

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36Table 1-3. Review of Linki ng Studies in Health Care First Author Year Instruments Data Source Procedure to Create Conversion Tables/Algorithm Results Conversion Algorithm Validation/ Evaluating Fisher (1995) [43] FIM-PECS Free-standing rehabilitation hospital N=54 Rasch true score common-person equating The correlation (Pearsons R) of the measures produced by the separately anchored FIM and PECS items was 0.91 PECS/FIM Rehabits conversion table None Williams (1997) [36] FIM MDS Six nursing homes By trained clinicians N=173 Expert Panel these experts were asked which items (or groups of items) from the MDS were most comparable to each of the 18 FIM items One-way conversion algorithm: derive a MDS score from the FIM FIM motor [Reliability]: Cronbach = 0.89 [Correlations between actual and converted scores] Spearman Brown intraclass correlation r =0.81 Pearsons correlation r =0.728 Item-to-item conversion criteria None Fisher (1997) [79] SF10 (LSUHSI) A convenient sample in a public hospital medicine clinic N=285 Rasch true score common-person equating The correlation (Pearsons R) of the measures produced by the separately anchored FIM and LSU-HIS items was 0.80. PF-10: Item separation reliability= 0.99 LSU HIS: Item separation reliability = 0.90 Two true score conversion table (i.e., raw score to person measure to raw score on the other instrument) None Fisher (1997) [48] Review more than 30 articles of physical functioning scale N/A Review articles Rasch pseudo-common item equating Support the quantitative stability of physical functioning construct across instruments and samples N/A None

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37Table 1-3. Continued Nyein (1999) [39] FIM Barthel N/A Review Manuals [Manual] The conversion criteria were established by careful examination of the Barthel Index and FIM manual One-way conversion algorithm: derive a Barthel score from the FIM Spearmans rho =0.99 Item-to-item conversion criteria Prospective study with 40 brain injury subjects McHorney (2000) [35] Item bank with 206 ADL and IADL items Survey of outpatient clinics of VAMC N=3,358 2-parameter IRT common-item equating Put all items onto a common metric Equating items parameters None McHorney (2002) [3] Nineteen common items and 2 sets of supplemental item that measure functional status Secondary data analysis N=4,655 2-parameter IRT common-item equating Put all items onto a common metric Equating items parameters None Jette (2003) [41] FIM, MDS, PF-10, and OASIS Patients drawn from six health provider network in Boston area N=485 Concurrent run via Rasch model Put all items onto a common metric None None Buchanan (2003) [40] FIM (MDSPAC) 50 rehab facilities By trained clinicians N> 3000 Study Team The conversion algorithm was decided by the study team item-by-item. Additionally, rating scales were modified and supplement items were added. One-way conversion algorithm: from the MDS-PAC items to FIMlike items Mean difference between actual and converted score for each item ranges from 0.5 to 1.5 points Item-to-item conversion criteria with modified rating scale and supplement items Factor Analysis Regression Analysis

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38 Table 1-3. Continued Buchanan (2004) [49] FIM (MDSPAC) 50 rehab facilities By trained clinicians N=3200 The same as previous study (Buchanan, 2003) The mean difference between the FIM and MDS-PAC motor scales translations were 2.4 with scale correlations of .85. Payment cell classification using FIM data agreed with that using MDS-PAC data only 56% of the time. Twenty percent of the facilities experienced revenue shifts larger than 10% The same as previous study (Buchanan 2003) CMG and payment comparison Smith (2004) [45] FIM-PECS Freestanding rehabilitatio n hospital By usual and trained clinicians N=500 Rasch true score common-person equating Person interval measure correlation is 0.92 Score conversion tables None Coster (2004) [42] FIM, MDS, MDS-PAC, and OASIS Convenience sample of patients receiving rehabilitation services N=477 Concurrent run via Rasch model Put all items onto a common metric None None

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39 CHAPTER 2 RASCH ANALYSIS OF THE MINIMUM DATA SET (MDS) ON THE PHYSICAL FUNCTIONING AND COGNITION DOMAINS Introduction According to the U.S. Census Bureau, there ar e more than 36.6 million individuals in the United States at age 65 and over, and this population is projected to be more than three times as many in 2050 as today [80]. The increasing ag e of the population is accompanied by a greater number of people living with ch ronic disease including functiona l limitations and disabilities [81, 82]. Based on the Center for Disease Controls health statisti cs report, 34 percent of the elderly population have activity limitations cause d by chronic conditions and 6.3 percent need help with personal care [83]. Cognitive impair ment, which is also common among the elderly people, was associated with a higher risk of functional decline and with a poor functional recovery [84]. Cognitive impairment also has an impact on the ability to perform activities of daily living (ADLs) and is associated with in creased cost of care for elderly people [85]. Nursing homes are a critical environment for tracking the health care status of the elderly population. Individuals who cannot ta ke care of themselves because of physical, emotional, or mental problems may choose or be pl aced in skilled nursing facilities (SNFs) Currently, there are 1.6 million residents living in nursing homes a nd their average length of stay is approximate 892 days [86]. More than 90 percent of current re sidents are 65 years of age or older and most residents require assistance in multiple activities of daily living [87]. Reports estimate that about 40 percent of nursing home residents need help with eating and more th an 90 percent require assistance with bathing [88]. To improve the quality of care in the SNFs, th e Centers for Medicare & Medicaid Services (CMS) developed a resident assessment instrume nt (RAI) in 1990 to assess and plan care for residents in long term care facili ties [89]. In 1998, with the regulations and the introduction of a

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40 prospective payment system, skilled nursing faciliti es are required to complete and transmit RAI data to the state for all resident s whose stay is covered by Medicare. As a central assessment core in the RAI, the Minimum Data Set (MDS) covers 18 clinically important domains. With approximately 450 items in a fully comprehensive assessment and about half of items needed to be completed during a quarterly assessment, the MDS gathers abundant resident background information for designing care plans, evaluating quality of care, and further monitoring the impact of policy changes [71, 89]. Numerous studies have inves tigated the psychometric prope rties of the MDS. Several reliability and validity properties of the MDS incl uding the inter-rater reliability [71, 72], testretest reliability [90], rater ag reement [71, 91], concurrent valid ity [92, 93], responsiveness [93], and dimensionality [71] have appeared in the li terature. Many studies su pport the reliability and clinical utility of the MDS items and suggest MD S data should be used for research purposes [70-73]. Hawes (1995) [74] reported that MDS items met a standard for excellent reliability in areas of functional status such as ADLs, con tinence, cognition, and di agnoses with intraclass correlation of 0.7 or higher. Casten and collea gues (1998) [71] found high correlations between the raters for each index (Cognition r = 0.80; ADL r = 0.99). Snowden et al. (1999) [93] showed that the MDS cognition scale corr elated with the Mini Mental State Examination (r = 0.45) and the ADLs scale correlated with the Dementia Rating scale (r = 0.59). However, the MDS has been criticized for being semi-str uctured rather than having sta ndardized interview procedures and for having multiple fields requiring information [74, 94]. Through the Nursing Home Quality Initiative (NHQI) in November 2002, the CMS continues to work with measurement experts to improve the quality of measures for nursing home facilities. For better understanding of health care instruments, it is central to document the

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41 psychometric properties of these assessments. Findings from these analyses may be suggestive of revision of the instrument, which is consistent w ith the commitment from the CMS to continue to revise and improve the RAI for care planning. Above-mentioned psychometrics analyses all focus on reliability and validity at the total-score le vel of the MDS. An alternative approach is to inspect the rating scale structur e and examine underlying psychomet rics of the MDS at the item level. A myriad of studies have used Rasch analysis to examine and refine instruments in the health related field [95-101]. However, there ar e no published studies that have applied Rasch analysis to explore the psychomet ric properties of MDS items. As a step to continue to build on the existing psychometrics studies related to th e MDS instrument, the pur pose of this study was to assess the physical functioning and cognitive domains of the MDS using Rasch analysis. Methods Sample A secondary, retrospective anal ysis using MDS data from a database collected by the Veteran Affairs (VA)s Austin Automation Ce nter (AAC) from June 1, 2002 to May 31, 2003 were used for this study. This is also the data set used in the VA Rehabilitation Research and Development Project, 03282R, Linking Measures across the C ontinuum of Care. The main purpose of that project was to de velop crosswalk tables/algorithms that link scores and measures from the Functional Independence Measure (F IM) and the Minimum Data Set (MDS). VA FIM and MDS data reside in two databases at the VAs Austin Automation Center (AAC). Data from both databases (the Functional Status and Outcomes Database (FSOD) and the Resident Assessment Instrument Minimum Data Set (R AI-MDS)) were downloaded and merged on the basis of social security numbers. In order to minimize the impact that change in a patients condition could have on FIM and MD S scores, data were restricted to those that involved those

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42 subjects whose FIM and MDS assessment dates were within 5 days of each other. Data with any missing values in FIM and MDS items were excl uded. Individuals with stroke, amputation or orthopedic impairments were selected for analys is. The dataset comprised a total sample of 654 records (302 stroke, 113 amputation, and 239 orth opedic impairment). The average age of this sample was 68 12 years, 96.6% were male, 74.2% were white, and 46.7% were married. The average difference between FIM and MDS assessme nt dates was approximately 2.85 days. Table 2-1 provides the demographic baseline characteri stics and information on impairment categories. This study was approved by the Institutional Review Board at the University of Florida and the VA Subcommittee of Human Studies. Access to VA MDS data was approved by Department of Veterans Affairs, Veterans Health Administration. Resident Assessment Instrument Minimum Data Set (RAI-MDS) The RAI-MDS database contains a core set of clinical and functional status elements (MDS), triggers, and 18 Resident Assessment Pr otocols (RAPs). State Veterans Homes (SVH), which are funded by the VA and also participate in the Medicare and Medicaid, are required to collect residents information for care pla nning and transmit MDS data to the Centers of Medicare and Medicaid Services (CMS). The physical functioning items are embedded in section G of Physical Functioning and Structural Problems section of the MDS. It cons ists of items intended to measure residents activity of daily living such as bed mobility, transferring, dre ssing, locomotion, eating, hygiene and bathing. All items have a 5-point rating scale ranging from (independent) to (total dependence) with lower scores re presenting higher level of performance. If the activity did not occur during the entire 7 days, the rater is instructed to score an (activity did not occur). In this study, instead of treating the MDS rating scale category of as missing values, this

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43 category was recoded to a (tot al dependence). It is based on the rationale that the most likely explanation of an activity not being observed during the entire observa tion period is due to incapability of performi ng such tasks [40, 41]. The cognition/communication items are embe dded within section B (Cognitive Patterns) and section C (Communication/Hear ing Patterns). These items are used for evaluating residents memory, perception/awareness, cognitive skills for daily decision making, and communication performance. The rating scale structure of th e cognition/communication domain varies across items, which include dichotomous to polytomous ra ting scales with four rating scale categories. Table 2-2 presents all the items and rating sc ales of MDS items used in the analysis. Administration of the MDS When the resident is admitted to a facility, the Registered Nurse Assessment Coordinator and the interdisciplinary team (e.g., physician, nu rsing assistant, social worker, and therapist) have a 14 day observation period to comple te the admission assessment. After the MDS assessment is completed, the Resident Assessment Pr otocol is reviewed to identify the residents strengths, problems, and needs for future ca re plan. Followed by an initial comprehensive assessment, a quarterly assessment is mandated 90 days after the initial assessment and an annual assessment is required to be completed no more than 366 days from the date of the prior comprehensive assessment. Furthermore, the staff must complete additional assessments when a resident is discharged or has significant change. Due to the la rge amount of paperwork, some facilities hire MDS contract nurses to complete the records based on information provided in the residents charts [93]. Rasch Analysis Rasch analysis (partial credit model) using the Winsteps pr ogram [version 3.16] [102] was used to evaluate the MDS physical functioning and cognition/communication items. The Rasch

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44 model (also called a one-parameter logistic item response theory model) is a probabilistic, mathematical model that assumes the probability of passing an item depending on the relationship between a persons abi lity and an items difficulty. It is based on the concept that data must conform to some reasonable hierarchy of less than/more than on a single continuum of interest [34]. By inspecting persons responses in which items are relatively more difficult or easier to endorse, the Rasch model derives person s ability measures. Similarly, the Rasch model establishes the item difficulty hierarchical or der by maximizing the likelihood of persons responses on a set of items. Persons will have a higher probability (> 50%) of succeeding on easier items; and a lower probability (< 50%) of succeeding on harder items. The basic form of the Rasch model can be explained by a probability equation ln (Pnik / Pni(k 1)) = Bn Di Fk [34] The left side of the equation is the logarithm function (ln is the natural logarithm which uses e = 2.718 as the base). Pnik is the probability that person n encountering item i would be observed in category k. By taking the probability of passing rating category k ( Pnik) divided by the probability of passing one less rating category k-1 ( Pni(k-1)), it computes the odds ra tio of passing the rating category from k related to k-1 le vel. The log transformation then turns ordinal-level data into interval-level data where the probability of passing the rating scale at the next higher level can be a conjoint measurement of the person ability (Bn), item difficulty (Di) and the step category between the rating categories (Fk). The unit of measurement that results when the Rasch model is used to transform raw scores into log odds ratios on a common interval scal e is called the logit [34]. The Rasch model has several advantages over the traditional classical test theory. First, besides exploring the data at the test level (e.g., reliability and validity), the Rasch model can

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45 inspect the data at the item level, including it em difficulty, rating scale structure and whether response patterns fit the expected measurement m odel. Second, the item parameters are invariant no matter which subgroups of sample are used (sample-free). Third, the person ability is estimated independently of the pa rticular set of items that ar e administered to the examinee (scale-free). Lastly, items in the instrument ar e reported on the same scale as ability scores, which enable an investigation of how well the ite m difficulties match with the sample abilities. Sample Size Requirement for Rasch Analysis One advantage of using the Rasch model is that relatively small sample sizes are required. Hambleton (1989) [103] suggested that a sample size of approximately 200 is adequate for studies of health-relate d quality of life using the Rasch model, whereas larger sample sizes greater than 500 may be required to obtain st able item parameter estimates with the twoparameter item response theory model. For polytomous rating scale questionnaires, Linacre (1999) [104] recommends sample sizes that result in at least 10 observations per rating-scale category to ensure certain accuracy a nd different levels of precision. Analysis Dimensionality Many measurement experts believe that meaningful objective measurement can only be achieved if each item contributes to measurement of a single attri bute [105]. Therefore, factor analysis (FA) was used to examine the dimensiona lity of the instrument. FA is a technique that can be used for dimension deduction [106]. The common factor model assumes that the observed variance is attributable to common factors a nd a single specific factor A determination of whether the scale is unidimensiona l is investigated by interpreting the factor loading matrix (the correlations between the original variables and the common factors), and the percent of variance explained by each factor. After initial factor analysis without rotation, FA Varimax (orthogonal

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46 transformation) and FA Promax (oblique transfor mation) were used as follow-up analyses for better interpretability of the results. How well the data fit the model Fit statistics were performed to investigate whether the response patterns on the physical functioning and cognition scales fi t the Rasch measurement model. A fit statistic index calculates the ratio of the observed variance divided by the expected variance with an expected value of 1 and a range from 0 to positive infinity. An infit mean square value of 1+ X indicates the observed variance contains 100*X% more variation than the mode l predicted [34]. Wright and Linacre (1994) [107] suggested a reasonable item mean-square (MNS Q) fit statistics ranges from 0.5 to 1.7 for clinical observati ons. MNSQs higher than 1.7 indicate that the response pattern of items have more variance than the model expected. Item difficulty hierarchy The empirical item difficulty hierarchical order produced by the Rasch analysis can be used as evidence of construct validity and suppor t or challenge to the th eoretical base of the instrument [101]. Item difficulty hierarchical order was inspected via the estimated item difficulty calibrations, which are expressed in lo gits with higher positive values indicating a more challenging task. Person-item match: targeting In Rasch analysis, both person ability a nd item difficulty are expressed on a common metric. The extent to whether the items are of appropriate difficulty for the sample can be examined by comparing the sample ability distri bution to the item difficu lty distribution. Ceiling effects can be depicted by a lack of items for persons of high ability and floor effects can be depicted by a lack of items matching persons of low ability. Furthermore, clusters of items or

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47 gaps between items (no items within a range of a person ability level) may indicate a redundancy of items or the need to add items within an instrument. Separation index The precision of measurement depends on how well the item of an instrument separate individuals of different ability le vels. The person separation inde x is an estimate of how well the instrument can differentiate persons on the meas ured variable. A separation index above 2 is required to attain the desired leve l of reliability of at least 0. 8 [108]. The person separation index (G) can be further computed into the number of statistically distinct person strata identified by the formula [(4G+1)/3] [34]. This value indicate s how many distinct levels of person ability can be statistically differentiated in ability strata with cen ters three measuremen t errors apart [109]. Rating scale structure The rating scale structure will be examined initially by inspecting the frequency count for each response option, as well as the rating s cale structures summarized by the Rasch model. Categories with low frequencies indicate that th e performance level/ratin g scale can be assigned to the respondent only in rare situations or with a narrowly de fined scope. Furthermore, Rasch analysis explores the relationship between the pr obabilities of obtaining a particular rating scale score to person ability measures Linacre (2002) [110] provided three essential guidelines to optimize rating scale categories via the Rasch mode l: 1) at least 10 observations should be in each rating scale category; 2) average measur es should advance monotonically within the category; and 3) outfit mean-squa res should be less than 2.0. Differential item functioning (DIF) DIF analysis can be used to examine whethe r the items function similarly across different groups and identify items that appear to be too easy or difficult after controlling for the ability levels of the compared groups. In this study, DIF method based on Wr ight and Stone (1979)

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48 [111] was used to explore whether items on th e MDS perform similarly across three different diagnostic groups (individuals wi th stroke, amputation, and ort hopedic impairment). Items with DIF t-statistics beyond two standa rd deviations were indicated as having significant DIF [111]. Results Dimensionality Within a conjoint run of all functional items t ogether, the results of f actor analysis showed that 5 factors had eigenvalues greater than 1. Th e first five factors had eigenvalue equal to 11.9, 3.7, 1.9, 1.3, and 1.0, respectively, which e xplained approximate 41%, 13 %, 7%, 4%, and 4% of the total variance. Table 2-3 presen ted the factor patterns from factor analysis. Initially, factor analysis without rotation was perf ormed. Results from the factor pattern revealed that, for the first component, all items had positive loadings ranging from 0.41 to 0.80, which indicated a general construct measuring functional status. For the second factor, all cognitive items had positive loadings (0.11 to 0.47) and all physical functioning items had negative loadings (-0.05 to -0.51), indicating two separate subconstructs were underlie the overall functional status domain. The third factor had relatively hi gh factor loadings (> 0.35) on si x items that were indicators of delirium (i.e., easily distracted, periods of altere d perception, restlessness, lethargy, and mental function varies over the course of the day). Lastly, while three communication items showed high factor loadings on the fourth factor (0.37 to 0.52), two walking items demonstrated relative high factor loadings on the fi fth factor (0.53 and 0.54). Orthogonal transformation was then performed, followed by oblique transformation where factors are allowed to be corre lated with each other. Factor patterns obtaining from orthogonal and oblique transformation were similar. All physical functioning items (except two walking items) highly correlated with the first factor (0.5 6 to 1.00). Severn cognitive items including two memory items, four recall items, and one cogni tive-skills-for-daily-decision-making item had

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49 high correlations with the second factor (0.41 to 1.00). For the th ird factor, six cognitive items (indicators of delirium) had relativ e high factor loadings (0.80 to 1.00). For the fourth factor, three communication items highly correlated with th e fourth factor (0.56 to 1.00). Lastly, two walking items demonstrated relativ e high factor loadings on the fi fth factor (0.97 to 1.00). While there were multiple factor loadi ngs, we separated the instrument into 2 factors, physical and cogntive, as a conservative interpretation. Rasch Analysis ADL/Physical functioning items Rasch analysis (partial credit model) was performed using the WINSTEPS software program. Overall, the physical functioning it ems showed good psychometric properties. Person reliability, analogous to Cronbachs alpha, was 0.89. With all infit MNSQ statistics (0.56 to 1.51) less than 1.7, no physical functioni ng items misfit the Rasch model. The physical functioning item difficulty calibrati ons were presented in Table 2-4. The item difficulty calibrations ranged from -1.37 to 1.49 logits with an average of 0.05 logits error associated with parameter estimations. Two walk ing items (walking-in-co rridor and walking-inroom) and one bathing item were the most challe nging items along this cons truct. Alternatively, eating, bed mobility, bladder, and bower, were the easiest items. Items such as toileting, dressing, transferring and hygiene represent items around the average difficulty level. In general, the score correlations (point-b iserial correlation) between the individual item response and the total test score were moderate to high (r = 0.62 to 0.82). The analysis placed persons and items on the common linear scale with the same local origin. Figure 2-1 illustrated the relationship of the sample scor e distribution (left) with the hierarchical order of the physic al functioning items (right). Lin ear measures, in logits, were represented along the cent ral axis. The distribution of person ability estimations (higher values

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50 representing high ability and lower values repr esenting lower ability) was normally distributed with a slight ceiling effect with 6.1 % of the sample receiving a maximum measure. The sample ability level (M on the left) of 0.58 1.76 logits matched well with item difficulties of the MDS items with the mean item difficulty (M on the right ) of 0.00 0.87 logits. With person separation index (G) equaled to 2.89, these physical functioning items statistically defined person ability into 4.19 [(4G+1)/3] statistically distinct strata. The rating scale structure was initially exam ined by inspecting the frequency count for each response category. Figure 2-2 showed th e frequency count of responses from (independent) to (total dependence) and the additional rating scale category of for activity did not occur du ring the entire 7 days. Three rating scale categories are presented on each graph to simplify the presentation. On the x-axis, 13 physical functioning items were listed and ordered from the easiest (ea ting) to the most challenging item (walk-in-corridor) (from left to right). The y-axis was the fre quency count of rating scale cate gory. As items increased in challenge, the frequency counts of (independence -) decreased as expect ed. In general, the frequency count of (supervision -) maintained a relatively low frequency count independent of the difficulty of the item. Items at the average difficulty level had a relatively high frequency count for being scor ed with (limited assistance --) or (extensive assistance-x-). There was a relatively high fr equency count for limited assistance with the dressing item and a particularly high frequency count for extens ive assistance with the bathing item. However, the trend of the freque ncy count of (t otal dependence -*-) did not monotonously increase as the difficulty of the task increased. Instead, the frequency count of total dependence had a relatively high frequenc y count for bathing and locomotion-off-unit and had a very low frequency count for the two most challenging items, walk-in-room and walk-in-

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51 corridor. For the special rating scale of (act ivity did not occur during the entire 7 days) (-), the frequency count was low across all items ex cept the two walking items and two locomotion items. Most of the physical functioning items met Li nacres (2002) criteria for optimizing rating scale categories. All the rating scale categories ha d at least 10 observations in each rating scale category. The average measures for each rating scale structure advanced monotonically within the category. Four items (eat, bladder, bowel, walk-in-corridor) had one rating scale category that showed misfit (outfit mean-square greater than the criteria of 2). The locomotion-off-unit item had two rating scale categ ories that showed misfit. To determine whether the rating scale for each MDS item was being used in an expected manner, we examined the probability of each rating (0) based on the residents overall performance on the MDS. We expected that as the function of the residents improves, there should be increasing probability of obtaining a highe r rating scale category. That is, we expected that individuals of lower ability would use lower parts of the rating scale (e.g., 4 or 3) and individuals of higher ability would use higher pa rts of the rating scale (e.g., 2, 1, and 0). Figure 2-3 showed the rating scale pattern for physical functioning items. The y-axis was the probability of endorsing a particular rating scal e category and the x-axis equaled the value of the person ability minus item difficulty. Figure 23 (a) (eating item) for example, as person ability is much lower than item difficulty; there is a high probability of getting a rating category of (total dependence). As person ability increases, a rating category of (limited assistance) becomes the next most probable rating. Finally, as person ability is much higher than the item difficulty, a rating category of (independent) becomes the most probable rating.

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52 Hence, three rating categories provide adequate information for evaluating the eating performance. Overall, the rating scale pattern showed that the rating scale of (supervision) rarely appeared to have a higher probabi lity of endorsement than othe r rating scale ca tegories. While the four-point rating scale struct ure may provide adequate informa tion for several items such as toileting, transferring, dressing, hygiene and be d-mobility, some items (bladder, bowel, walk-incorridor, and walk-in-room) a ppear to use only two rating sc ale categories to distinguish residents status. The partial credit model enables each item to have its own rating scale structure. The keyform output allows a connection between th e item difficulty hierarchy and person ability measures. In addition, the keyform provides a met hod to interpret and repo rt a persons expected performance pattern. Figure 24 presents the keyform structur e of the 13 physical functioning items in the MDS. Items were arranged by item difficulty calibrations with the easiest item on the bottom of the y-axis to the most difficult item on the top. The x-axis indicates person ability measures (in logits) estimated by the Rasch model. For a resident at the average function level (dashed vertical line at 0.4 logits ), he/she is expected to be in dependent (score 0) with eating, bladder and bowel; supervised (score 1) on loco motion-in-unit and bed-mobility; independent or needs limited assistance on hygiene (score 1 or 2); needs limited assistance (score 2) on dressing, toileting, and transferring; requires limited to extensive assistance (score 2 or 3) on locomotionoff-unit; needs extensive assistance or total depend ent (score 3 or 4) on walking tasks (walk-inroom and walk-in-corridor. As a resident impr oves to 1 standard deviation above the average (approximate 1.73 logits), the resident is exp ected to have the func tional level of being

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53 supervised on walking activities and locomotion-off-unit; need supervision or limited assistance on bathing; and be independent on al l other physical functioning items. After performing the differentia l item functioning analysis acr oss three impairment groups, several items were found to have significant DIF. In comparing stroke with amputation, subjects with amputation had more difficulty walking (walking-in-room and walk-in-corridor) and subjects with stroke had more difficulty in locomotor-off-un it, tasks which involved upper extremity function (hygiene and eating) and c ontinence (bladder and bowel). In comparing stroke with orthopedic impairment subjects with orthopedic impa irments had more difficulty in walk-in-corridor, transferring, dressing, and bed-mobility. Similar to the stroke-amputation comparison, subjects with stroke had more difficulty in some tasks which involved upper extremity function (hygiene, eating) and c ontinence (bladder and bowel). Lastly, when comparing amputation with orthopedic impairment, where both the majority of individuals have lower extremity deficits, subjects with amput ation experienced more challenges in walking (walk-in-room and walk-in-corr idor) and subjects with orthopedic impairment had more difficulty with locomotor-off-unit, transferring, bed mobility, bathing and dressing. Cognitive items The psychometric characteristics of the MDS cognition/communication items were good but slightly less sound as those characterist ics of the physical functioning items. Person reliability, analogues to Cronbachs alpha) was 0.68. No cognition/communication items showed infit statistics that exceeded the critical value of 1.7. Table 2-5 presents the item difficulty estim ates of cognition/communication items. The item difficulty calibrations ranged from .71 to 2.20 logits with an average of 0.14 logits error associated with parameter estimations. Short-term -memory, ability-to-recall, and daily-decisionmaking items formed the most challenging item s along this construct. Communication items

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54 (making-self-understood, speech-clarity, and abil ity-to-understand-others) were the next difficult items. Items that indicated delirium (altered-perception-or-awareness, easily-distracted, disorganized-speech, and lethargy) were the easie st items. In general, the score correlations (point-biserial correlation) betw een the individual item response and the total test score were moderate to high (r = 0.54 to 0.75). However, th e score correlations were low (r = 0.32 to 0.49) for those items associated with periodic diso rdered thinking/awarene ss and communication items (except the making-self-understood item). Figure 2-5 showed a map of the person cogni tive measures to the left, and MDS item measures to the right. The Rasch analysis pla ced persons and items onto the same linear scale with the same local origin. In contrast to th e physical functioning measure, which showed a good match between person measures and item measur es, the cognition/communication measure was easy for this sample. The average item difficu lty (0.00 1.26 logits, M to the right) was much lower than the average ability of the sample (3 .49 1.74 logits). If excluding extreme persons who obtained the total maximum score, the averag e ability of the sample was about 2.13 1.35 logits (M to the left in the figure). In contrast to the physic al functioning map which showed a normal distribution of person measures, the c ognition/communication was highly skewed with 47.4 percent of the sample showing perfect scores With person separation index equaled to 1.46, the cognition/communication items di stinguished persons into 2.28 st atistically distinct strata. The observations that cognition/communicati on items were found too easy for most of residents were also shown on the rating scale patt erns. The majority of residents (68-96%) were rated independent/able/behavior-not-present fo r their cognitive status on multiple cognitive items. Several items (8 out of 16 items) had very low frequency count (< 10) in the rating scale

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55 category that indicates the severe impaired cognition/communication status (i.e., severe impaired, or have problem). To determine whether the rating scale struct ure for each MDS item was being used in an expected manner, we examined the probability of each rating in the cognition/communication items. Figure 2-6 showed the probability of resp onses for each item as a function of the overall performance on the MDS cognitive measure. Since two memory items and four recall items were dichotomously rated, the rating scale structure si mply showed that the probability of passing an item increases when person ability is higher than the item difficulty (Figure 2-6 [A]). Several items (e.g., easily-distracted, lethargy, mental-f unction-varies-over-thecourse-ofthe-day, and speech-clarity items) had a well-functioning rating scale structure meaning that when a persons ability increased, the probability of getting a hi gher rating increased gradually and distinctly for each rating category (Figure 2-6 [B]). In co mparing Figure 2-6 (C) (restless, alteredperception/awareness) with Figur e 2-6 (B), the middle rating scal e category (i.e., behavior present, not recent onset) out of the 3-point rati ng scale covered a slightly smaller range of person ability. As for disorganized-speech item (F igure 2-6 (D)), the probability of getting the middle rating scale of (behavior present, not resent onset) was lower than the other rating categories. Lastly, the 4-point rating scale structur e in Figure 2-6 (E), th e probability of getting a rating move from to increased as a pers ons ability increases, th ough the probability of getting a became more probable than other ra ting categories only for a small range of person abilities. Most of the cognitive/communi cation items met Linacres (2 002) criteria for optimizing rating scale categories. In general, the average m easures for each rating scale structure advanced

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56 monotonically. Three items (speech -clarity, restlessness, disorg anized-speech) had one rating scale category misfit with outfit m ean-square statistics slightly gr eater than the criteria of 2. Figure 2-7 presents the keyform output for th e cognition/communication items. This output provided a means to interpret and report a resi dents performance and progress. Since the cognition/communication domain had a severe ce iling effect, we recalibrated the average function level of the residents by removing those data with pe rfect scores. This procedure resulted in an average ability level at of 2.13 (logits) for non-ex treme persons. For a resident at this cognitive level (dashed vertical line), he/she is expected to have no indicators of delirium (periodic disordered thinking/awareness), be ab le to make self understood, speech clarity, and able to understand others (score 0). Meanwhile, he/she should be able to have good long-term memory (score 0), able to recall that he/she is in a nursing home, location of their own room, and current season (score 1), but probably will have problems recalling staffs names or faces (score 1). The individuals short-term memory also wo uld probably be challeng ed (score 1 or 0). Cognitive skills for daily decision making probably will not be totally independent and might have some difficulty when confr onting new situations (score 1). Differential item functioning analysis show ed that few cognitive items exhibited significant DIF. When comparing stroke with amputation, only two items demonstrated marginally significant DIF (t-statistics just a bove 2). While cognitive-skills-for-daily-decisionmaking was more difficult for subjects with stroke and recall-that he/she-is-in-a-nursing-home was relatively more challenging fo r subjects with amputation. Fo r stroke versus orthopedic impairment, two items (recall-current-season a nd cognitive-skills-for-daily-decision-making) were more difficult for subjects with stroke and one item (periods-of-lethargy) was more challenging for subjects with ort hopedic impairments. Lastly, while comparing amputation with

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57 orthopedic impairment, only one item (recall-current season) was more difficult for subjects with amputation. But this DIF effect showed only marginal significance. Discussion Rasch analysis has been widely used for th e evaluation and revision of functional outcome measures [47, 112]. This study used Rasch (par tial credit model) to assess the physical functioning and cognition/communication items of the Minimum Data Set (MDS) [113]. Because few studies have investigated those functi onal status items of the MDS at the item-level, this study provides further insight in to its item-level psychometrics. Overall, the physical functioning items demons trated better psychometric properties than the cognition/communication items. The averag e difficulty of physical functioning items matched well to the mean of sample ability. Th e physical functioning items also cover a wide range of the residents functioni ng change with the spread of items efficiently discriminating residents performance into approximate 4 sta tistically distinct strata. The findings of the empirical item difficulty hi erarchical order are supporte d by Fisher (1997) [48], who demonstrated a similar item difficulty hierarchy based on a review of more than 30 Rasch studies related to physical functioning construct. Fisher proposed a theory of physical disability based on task difficulty that feeding and grooming tasks, which only require upper extremity functioning, are usually the easiest tasks; transferring activities, which ar e more physically demanding and involve coordinating both upper and lower extrem ities, are of medium difficulty; and walking activities, which are the most phys ically demanding are the most diffi cult tasks. As in the present study, this item difficulty hierarchical order also replicates findings of Ra sch analysis studies of the motor scale in the FIM, which is widely used in the inpatient rehabilita tion facilities [41, 77, 78, 114, 115].

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58 In contrast to the physical functioning measure, which showed a good match between person measures and item measures, the MDS cognition/communication items are easy for most of the residents. Similar ceiling effects have been reported for th e in the FIM cognitive scale in studies of rehabilitation patients even at admission [77]. Coster (2004) co-calibrated cognition/communication items fr om several widely used f unctional outcome assessment (including the FIM, MDS, the Outcome and Asse ssment Information Set (OASIS), the Minimum Data Set for Post-Acute Care (MDS-PAC) and the newly developed Activity Measure for PostAcute Care (AM-PAC)) using the Rasch partial credit model [42]. Based on a sample of 477 adults who were receiving rehabi litation services rangi ng from inpatient acute rehabilitation to home care services, the results showed a severe cei ling effect with approximately a quarter of the sample receiving maximum scores across all items Hence, these findings suggest that more challenging items should be included on these in struments or that the cognitive/communication scales should only be applied to diagnostic groups likely to ha ve cognitive or communication deficits. The item difficulty hierarchical order of the MDS cognition/communication items seems to have a pattern illustrating that memory, recall and daily-decision-making items are more challenging than communication item s. Similar findings also appear ed in Rasch analysis studies of the cognitive scale in the FIM, which demonstr ated that memory and problem solving items in the FIM are more difficult than comprehension, soci al interaction, and expr ession items [41, 77]. The MDS physical functioning items have an additional rating scale category of activity did not occur. Several researchers have i ndicated that this scoring level was used when individuals were unable to perfor m a task and hence converted th ese codes to the lowest score for that item, namely total dependence [40, 41]. It is possible that the raters score this category

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59 because they did not observe the residents pe rforming the action during the entire observation period. Since these items are activities that th e majority of people perform on daily basis, however, the most likely explana tion may be that residents are incapable of performing such task. In a preliminary analysis, we found that th e results of item difficu lty calibrations for two walking items (walk-in-room and walk-in-corrido r) changed dramatically when we treated the score as missing values. As previous menti oned, frequency count analysis revealed that walking items have relatively much higher percen tage being recoded in this category comparing to the rest of items, followed by the locomoti on items. One plausible explanation for this observation is that walking and locomotion items are not routine activities for nursing staff to assist the residents as compared to other activit ies of daily living such as eating, dressing, or bathing. Nonetheless, if a resi dent does not walk within the nursing facility for the entire observation period, a likely reason is that the resident is incap able of walking on his own. To be Medicare and Medicaid compliance, th e skilled nursing facilities have to follow regulations to complete the RAI assessment for residents. Besides comprehensive assessments, nursing facilities have to perf orm quarterly assessments and annually assessments. Furthermore, a significant change form needs to be complete d when a resident has significant change. With approximately 450 items for a comprehensive assessment, and 250 items for quarterly assessment, the massive amounts of paperwork a nd staff time committed to the MDS raises the concern of administrative burden [116]. The burden of assessment loadings and rules such as the requirement of 21 times observati ons to obtain ADL data might cause nursing home staff to find it difficult to follow the protocol. This may result in the assessment being completed hastily which might further compromise the validity of the MDS data [90]. Moreover, the MDS has been criticized for having different fields of clinicians providing info rmation and inadequate

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60 evaluation training for nursing home staff [90]. With a semi-structured assessment procedure, different procedures for completing the MDS ha ve been reported: a) the Registered Nurse Assessment Coordinator asks questio ns of other staff orally; b) all members of the team have to complete their portions of the assessment; c) all members are asked for their ratings, but the Assessment Coordinator provides the final judgments; d) use a combination of chart review, direct observation, or asking other information re sources; e.) hire an MDS nurse to perform MDS assessments [71, 90]. Therefore, studies using data from MDS clinical databases may contain inestimable noise and error. There are several limitations of this study. Th e sample only represented individuals with stroke, amputation, and orthopedi c impairment groups. The data selection was connected to an existing projects criteria. Although the MDS dem onstrated multiple factors, we analyzed all functional status items as physical functioning an d cognitive subconstructs. More representative samples and dividing the cognitive construct further should be considered in future studies. Over the past few years, the CMS had conti nued to revise the MDS version 2.0 and had updated technical information on the website. Re cently, the CMS has been working on the MDS version 3.0 with the purpose of reducing burden, updating sections and increasing the responsiveness of the scale for measuring of health conditions [117]. While CMS continues to develop additional menu items, it is critical to co ntinue to evaluate and monitor the psychometric properties of existing and new items to ensure that the MDS not only is clin ical relevant but also can be used for research purposes. This study pr ovided an alternative perspective other than traditional reliability and validity test of the MDS domains.

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61 Table 2-1. Demographic Characteristics Characteristic N=654 Mean age SD (y) 68 12 Median age (y) 69 Gender, n (%) Male 630 (96.6 %) Female 22 ( 3.4 %) Race, n (%) White 485 (74.2 %) Black 120 (18.3 %) Hispanic 26 ( 4.0 %) Native American 8 ( 1.2 %) Asia 2 ( 0.3 %) Other 5 ( 0.8 %) Missing 8 ( 1.2 %) Impairment Groups, n (%) Stroke Left Body Involvement 140(21.4 %) Right Body Involvement 134(20.5 %) Bilateral Involvement 7(1.1 %) No Paresis 8(1.2 %) Other Stroke 13(2.0 %) 302(46.2%) Amputation Unilateral Lower Limb Above the Knee (AK) 30(4.6 %) Unilateral Lower Limb Below the Knee (BK) 71(10.9 %) Bilateral Lower Limb Above the Knee (AK/AK) 1(0.2 %) Bilateral Lower Limb Above/Below the Knee (AK/BK) 2(0.3 %) Bilateral Lower Limb Below the Knee (BK/BK) 9(1.4 %) 113(17.4%) Orthopedic Unilateral Hip Fracture 31(4.7 %) Bilateral Hip Fractures 1(0.2 %) Femur Fracture 5(0.8 %) Pelvic Fracture 3(0.5 %) Major Multiple Fractures 6(0.9 %) Unilateral Hip Replacement 74(11.3 %) Unilateral Knee Replacement 84(12.8 %) Bilateral Knee Replacement 2(0.3 %) Other Orthopedic 33(5.0 %) 239(36.5%)

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62 Table 2-2. Minimum Data Set (MDS) Physical Functioning and Cognition Items Physical Functioning Items Cognition items Bed Mobility Transfer Walk in Room Walk in Corridor Locomotion on Unit Locomotion off Unit Dressing Eating Toilet Use Personal Hygiene Bathing Bladder Continence Bowel Continence Ability to understand others Making self understood Speech clarity Cognitive skills for daily decision making Short-term memory Long-term memory Recall-Current season Recall-Location of own room Recall-Staff names/faces Recall-that he/she is in a nursing home Easily distracted Periods of altered per ception or awareness of surroundings Episodes of disorganized speech Periods of restlessness Periods of lethargy Mental function varies over the course of the day Rating Scale Physical Functioning 0 Independent 1 Supervision 2 Limited Assistance 3 Extensive Assistance 4 Total Dependence 8 Activity did not occur during the entire 7day period Rating Scale Cognition Communication: 0-Ok, 1-Usually/sometimes, 2-Rarely/never understand/understood Speech clarity: 0-Clear, 1Unclear, 2-No speech Cognitive decision making: 0-Independent 1-Modified independence 2-Moderately impaired 3-Severy impaired Memory: 0-Ok, 1-Problem Recall: 1-Able, 0-Disable Awareness: 0-Behabvior not present 1-Behavior present, not recent onset 2-Behavior present, over last 7 days

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63Table 2-3. Factor Analysis on MDS Items Factor Pattern Without Rotation Oblique Rotation Items Factor 1 2 3 4 5 1 2 3 4 5 Short-Term Memory 0.64 0.29 -0.28 -0.29 0.08 0.03 0.90 0.00 0.00 -0.00 Long-Term Memory 0.68 0.36 -0.24 -0.19 0.13 0.02 0.80 0.02 0.01 0.00 Recall-Season 0.68 0.30 -0.21 -0.21 0.14 0.03 0.79 0.02 0.00 0.00 Recall-Location of Room 0.70 0.26 -0.23 -0.24 0.08 0.06 0.77 0.01 0.00 0.00 Recall-Staff Names/Faces 0.51 0.29 -0.25 -0.24 0.18 0.00 1.00 0.00 0.00 0.00 Recall-Nursing Home 0.41 0.32 0.06 -0.08 0.19 0.00 0.41 0.27 0.00 0.02 Cognitive Skills for Daily Decision Making 0.77 0.32 -0.21 -0.15 0.03 0.06 0.61 0.04 0.02 -0.00 Easily Distracted 0.41 0.45 0.46 0.02 -0.14 0.00 0.00 1.00 0.00 -0.00 Periods of Altered Perception or Awareness 0.49 0.47 0.43 0.04 0.00 0.00 0.02 0.92 0.00 0.00 Episodes of Disorganized Speech 0.45 0.45 0.35 0.19 -0.02 0.00 0.00 0.86 0.03 0.00 Periods of Restlessness 0.45 0.42 0.43 0.00 -0.15 0.00 0.00 0.94 0.00 -0.00 Periods of Lethargy 0.50 0.35 0.35 0.07 0.03 0.01 0.02 0.80 0.00 0.00 Mental Function Varies Ov er the Course of the Day 0.47 0.41 0.40 -0.04 0.00 0.00 0.03 0.88 0.00 0.00 Making Self Understood 0.63 0.27 -0.34 0.52 0.10 0.01 0.06 0.00 0.81 0.00 Speech Clarity 0.50 0.11 -0.32 0.61 -0.03 0.03 0.00 0.00 1.00 -0.00 Ability to Understand Others 0.65 0.33 -0.27 0.37 0.13 0.01 0.15 0.02 0.56 0.00 Bed Mobility 0.71 -0.36 0.02 0.07 -0.14 1.00 0.00 0.00 0.01 0.00 Transfer 0.75 -0.49 0.12 0.04 -0.02 0.93 0.00 0.00 0.00 0.05 Walk in Room 0.51 -0.51 0.25 0.04 0.53 0.17 0.00 0.00 0.00 0.97 Walk in Corridor 0.50 -0.50 0.25 0.02 0.54 0.16 0.00 0.00 0.00 1.00 Locomotion on Unit 0.75 -0.28 0.06 -0.04 -0.12 0.92 0.02 0.00 0.00 0.00 Locomotion off Unit 0.66 -0.31 0.10 -0.06 -0.04 0.90 0.01 0.00 0.00 0.02 Dressing 0.77 -0.40 0.08 0.04 -0.11 0.98 0.00 0.00 0.00 0.01 Eating 0.76 -0.11 -0.12 0.06 -0.20 0.67 0.06 0.00 0.04 -0.00 Toilet Use 0.79 -0.43 0.06 0.00 -0.08 0.97 0.00 0.00 0.00 0.01 Personal Hygiene 0.80 -0.31 0.00 -0.00 -0.14 0.93 0.02 0.00 0.00 0.00 Bathing 0.71 -0.39 0.06 -0.02 -0.04 0.95 0.00 0.00 0.00 0.02 Bowel 0.74 -0.14 -0.14 -0.08 -0.24 0.73 0.09 0.00 0.00 -0.00 Bladder 0.66 -0.05 -0.15 -0.21 -0.26 0.56 0.19 0.00 0.00 -0.01

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64 Table 2-4. Physical Functio ning Item Statistics (Liste d by Item Difficulty Order) INFIT OUTFIT SCORE ITEM MEASURE ERROR MNSQ ZS TD MNSQ ZSTD CORR. Walk-corridor 1.49 0.041.28 3.9 2.16 2.6 0.68 Walk-room 1.22 0.041.28 3.9 2.01 3.5 0.69 Bathing 1.11 0.05 0.91-1.5 0.852.1 0.77 Loco-off-unit 0.61 0.041.51 7.3 1.77 5.8 0.67 Dressing 0.14 0.05 0.82-3.5 0.842.8 0.79 Toileting 0.12 0.05 0.56-9.5 0.538.6 0.82 Transfer -0.07 0.05 0.72-5.7 0.695.5 0.80 Hygiene -0.27 0.05 0.78-4.2 0.783.5 0.78 Loco-in-unit -0.35 0.051.24 3.4 1.23 1.9 0.69 Bowel -0.78 0.05 0.98-0.2 1.70 2.7 0.68 Bladder -0.82 0.051.63 6.5 2.29 5.1 0.62 Bed-mobility -1.03 0.051.12 1.8 1.04 0.3 0.70 Eating -1.37 0.06 0.99-0.2 1.05 0.4 0.70 Mean 0.00 0.051.06 0.1 1.30 0.0 S.D. 0.87 0.00 0.30 4.8 0.584.1 MEASURE: item difficulty calibration MNSQ: mean square fit statistics ZSTD: standardized fit statistics

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65 Table 2-5. Cognition/Comm unication Item Statistics (Listed by Item Difficulty Order) INFIT OUTFIT SCORE ITEM MEASURE ERROR MNSQ ZS TD MNSQ ZSTD CORR. Short-term memory 2.200.130.88-2.00.81 -2.3 0.75 Recall staff names/faces 1.540.131.182.71.23 2.3 0.61 Recall location of ow n room 1.240.140.88-1.80.83 -1.7 0.67 Daily decision making 1.230.080.74-3.70.74 -3.3 0.85 Recall current season 1.150.140.81-3.00.71 -2.9 0.69 Long-term memory 0.960.140.77-3.40.69 -2.8 0.68 Recall in a nursing home 0.860.141.091.31.58 3.8 0.54 Making self understood -0.110.091.262.61.09 0.6 0.64 Speech clarity -0.330.121.312.91.78 3.7 0.47 Ability to understand others -0.410.100.98-0.20.99 0.0 0.64 Mental function varies -1.020.150.97-0.20.68 -1.4 0.49 Altered percept/awareness -1.190.161.181.30.83 -0.6 0.43 Restlessness -1.290.161.050.40.97 0.0 0.43 Easily distracted -1.430.170.98-.10.73 -0.9 0.43 Disorganized speech -1.680.181.251.50.96 0.0 0.36 Lethargy -1.710.191.110.71.74 1.9 0.32 Mean 0.000.141.03-0.11.02 -0.2 S.D. 1.260.030.172.10.36 2.2

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66 4+ 3+ . 2+ . walk-corridor (1.49 .04) walk-room (1.22 .04) bathing (1.11 .05) 1+ loco-off-unit(.61 .04) M . dressing (.14 .05) toileting (.12 .05) 0+M transfer (-.07 .05) hygiene (-.27 .05) loco-in-unit (-.35 .05) bowel (-.78 .05) bladder (-.82 .05) -1+ bed-mobility (-1.03 .05) . eating (-1.37 .06) . -2+ -3+ . -4+ Note: Each ' indicates 4 persons. M represents the mean of person ability measures (left) and item difficulty calibrations (right) Figure 2-1. Person Score Distri bution Item Difficulty Hier archy Map Physical Functioning More Able Less Able Less Able Easier to Perfor m Harder to Perfor m Sa m p le +1 S.D. +2 S.D. -1 S.D. -2 S.D. Item (item calibration error)

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67 Eat Bed-Mobility Bladder Bowel Loco-in-Unit Hygiene Transfer Toilet Dressing Loco-Off-Unit Bathing Walk-Room Walk-Corrido r Figure 2-2. Frequency Count of Item Rating Scale Physical F unctioning Items (A) Rating scale category from 0 to 2 (B) Rating scale category 3, 4, and 8 0 50 100 150 200 250 300 350 400 450 500 012345678910111213 Items have been ordered by item difficulty Frequency Count 3 Extensive Assistance 4 Total Dependence 8 Activity Did Not Occur 0 50 100 150 200 250 300 350 400 450 500 012345678910111213Items have been ordered by item difficulty Frequency Coun t 0 Independent 1 Supervision 2 Limited AssistanceA. B.

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68 (A) Eating (D) Bladder; Bowel P P R 1.0 + R 1.0 4444 O 444444 O 444444444 000 00000 B 4444 00 B 4444 0000 A 44 00 A 444 00 B .8 44 00 B .8 44 00 I 44 00 I 4 0 L 44 0 L 44 0 I 4 00 I 4 0 T .6 4 0 T .6 4 0 Y 4 0 Y 4 0 .5 4 22222 0 .5 4 0 O 4 22 22 0 O 4 0 F .4 4 2 2 0 F .4 4 0 422 220 4 0 R 33**4 1**111 R 4 0 E 333322 3*33 11*0 22 111 E 3333333* S .2 333 2 4 33111 0 2 1111 S .2 333 03* P 3333 22 4*133*0 22 111 P 3333 22*22****11111 O 3333 222 111 4*0 33 222 111 O 3333 222 0111 43*22 11111 N 3333333 22222 1111 0000 444433333 22222 N 3333333333 22222 ***1 44*3*2222 11111 1111 S .0 ***********************00000 44444*************** S .0 ************************** 44*********** ***** E -4 -3 -2 -1 0 1 2 3 E -4 -3 -2 1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE PERSON ABILITY MINUS ITEM MEASURE (B) Bathing (E) Walk-corridor; Walk-room P R 1.0 P O R 1.0 44444444444444 B 0 O 444444 0 A 44 000 B 44 0000 B .8 444 00 A 4 000 I 44 333 00 B .8 44 00 L 44 333 333 00 I 4 00 I 44 333 3 0 L 4 00 T .6 4 3 3 0 I 4 0 Y 44 33 3 0 T .6 4 0 .5 ** 3 00 Y 4 00 O 3 4 3 0 .5 4 0 F .4 33 44 3 1*11 O 4 0 33 4 *10 111 F .4 4 1* R 33 44 1130 11 4 1110 1111 E 33 44 1 03 11 R 0 11 S .2 33 44 11 0 3 111 E 1* 0 111 P 333 444 11 0 33 111 S .2 2**2 *22 11 O 1*44 00 33 1 P 221 00 4 222 1111 N 2****2********2222222*33 O 2211 0 44 222 1111 S .0 ************************00000 44444444************ N 22*****3***3333 44 22222 1 E S .0 **********************0000 33333************** ***** -4 -3 -2 -1 0 1 2 3 E -4 -3 -2 1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE PERSON ABILITY MINUS ITEM MEASURE (C) Toileting; Transfer; Dressing; Hygiene; Bed-mobility (F) Loco-in-unit; Loco-off-unit P P R 1.0 R 1.0 44444 O 4 O 44444444 00000 B 4444 000 B 4444 000 A 444 000 A 44 000 B .8 444 00 B .8 44 0 I 44 0 I 4 00 L 4 0 L 4 0 I 44 00 I 4 0 T .6 4 0 T .6 4 0 Y 44 0 Y 4 0 .5 4 0 .5 4 0 O 4 22222222 0 O 4 0 F .4 33*333333*2 2 0 F .4 4 22222 0 33 44 2 33 *2 *2 *2 R 333 422 33 0 2 R 2 4 0 2 E 33 224 3 00 2 E 22 4 0 22 S .2 333 2 44 33*111111**11 S .2 2 4 0 11 2 P 333 22 44 11*33 221111 P 3**3333333***111 11**11 O 33333 222 **100 33 22 11111 O 3333**2 1*133* 22*1111 N 3 222222 1111*00*4444 33333 22222 1 N 3333333332222 11**0 ***33 222211 11111 S .0 *************************0000 44444444************ S .0 *************************00 44************ ***** E -4 -3 -2 -1 0 1 2 3 E -4 -3 -2 1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE PERSON ABILITY MINUS ITEM MEASURE Note: y-axis is the probability of endorsing a particul ar rating scale category; x-axis equals the value of the person ability minus item difficulty; 0=independent; 1=supervision; 2=limited assistance; 3=extensive assistance; 4=total dependence Figure 2-3. Rating Scale Structure of the Physical Functioning Items

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69 -2SD -1SD Mean +1SD +2SD Walk-corridor 4 : 3 :2 : 1 : 0 Walk-room 4 : 3 : 2 : 1 : 0 Bathing 4 : 3 : 2 : 1 : 0 Loco-off-unit 4 : 3 : 2 : 1 : 0 Dressing 4 : 3 : 2 : 1 : 0 Toileting 4 : 3 : 2 : 1 : 0 Transfer 4 : 3 : 2 : 1 : 0 Hygiene 4 : 3 : 2 : 1 : 0 Loco-in-unit 4 : 3 : 2 : 1 : 0 Bowel 4 : 3: 2: 1 : 0 Bladder 4 : 3 : 2: 1 : 0 Bed-mobility 4 : 3 : 2 : 1 : 0 Eating 4 : 3 : 2 : 1 : 0 -4 -3 -2 -1 0 1 2 3 4 Person Ability Measure (logits) Note:(":" indicates half-score point) The mean and standard deviation is computed after removing persons with maximum or minimum scores. Figure 2-4. General Keyf orm Structure of the Physical Functioning Items

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70 4+ . 3+ Short-term memory ( 2.20 .13) M 2+ . Recall-face/name (1.54 .13) Recall-room (1.24 .14) ; Daily-Decision-Making (1.23 .08) Recall-current season (1.15 .14) 1+ Long-term memory ( 0.96 .14) Recall-in-nursing ( 0.86 .14) . . 0+M Make-self-understood (-0.11 .09) Speech-clarity (-0.33 .12) ; Understand-others (-0.41 .10) . -1+ Mental-function varies (-1.02 .15) Altered-percep/awareness (-1.19 .16) ; Restless (-1.29 .16) Easily-distracted (-1.43 .17) Disorganized-speech (-1.68 .18) Lethargy (-1.71 .19) -2+ -3+ Note: Each ' in the person column is 11 persons; each '.' is 1 to 10 M represents the mean of person ability measures (left) and item difficulty calibrations (right) Figure 2-5. Person Score Distribution It em Difficulty Hierarchy Map Cognition More Able Less Able Easier to Perfor m Harder to Perfor m Sam p le Item ( item calibration error )

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71 (A) Short-term memory, Long-term memory, Recall-current season, Recallroom, Recall-face/name, Recall-in-nursing (D) Disorganized-speech P P R 1.0 R 1.0 O 11111 00000 O 22222 00000 B 111111 000000 B 22222 00000 A 1111 0000 A 2222 0 000 B .8 111 000 B .8 22 00 I 111 000 I 22 00 L 11 00 L 22 00 I 11 00 I 22 00 T .6 11 00 T .6 22 00 Y 11 00 Y 2 0 .5 *** .5 22 00 O 00 11 O 2 0 F .4 00 11 F .4 2 0 00 11 *** R 00 11 R 1111110 2111111 E 000 111 E 1111 00 22 1111 S .2 000 111 S .2 111 00 22 111 P 0000 1111 P 1111 00 22 111 1 O 000000 111111 O 111111 0000 2222 111111 N 00000 11111 N 111111 000000 222222 111111 S .0 S .0 0000000000000 2222222222222 E -3 -2 -1 0 1 2 3 E -3 -2 1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE PERSON ABILITY MINUS ITEM MEASURE (B) Easily-distracted Lethargy, Mentalfunction varies, Speech-clarity (E) Understand-othe rs, Daily-DecisionMaking, Make-self-understood P P R 1.0 R 1.0 O O B B A 222 000 A 3333 0 B .8 222 000 B .8 33 000 I 222 000 I 333 00 L 22 00 L 33 00 I 22 00 I 33 00 T .6 22 11111111111 00 T .6 3 00 Y 22 111 111 00 Y 33 111 0 0 .5 22111 11100 .5 33 11111 11111 00 O 1122 0011 O 3 11 0*1 F .4 111 22 00 111 F .4 2**22222211 0 11 1 11 22 00 11 2222 3 11222 00 111 R 111 22 00 111 R 222 3*1 222 00 11 E 11 22 00 11 E 222 11 3 22 00 111 S .2 111 *** 111 S .2 222 11 33 0*22 111 P 1111 000 222 1111 P 2222 111 333 000 222 1 O 0000 2222 O 2 111 00*33 2222 N 0000000 2222222 N 1111111 000000 333333 222 2222 S .0 000000000000000 222222222222222 S .0 ******0000000000000000 333333333 3333********* E E -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE PERSON ABILITY MINUS ITEM MEASURE (C) Restless, Altered-perception/awareness P R 1.0 O B 22222 00000 A 222 000 B .8 222 000 I 222 000 L 22 00 I 22 00 T .6 22 00 Y 2 0 .5 22 111 00 O 2*1111 1111*0 F .4 111 2 0 111 111 22 00 111 R 111 22 00 111 E 111 0*2 111 S .2 111 00 22 111 P 1111 000 222 1111 O 11111 000 222 11111 N 0000000 2222222 S .0 00000000000000 22222222222222 E -3 -2 -1 0 1 2 3 PERSON ABILITY MINUS ITEM MEASURE Figure 2-6. Rating Scale Structure of the Cognition/Co mmunication Items

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72 -2SD -1SD Mean 1SD Short-term memory 1 : 0 Recall-face/name 0 : 1 Recall-room 0 : 1 Daily-decision-making 3 : 2 : 1 : 0 Recall-current season 0 : 1 Long-term memory 1 : 0 Recall-in-nursing 0 : 1 Make-self-understood 3 : 2 : 1 : 0 Speech-clarity 2 : 1 : 0 Understand-other 3 : 2 : 1 : 0 Mental-function varies 2 : 1 : 0 Alteredperception/awareness 2 : 1 : 0 Restless 2 : 1 : 0 Easily-distract 2 : 1 : 0 Disorganized speech 2 : 1 : 0 Lethargy 2 : 1 : 0 -4 -3 -2 -1 0 1 2 3 4 Person Ability Measure (logits) Note: (":" indicates half-score point ) The mean and standard deviation is computed after removing persons with maximum or minimum scores. Figure 2-7. General Keyform Structur e of the Cognition/Communication Items

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73 CHAPTER 3 DIFFERENTIAL ITEM FUNCTIONING OF THE FUNCTIONAL INDEPENDENCE MEASURE ACROSS DIFFERENT DIAGNOSTIC GROUPS Introduction Measuring functional status is important in bo th patient care and clinical research for evaluating the net impact of re habilitation intervention and hea lthcare services. Information pertaining to functional status en ables clinicians and therapists to plan interventions for their patients [118]. Without functional status informa tion, the effectiveness of these rehabilitation interventions in fulfilling propos ed goals toward independence is unknown [119, 120]. Currently, functional status information is not only one of the most critical health data in rehabilitation settings, but also directly re lated to resource util ization [121] and outcomes prediction [122, 123]. In inpatient rehabilitation, the Functional Independence Measure (FIM) is the most widely used functional assessment [6 4]. Through the conjoint efforts of several major organizations in rehabilitation, the FIM was developed as a centra l core measure of the Uniform Data Set for Medical Rehabil itation (UDSMR) to document the functional level [65, 124]. To date, more than 60% of comprehensive rehabili tation programs in the U.S. use the FIM [125]. Since 2002, the FIM has been added to the Inpatie nt Rehabilitation Facilities Patient Assessment Instrument (IRF-PAI) for inpatient medical re habilitation prospective payment system [126]. Based on age, functional status (provided by FIM) comorbidities (the presence of disorders or diseases in addition to a primary diagnosis), a nd rehabilitation impairment categories, patients are classified into discrete case-mix groups (CMG s). These classifications are used to determine the financial resources Medicare provides for a particular patients care [127]. The FIM instrument was designed to assess f unctional independence and predict burden of care. It consists of 18 items that are rated from a minimum score of 1 (total assistance) to a

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74 maximum score of 7 (complete independence). Previous studies demonstrate that the FIM represents two statistically and clinically dist inct constructs with 13 items that define an ADL/motor function domain and five items that define a cognition/communication domain [69, 115, 128-130]. A myriad of studies provide evidence that FIM has good psychometric properties in terms of reliability and va lidity [57-60, 62]. Ottenbacher (1996) [64] performed a meta analysis on the basis of 11 published studies and concluded that the FIM demonstrated sound reliability across a wide variety of settings, raters and patients (median interrater reliability and test-retest reliabili ty values both are .95). Stineman a nd her colleagues (1996) [129] found good internal consistency in the motor scale (0.860.97) and the cognitive scale (0.86-0.95) across 20 impairment groups. Additionally, the total summed FIM measure has been shown to be correlated with minutes of care therefore provi ding a measure of burden of care [66, 67, 131, 132]. Granger et al. (1990) found a change of one point in FIM total score represented 3.8 minutes of care per day [66]. For detecting ch anges in performance during the hospital stay, Hsueh et al. (2002) [133] found an effect size of 1.3 for FIM motor scale (effect si ze greater than 0.8 demonstrate a large responsiven ess to detect change over time). Several studies have examined the psychomet ric properties of the FIM using the Rasch model [48, 75-78]. Stairs, which requires extensive st rength and coordinati on of the whole body, usually appears to be the most challenging item. Walking and tran sfer-to-tub are usually the next most difficult items. Transferring activities are usually at averag e difficulty. Tasks that require upper extremity function and mild muscle streng th, such as eating and grooming are commonly found to be the easiest. While bowel and bladde r management involve an involuntary muscle control component, these two ite ms often misfit in the Rasch model. For cognitive items, problem solving and memory function were found to be relatively more challenging than social

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75 interaction, expression, and comprehension [41, 75, 134]. However, cognitive items have been found to be easy for most of rehabilit ation patients even at admission [77]. To compare outcomes, item characteristics shou ld be consistent across different patient groups. Granger and his colleagues (1993) [75] i nvestigated the patterns of difficulty in performing FIM items according to types of impair ment. By plotting item difficulty calibrations estimated by the Rasch model for each domain and inspecting the difference, they concluded that the patterns were consistent across impairme nt groups, although not identical [75]. Using similar analytical procedure, Heinemann et al ( 1993) [76] also demonstrated the similarity of scaled measures across impairment groups for the FIM instrument. While these studies support the consistency of item performa nce across different impairment group, the analytical procedure was not based on statistical tests. Differential item functioning (DIF) has been ut ilized in the health-related measurement field to compare response patterns across gender, ethnicity, educational level, age, countries, severity groups, and different diagnostic groups [135-141]. DIF analysis is a statistical methods used to identify items that appear to be have difficulty levels that ar e dependent on membership to a particular group (e.g., male/female, Caucasia n/Black) after controlling for the ability levels of the compared groups [142]. It is based on the rationale that persons at a given level of the attribute being measured (e.g., obtain the same to tal scores) should have an equal probability of passing an item regardless of their group membership. In 2005, Dallmeijer et al. [130] applied DIF analysis of FIM in higher performing neur ological patients. They found that almost all the items showed significant DIF and suggested that adjustments may be required when FIM data is compared between groups [130]. Nonetheless, Da llmeijers study is based a Dutch version of the FIM. The results may not generalize to the original English version of the FIM.

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76 The focus of this study is to investigate whether FIM items function similarly across different impairment groups. To some extent, this is an extension of Dallmeijers study, but has several methodological differences. In this study, the original English ve rsion of the FIM was used. Instead of focusing on patient groups with different neurological disorders, three major impairment groups in rehabilitation: stroke, amputation, and orthopedic impairment were compared. Furthermore, while Dallmeijer and colleagues removed two items that misfit the Rasch model, this study performe d DIF analysis under two different scenarios. The DIF analysis was conducted with 1) all items and 2) misfit items removed to explore whether misfit items have an effect on DIF results. While Dallmeijer and colleagues collapsed the FIM 7-point rating scale into 3-category scale, we chose to keep th e original 7-point rating scale to investigate its properties in the form that it is most frequently used. In addition, instead of using a trend line to construct the 95% confidence interval, separate joint measurement errors associated with each item calibrations were used to improve accuracy [111]. Lastly, while previous studies merely focus on the Rasch model (also called the one-par ameter logistic item response theory model), another DIF method based on a higher order twoparameter logistic model was used. The DIF results based on different models were then compared. Method Participants A secondary, retrospective anal ysis using Veteran Affairs (V A) data from the Functional Status and Outcomes Database (FSOD) collect ed by the VAs Austin Automation Center (AAC) during June 1, 2002 to May 31, 2003 were used for this study. This database contains all VA rehabilitation records previously stored at the UDSMR. VA and non-VA researchers may access the data stored in the FSOD with approval of Department of P hysical Medicine and Rehabilitation (PM&R) administrative office. S ee Appendix A for data request information.

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77 This is also the data set used in the VA Rehabilitation Research and Development Project, 03282R, Linking Measures across the Continuum of Ca re. The main purpose of that project was to develop crosswalk tables/al gorithms that link scores and measures from the Functional Independence Measure (FIM) and the Minimu m Data Set (MDS). VA FIM and MDS data reside in two databases at the VAs Austin Auto mation Center (AAC). Data from both databases (the Functional Status and Outcomes Database (FSOD) and the Resident Assessment Instrument Minimum Data Set (RAI-MDS)) were downloaded and merged on the basis of social security numbers. In order to minimize the impact that ch ange in a patients cond ition could have on FIM and MDS scores, data were restricted to those that involved those subj ects whose FIM and MDS assessment dates were within 5 days of each ot her. Data with any missing values in FIM and MDS items were excluded. Individuals with stro ke, amputation or orthopedic impairments were selected for analysis. The dataset comprised a total sample of 654 records (302 stroke, 113 amputation, and 239 orthopedic impairment). The average age of this sample was 68 12 years, 96.6% were male, 74.2% were white, and 46.7% were married. The average difference between FIM and MDS assessment dates was approxima tely 2.85 days. Table 2-1 provides the demographic baseline characteristics and inform ation on impairment categories. This study was approved by the Institutional Review Board at the University of Florida and the VA Subcommittee of Human Studies. Access to VA MDS data was approved by Department of Veterans Affairs, Veterans Health Administration. Differential item functionin g based on the Rasch model In this study, the DIF method based on Wright and Stone (1979) [143] was used to explore whether items on the FIM perform similarly across three different diagnos tic groups (individuals with stroke, amputation, and orthopedic impairme nt). This method is based on the differences

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78 between two parameters calibrated on the same item from two subpopulations of interest. Given the pairs of item calibrations and the associated es timates of the standard error of estimate from the Rasch model, a t-statistic can be cons tructed for each item using the formula: 2 1 2 2 2 1 2 1) (i i i is s d d t where 1 id and 2 id are the item difficulty of item i in the calibration base d on subpopulation 1 and 2, 1 is is the standard error of estimate for 1 id, and2 is is the standard error of estimate for2 id. A graphical representation method equivalent to the t-statistic method was also proposed. After obtaining initial item parameter calibrations a nd estimated errors associated with each item calibration, paired item difficulty parameters from compared groups are cross-plotted. A pair of 95% confidence interval lines base d on the conjoint error estimates is constructed. Points outside the 95% confident interval are flagged as potential DIF items. The motor and cognitive scales were analyzed separately. Rasch anal ysis (partial credit model) using Winsteps program [version 3.16] [ 102] was used to obtain the FIM item difficulty calibrations. Fit statistics were performed first to examine whethe r the response pattern fits the Rasch measurement model. Fit statistics with a m ean square (MNSQ) greater than 1.7 indicate the response pattern of items are more unusual than the model pr edicted [107]. If the data fits the Rasch model, Rasch analysis allows for the det ection of differences in item difficulties between groups. Some studies exclude misfit items from furt her analysis based on th e rationale that items have to fit the Rasch model to investigate DIF. However, removing items from a standardized measurement instrument may damage the integrity of the instrument. To ex plore the influence of misfit items on a DIF analysis, the DIF analytic procedure was performed using all items from

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79 the motor and cognitive scale, the same proce dures was performed with misfit items removed from each scale. Furthermore, to investigate the effects of the DIF items on estimated person ability measures, person ability measures for the motor and cognitive scales were estimated for each group by the Rasch model under the following scenarios. First, the person ability measures were estimated using all items in the motor and cognitive scales. Second, the person ability measures were estimated using all motor and cognitive items with misfit items removed. Third, the person ability measures were estimated with all items adjusted for DIF, by splitting the items that showed significant DIF into impairment-specific items. For example, if a walking item exhibited significant DIF across all 3 dia gnostic groups, data was encoded into 3 variables by their impairments (walking-stroke, walking-amputa tion, and walking-orthopedic). Correlation coefficients between person ability measures unde r each scenario were computed to investigate the impact of DIF items on person ability measures estimated by the Rasch model. Differential Item Functioning Based on Two-Parameter Logistic IRT Model The Rasch model has a strong assumption that item discrimination parameters are equal across all items. This assumption makes Rasch m odel only allows to detect uniform DIF where there is a relative advantage for one group over th e other group through the entire ability range (low to high ability level). Compared to th e one-parameter Rasch model, the two-parameter logistic (2PL) IRT model, a higher-order it em response theory (IRT) model, allows item discrimination parameters to vary across items. Non-uniform DIF thus can be detected, where one group has a relative advantag e over the other group at certai n person ability range but has a relative disadvantage at othe r person ability range.

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80 Uniform and non-uniform DIF can be further illustrated via item characteristic curve (ICC). The ICC curve illustrates the relationship between person ability ( ) and the probability of passing an item P( ) within the IRT model. In Figure 3-1, the x-axis is the person ability ( ) (logits is the measurement unit), and the y-ax is is the probability of passing an item P( ). Figure 3-1 (A) provides an example of uniform DIF where a) persons at the same ability level ( ) but from different groups do not have equal opportun ity of passing an item and b) one group has relative advantage through the entire person abilit y range. The magnitude of DIF, thus, could be expressed as a summation of differences betw een probabilities of passing an item from two groups across the entire person ability range and can be defined mathematically as the integration of the area/space between the two ICCs (i.e., )]d ( P ) ( [P index area signed2 1) [142]. The size of the area index value indicates the magnitude of DIF. When two ICCs cross at some point on the pe rson ability scale, non-uniform DIF indicates a) persons at the same ability level ( ) but from different groups do not have equal opportunity of passing an item and b) one group has relative advantage at a certain person ability range but has disadvantage at other person ability range (F igure 3-1 (B)). When non-uniform DIF occurs, the signed area index (mentioned above) will confront a situation where positive and negative areas in different regions of the graph canceling each ot her out to some extent. In this scenario, an alternative method using the squared probability differences is useful ( d )] ( P ) ( [P index area unsigned2 2 1) [142]. When the unsigned area index is much higher than the signed area index, it indicates that non-uniform DIF occurs. The DIF method based on computing the area between two ICCs however, does not provide significant test. Therefore, there is no clear-cut method of de termining whether a particular item exhibits significant DIF.

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81 In this study, the two-parameter (2PL) logistic IRT model (graded response model) was used to analyze the FIM items with the Multilog program [version 7.0] [144]. Again, the motor and cognitive scales were analyzed separately After obtaining item parameters from the 2PL model, the parameters from separate runs were rescaled onto the same scale. This is due to the property of indeterminacy of scale location and spread within the IRT model. To convert the parameters for each item from scale I to scale J, for example, the item parameters on the two scales are rescaled as follows: ,A a aIj Jj B Ab bIj Jj ) ( ) (J Ia u a u A ), ( ) ( BI Jb Au b u where Jja and Jjb are the item discrimination (a) and item difficult (b) parameters for item j on scale J; Ija andIjb are the item parameters for item j on scale I; ) (Ia u,) (Ja u ,) (Ib u, and) (Jb u are the means of item discrimination parame ter and item difficulty parameter on each scale. After the parameter transformation, the item characteristic curves can be constructed based on item parameters obtained from each group. The DIF analysis was then performed by calculating the area/space between two item ch aracteristic curves (singed and unsigned area index). With three impairment groups, three co mparisons were conducted (stroke-amputation, stroke-orthopedic, and amputati on-orthopedic). Areas between tw o item characteristic curves were summed across the-3 to +3 logits person ability range.

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82 Results Subjects This sample comprised a total of 654 s ubjects, with 302 (46%) stroke, 113 (17%) amputation, and 239 (37%) orthopedic impairment. Among individuals with stroke, the majority had either right-brain involvement (n=140) or left-brain involvement (n=134). For individuals with amputation, most of the subjects had un ilateral below the knee amputation (n=71) or unilateral above the knee amputation (n=30). For subjects with orthope dic impairment, most subjects involve lower extremity impairment (unilateral joint replacement at knee (n=84); unilateral joint replacement at hip (n=74); unilate ral hip fracture (n=31)). Overall, 96.6% were male, 74.2% were White, and 46.0% were marri ed. The average FIM motor score was 54.3 and the average FIM cognitive score was 27.7. In gene ral, individuals with orthopedic impairment had higher FIM-motor and cognitive scores than individuals with amputation and stroke. Ceiling effects were found in FIM-cognition subscale acr oss three impairment groups; 12.6% stroke, 37.5% amputation, and 45.2% orthopedic impairme nt received maximum scores in the cognitive scale. Table 3-2 summarizes the demographics information and average FIM scores for this sample. DIF Analysis Based on Rasch Model Table 3-3 presents the FIM-motor item difficulty calibrations for the entire sample and each impairment group. The results of Rasch anal ysis showed 4 out of 13 motor items (bladder, bowel, walk, and stairs) had high infit statistics (mean-square fit statistics (MNSQ) greater than 1.7) for at least one impairment group. Climbi ng stairs was the most challenging items on the motor scale. Walking and transferring-to-tub item s were the next most difficult items for this sample. Several items such as bathing, toileting, dressing-lower-extremity transferring-to-toilet and transferring-to-chair were near the averag e item difficulty. Dressing-upper-extremity, bowel,

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83 bladder, and grooming were shown to be the ea sier items. Among all motor items, the eating item was the easiest. Table 3-4 lists the FIM-cogniti on item difficulty calibrations for the entire sample and each impairment group. None FIM-cognition items had high fit statistics. Problem solving item was the most challenging item among five cognitive items followed by the memory item. Comprehension was at the average difficultly. Expr ession and social interaction items were the easier items along this scale. Figure 3-2 shows the DIF plots for both moto r and cognitive items. Items demonstrated significant DIF were labeled with item numbers as presented in Table 3-3 for the motor items and Table 3-4 for cognitive items. For motor scal e, 9 out of the 13 motor items were found to have significant DIF when comparing stroke with amputation group. The amputation group had more difficultly transferring and walking and the stroke group had more difficulty with eating, grooming, dressing-upper-extremity and bladder. When comparing the stroke and the orthopedic impairment groups, 10 out of 13 motor items showed significant DIF. Similar to what had found in stroke versus amputation comparison, items with higher item calibrations (more difficult items) turned out to be more difficult for orthop edic group and items with lower item calibrations (easier items) were more challenging for stroke group. When we compared item calibrations between amputation and orthopedic impairment gr oups, only four items showed significant DIF. The results revealed that bath ing and dressing-lower-extremity were more challenging for individuals with orthopedic im pairment, while individual with amputation had more difficulty climbing stairs and eating. For the FIM-cognition items, 2 out of the 5 cognition items exhibited significant DIF. Compared to the amputation group, the stroke group showed more difficultly with expression.

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84 Compared to orthopedic impairment group, the str oke sample demonstrated more difficultly with problem solving. When comparing item calib rations between the amputation and orthopedic impairment groups, problem solving was shown to be more challenging for the orthopedic impairment group and expression was relati vely more difficult for amputation group. DIF Analysis Removing Misfit Items After the DIF analytic procedure was perf ormed using all items from the motor and cognitive scale, the same procedure was perfor med with misfit items removed from each scale. Since there were no misfit items among the cognitiv e scale, this procedure only applied to the motor scale. Therefore, four misfit items (ite m number bladder, bowel, walk, and stairs) were removed. Figure 3-3 shows th e DIF plots for the motor items after removing misfit items. In general, the DIF findings were similar to those found when including the misfit items. When comparing amputation and st roke groups, individuals with amputation had more difficulty with transferring task and indi viduals with stroke had more difficulty grooming and dressing their upper extremity. When comparing orthopedi c impairment and stroke groups, individuals with orthopedic impairments had more difficulty transferring and dressi ng lower extremity and individuals with stroke agai n had more difficulty with gr ooming and dressing their upper extremity. The DIF results changed when compar ing the amputation with orthopedic impairment groups after removing misfit items. Three transfer items were more difficult for individuals with amputations, while the dressing lower extremity ite m was more challenging for individuals with orthopedic impairments. The Impact of DIF Items on Person Ability Measures To investigate the effects of DIF items on es timated person ability measures, person ability measures estimated 1) using all items, 2) with misfit items removed, and 3) adjusting for effects

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85 of DIF by splitting significant DIF items into impairment-specific items, were compared. For motor scale items, the estimated pe rson ability measures were highly correlated with each other. The estimated person ability measures correlated at 0.97 between using all items and with misfit items removed. The estimated person ability meas ures correlated at perf ectly (r = 1.0) between using all items with and without adjusting for DIF. Since the cognition scale did not have any misfit items, person ability measures were compar ed between using all items and adjusting for DIF. The estimated person ability measure wa s also found to have a perfect correlation coefficient of 1.0. DIF Analysis Based on 2PL IRT M odel Table 3-5 presents the item parameter calibra tions for 13 FIM motor items based on twoparameter logistic IRT model. Initially, each it em contained one item discrimination parameter and six item difficulty parameters (category thre shold) due to a 7-point rating scale structure. The category thresholds were then divided by 6 to obtain the average item difficulty parameter (b) for easier comparison. The results demonstrated that item discrimi nation parameters varied across items. Among them, several items such as bath, dress-upperextremity, dress-lower-extremity, toilet, and transfer-to-toilet showed relatively higher discri mination than other motor items. Item difficulty calibrations revealed a similar difficulty hierarch ical order as those results shown in the Rasch model. Stairs appeared to be the most challe nging item, followed by the walking item. Transfer activities were at average diffi culty. Eating and grooming were found to be the least difficult items. Table 3-6 provides results of DIF analysis for FIM motor items including the signed area index and unsigned area index. For the signed area index, positive values indicate the specific item is more challenging for the second group comparing the first gr oup and negative values

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86 indicates the first group has more difficult performing such task s. For purposes of comparison, items that have greater than 0.4 for signed area index and 0.3 for unsigned area index are considered as potential items show ing differential item functioning In comparing stroke versus amputation group, items that involved more upper extremity function (e.g., eat, groom, and dress-upper-extremity ) were found to be more difficult for stroke and items that depends mostly on lower extremity functions (e.g., stair, walk, transfer-to-tub) were found to be more difficult for subjects w ith amputation. While co mparing stroke with orthopedic impairment group, st roke group had more difficulty in eating and bowel tasks and orthopedic impairment group had more difficulty with several tasks requiring lower extremity functions (e.g., dress-lower-extre mity, transfer-to-tub, and walk). When comparing amputation with orthopedic impairment group, two items (b ath and dress-lower-extremity) were found to be more difficult for subjects with orthopedic im pairment, and the other two items (bowel and stairs) were found to be more challenging for subj ects with amputation. It should be noted that the above-mentioned results were not consistent through the entir e person ability range (i.e., nonuniform DIF). If the relative advantage changes the direction toward the other group (i.e., when two ICCs cross at some point along the person ab ility range), the signed index will reveal a smaller value. The results from unsigned area i ndex were similar to that fr om the signed area index. For most items, when the signed area index revealed larger values than other items, the unsigned area index was also greater within the same compar ison. The FIM-walk items (amputation versus orthopedic) revealed to be a non-uniform DIF where the unsigne d area index (0.32) was much higher than the signed area index (-0.20) within the same compar ison. Figure 3-4 presents the ICC DIF plots of two FIM items (FIM-walking a nd FIM-stairs) as an example. Figure 3-4 (C)

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87 showed the ICC plots for walking item (amputa tion versus orthopedic) in which the two ICCs crossed at about 0 (logits) person ability range. At lower person ability level (< 0 logits), subjects with amputation had relative advantage of perfor ming the walking task. At higher person ability level (> 0 logits), however, subjects with or thopedic impairment had advantages over the amputation group. Table 3-7 presents the item parameter calibra tions for 5 FIM cognitive items. Again, the category thresholds were divided by 6 to obtain the average item difficulty parameter (b). Similar to the motor items, the results demonstrated that item discrimination parameters varied across items. For cognitive items, problem solving and memory function were found to be relatively more discriminating than social interaction, e xpression, and comprehension. Table 3-8 provides results of DIF analysis for FIM cognitive it ems including the signed area index and unsigned area index. When comparing st roke with amputation group, e xpression was found to be more challenging to the stroke and pr oblem solving was more difficult for subjects with amputation. Expression was also found to be more challe nging when comparing stroke to orthopedic impairment group. When comparing amputation w ith orthopedic impairment group, no items revealed potential DIF. The unsigne d area index revealed a pattern similar to the signed index. Discussion This study used DIF analysis to investigate whether items in the FIM instrument function similarly across three major impairment groups in rehabilitation (stroke, amputation, and orthopedic impairment). If items exhibited significant DIF across groups, adjusting for differential item functioning may be required when data is compared between groups or when used in a pooled analysis [130]. It has also been st ated that If items with DIF are retained in test equating, they not only increase th e errors of test equating or pa rameter estimates, but also could cause bias towards some examinees [20] Therefore, some inves tigators suggest that DIF items

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88 be removed when conducting test equating to avoid poten tial biases that might result against a particular subpopulation [20]. Dallmeijer and colleagues study of DIF in the Dutch version of the FIM was based on a DIF method (b-difference) using Rasch (rating scale) model. Similar to their results, our DIF analysis showed several items demonstrated sign ificant DIF. In Dallmeije rs study, 4 of 11 motor items and 4 of 5 cognition items showed statistically significant DIF across stroke, multiple sclerosis, and traumatic brain injury. In our st udy, 4 to 9 of 13 motor items and 2 of 5 cognition items exhibited significant DIF. Removing misfit items revealed slightly different DIF results in certain groups. However, removing misfit items or adjusting for DIF had little impact on overall person ability measures (r 0.97). Dallmeijer and colleagues ( 2005) also had similar findings in regards to correlations between the adjusted a nd unadjusted person abilit y measures under the Rasch model (r = 0.99). DIF results seemed to reflect the characteristics of the impair ment typically found for each diagnostic group. For example, tasks which i nvolved upper extremity function (such as groom and dress-upper-extremity) were more challenging for individuals with stroke (possibly due to the result of unilatera l paresis of upper extremity limb). On the other hand, since most amputation and orthopedic impairment in this sample involved lowe r extremity impairment (e.g., hip and knee joint replacement, lower extremity am putation, or hip fracture), individuals with amputation or orthopedic impairment had more difficulty with tasks that involved lower extremity function (such as tran sfer and dress-lower-extremity). Some of the findings were unexpected. Tennant et al. (2004) [114] used DIF analysis to investigate th e item difficulty hierarchical order of FIM motor scale items with respect to age, gender, and country (translated FIM). They

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89 found that 7 out of 9 items having significant DI F by country, but no items were found to have DIF by gender or age. The item difficulty hierar chical order in Dallmeijers Dutch study also showed a slightly different patt ern than previous studies using the FIM in the original English version [48, 75-78]. For example, their results showed the eating item was at the average item difficulty and was more challenging than tran sfer, toilet, dress-upper-extremity, and groom items. Another inconsistency betw een English and Dutch studies is that the Dutch translated problem-solving item was not consistently the mo st difficult item. For individuals with multiple sclerosis, the problem solving wa s shown to be the easiest item. In general, DIF results were consistent acro ss different methods. Individuals with stroke consistently had more difficulty grooming a nd dressing upper extremity while the other two groups (amputation and orthopedic impairment group) had more difficulty with several tasks involving lower extremities (e.g., dress-lowerextremity, transfer-to-tub, and walk). There were some differences found across the different IRT and DIF methods. The bdifference DIF method based on the Rasch model a ssumed that item discrimination parameters are equal across different test items. In this study, the two-parameter model showed items had different item discriminations. When items exhi bited similar discriminations across different impairment groups (e.g., bathing item showed re latively high discriminations across different impairment group: stroke (a = 3.59); amputation (a = 3.00), orthopedic (a = 3.46)), uniform DIF method may be adequate. However, when items exhibited dissimilar discriminations across different impairment groups (e.g., walking item showed relatively high discriminations for stroke (a = 1.62) and orthopedic (a = 1.99) groups, but relatively lo w discrimination for amputation group (a = 0.92)), non-uniform DIF may occur, a finding that is not possible when using the Rasch model.

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90 DIF results may also depend on how group memb ership is defined. Some variables are clearly defined (such as gender), while other variables are more s ubjectively defined (such as age and severity). DIF results may be dependent on how a particular variable is defined. In this study, we classified patients into three impairment groups. The results may show different patterns when patients are divided into more specific diagnostic groups (e.g., when dividing stroke into left and right body involvement or dividing orthopedic impairment into upper and lower limb involvement). In future studies, mo re diverse and comprehensive impairment groups should be further examined. In conclusion, the purpose of this study was to investigate whether FIM motor and cognitive items function similarl y across different impairment groups (stroke, amputation, and orthopedic impairment). These inconsistencies in item calibrations led to the development of separate crosswalk conversion ta bles for each impairment group. Removing misfit items led to a similar DIF results. However, removing misfit items or adjusting for DIF seemed to have little effect on overall person ability measures estimat ed by the Rasch model. The 2PL logistic IRT model showed that item discrimination paramete rs varied across FIM items. Although the DIF results based on different models showed a sligh tly different set of items showing significant DIF, items that exhibited significant DIF appeared to be connected to specific characteristics of the impairment typically found for each diagnosti c group. For example, individuals with stroke tended to have more difficulty with tasks that involved more upper extremity functions (e.g., grooming, and dressing-upper-extremity). Since majority of the amputation and orthopedic groups involved lower extremity impairment, thes e individuals tended to have more difficulty with tasks that depend on lower extremity strengt h and functions (e.g., st air, walk, transfer-totub). For cognitive items, two items (expression and problem solving) consistently showed

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91 significant DIF across three impairment groups. Wh ile individuals with stroke showed greater difficulty in expression item, than amputation and orthopedic groups, the latter two groups did not show cognitive DIF. These inconsistencie s in item difficulty calibrations led to the development of separate crosswalk conve rsion tables for each impairment group.

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92 Table 3-1. FIM Instrument The Functional Independence Measure (FIM) Motor Items Eating Grooming Bathing Dressing-Upper Body Dressing-Lower Body Toileting Bladder Management Bowel Management Transfer to Bed/Chair/Wheelchair Transfer to Toilet Transfer to Tub/Shower Walk/Wheelchair Stairs Cognition Items Comprehension Expression Social Interaction Problem Solving Memory Rating Scale 7 Complete Independence (Timely, Safely) 6 Modified Dependence 5 Supervision (Subject=100%) 4 Minimum Assist (Subject=75%+) 3 Moderate Assist (Subject=50%+) 2 Maximal Assist (Subject=25%+) 1 Total Assist (Subject=less than 25%)

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93 Table 3-2. Participants Descriptive Statistics for Each Diagnostic Group Characteristic Stroke (N=302) Amputation (N=113) Orthopedic (N=239) All (N=654) Age (year) Mean ( SD) 69.40 (.0) 67.70 ( 11.0) 66.36 (.2) 67.99 (.0) Range 37-100 46-90 20-93 20-100 Males (%) 97.7% 99.1% 93.3% 96.6% Race, n (%) White 211 (69.9 %) 75 (66.4 %) 199 (83.3 %) 485 (74.2 %) Black 67 (22.2 %) 24 (21.2 %) 29 (12.1 %) 120 (18.3 %) Hispanic 15 (5.0 %) 4 (3.5 %) 7 (2.9 %) 26 ( 4.0 %) FIM-motor Mean (SD) 46.77 ( 24.6) 53.14 ( 21.6)64.44 (.2) 54.33 (.4) Range 13-91 13-86 15-89 13-91 Median 44.00 56.00 67.00 57.00 Maximal Score N (%) 4 (1.3%) 0 (0%) 0 (0%) 4 (1.3%) FIM-cognition Mean (SD) 23.29 ( 8.8) 29.7 ( 6.9) 32.16 ( 4.9) 27.72 ( 8.3) Range 3-35 5-35 7-35 3-35 Median 25.00 32.50 34.00 31.00 Maximal Score N (%) 37 (12.6%) 45 (37.5%) 108 (45.2%) 190 (29.1%)

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94Table 3-3. Difficulty Calib rations for FIM Motor Items Motor Entire Sample Stroke Amputation Ortho # Item Item Difficulty Error Infit Item Difficulty Error Infit Item Difficulty Error Infit Item Difficulty Error Infit 1Eat -1.58 0.051.38 -1.20 0.06 1.37 -1.60 0.111.38 -2.22 0.111.36 2Groom -0.90 0.040.88 -0.53 0.060.82 -0.95 0.090.84 -1.00 0.081.02 3Bath 0.33 0.040.71 0.30 0.060.61 0.13 0.080.85 0.50 0.060.64 4Dress-up -0.58 0.040.81 -0.22 0.060.61 -0.62 0.080.76 -0.67 0.071.32 5Dress-low 0.27 0.040.77 0.21 0.060.57 -0.03 0.080.76 0.67 0.060.68 6Toilet 0.08 0.040.59 0.24 0.060.66 0.03 0.080.58 0.14 0.060.55 7Bladder -0.48 0.031.39 -0.33 0.061.86 -0.65 0.081.56 -0.55 0.072.31 8Bowel -0.62 0.041.14 -0.47 0.061.66 -0.70 0.081.28 -0.90 0.081.72 9Transfer-chair -0.19 0.040.77 -0.27 0.060.74 0.05 0.080.66 -0.01 0.060.56 10Transfer-toilet 0.26 0.040.74 -0.04 0.060.60 0.30 0.080.69 0.26 0.060.62 11Transfer-tub 0.73 0.041.32 0.29 0.061.02 0.80 0.081.04 0.82 0.061.40 12Walk 0.83 0.041.89 0.45 0.061.71 0.76 0.082.47 0.98 0.061.50 13Stairs 1.84 0.041.71 1.57 0.071.74 2.47 0.131.58 1.98 0.071.22 Table 3-4. Item Difficulty Ca librations for FIM Cognition Items Cognition Entire Sample Stroke Amputation Ortho # Item Item Difficulty Error Infit Item Difficulty Error Infit Item Difficulty Error Infit Item Difficulty Error Infit 1Comprehension 0.15 0.070.99 0.05 0.080.91 -0.14 0.171.20 0.14 0.151.05 2Expression -0.55 0.061.12 -0.33 0.071.23 -0.88 0.190.88 -0.31 0.160.64 3Social Interaction -0.64 0.061.10 -0.86 0.080.97 -0.50 0.161.13 -0.71 0.151.44 4Problem Solving 0.72 0.060.74 0.81 0.080.87 0.99 0.150.64 0.22 0.120.58 5Memory 0.33 0.060.86 0.34 0.080.88 0.52 0.150.65 0.67 0.131.14

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95 Table 3-5. Item Parameter Calibrations for FIM Motor Items Items Item Discrimination Parameter (a) Average Item Difficulty Parameter (b) Stroke Amputation Ortho Stroke Amputation Ortho Eat 1.76 2.22 1.16 -1.59 -2.11 -2.81 Groom 2.68 2.50 2.68 -1.01 -1.53 -1.19 Bath 3.59 3.00 3.46 -0.35 -0.53 -0.12 Dress-up 3.71 3.51 2.70 -0.76 -1.16 -1.01 Dress-low 3.70 3.87 3.29 -0.42 -0.66 0.04 Toilet 3.47 4.33 4.28 -0.41 -0.61 -0.32 Bladder 1.83 1.89 1.63 -0.86 -1.15 -0.96 Bowel 2.02 1.96 1.03 -0.96 -1.20 -1.85 Transfer-chair 2.60 2.82 3.90 -0.76 -0.57 -0.50 Transfer-toilet 3.03 3.18 4.27 -0.56 -0.34 -0.24 Transfer-tub 2.48 2.11 2.76 -0.32 0.11 0.13 Walk 1.62 0.92 1.99 -0.09 0.63 0.35 Stairs 1.98 2.14 1.31 0.63 1.60 0.99 Table 3-6. DIF Analysis for FIM Motor Items Signed Area Unsigned Area Items Stroke vs Amput. Stroke vs Ortho Amput. vs Ortho Stroke vs Amput. Stroke vs Ortho Amput. vs Ortho Eat -0.51 -0.76 -0.25 0.30 0.51 0.29 Groom -0.51 -0.18 0.33 0.34 0.12 0.22 Bath -0.18 0.23 0.41 0.14 0.18 0.30 Dress-up -0.40 -0.25 0.15 0.31 0.20 0.13 Dress-low -0.24 0.46 0.70 0.19 0.34 0.52 Toilet -0.20 0.09 0.29 0.17 0.09 0.24 Bladder -0.29 -0.09 0.20 0.16 0.07 0.12 Bowel -0.23 -0.65 -0.41 0.14 0.46 0.35 Transfer-chair 0.19 0.26 0.07 0.13 0.21 0.10 Transfer-toilet 0.22 0.32 0.10 0.16 0.26 0.11 Transfer-tub 0.43 0.45 0.02 0.27 0.30 0.08 Walk 0.64 0.44 -0.20 0.38 0.25 0.32 Stairs 0.95 0.32 -0.64 0.55 0.23 0.36 Note: Positive values indicated that item is more challenging to the second group Negative values indicated that item is more challenging to the first group

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96 Table 3-7. Item Parameter Calibrations for FIM Cognitive Items Item Discrimination Parameter (a) Average Item Difficulty Parameter (b) Stroke Amputation Ortho Stroke Amputation Ortho Comprehension 4.55 2.11 3.54 -1.70 -1.96 -1.96 Expression 3.59 2.52 5.92 -1.56 -2.17 -1.94 Social Interaction 4.49 2.60 3.03 -1.71 -1.55 -1.53 Problem Solving 5.40 10.00 6.42 -1.24 -0.83 -1.00 Memory 5.57 6.36 4.69 -1.34 -1.04 -1.12 Table 3-8. Item Parameter Calibrations for FIM Cognitive Items Signed area Unsigned area Stroke vs Amput. Stroke vs Ortho Amput. vs Ortho Stroke vs Amput. Stroke vs Ortho Amput. vs Ortho Comprehension -0.21 -0.25 -0.04 0.26 0.22 0.14 Expression -0.57 -0.38 0.18 0.42 0.34 0.26 Social Interaction 0.17 0.18 0.02 0.18 0.17 0.04 Problem Solving 0.41 0.24 -0.17 0.43 0.24 0.20 Memory 0.30 0.22 -0.08 0.29 0.20 0.10

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97 (A) Uniform DIF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Group1 Group2 (B) Non-uniform DIF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Group1 Group2 Figure 3-1. Examples of DIF A) Uniform DIF and B) Non-uniform DIF P1 ( ) P2 ( )

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98 A. ADL/Motor Items B. C ognition/Communication Items -2 -1 0 1 2 3 -2-10123 Stroke (Lo g its) Amputation (Logits) 13 12 11 10 9 4 7 2 1 -2 -1 0 1 2 -2-1012 Stroke (Lo g its) Amputation (Logits) 2 -3 -2 -1 0 1 2 3 -3-2-10123 Stroke (Logits)Ortho (Logits) 13 12 11 5 10 9 4 8 2 1 -2 -1 0 1 2 -2-1012 Stroke (Lo g its) Ortho (Logits) 4 -3 -2 -1 0 1 2 3 -3-2-10123 Am p utation (Lo g its) Ortho (Logits) 13 5 3 1 -2 -1 0 1 2 -2-1012 Am p utation (Lo g its) Ortho (Logits) 4 2 Figure 3-2. Differential item functioning plots for A) Motor and B) Cognition items across differential impairment groups (Stroke, Amputation, and Orthopedic Impairment)

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99 ADL/Motor Items -2 -1 0 1 2 -2-1012 Stroke (Lo g its) Amputation (Logits) 11 10 9 5 4 2 1 -2 -1 0 1 2 -2-1012 Stroke (Lo g its) Ortho (Logits) 115 10 4 2 1 -3 -2 -1 0 1 2 -3-2-1012 Am p utation(Lo g its) Ortho (Logits) 9 5 10 11 Note: Misfit items in the motor scale: bladder, bowel, walk, and stair Misfit items in the cognition scale: none Figure 3-3. Differential item functioning plots for A) Motor and B) Cognition items across differential impairment groups after removing misfit items

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100 FIM-walking item FIM-stair item 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Stroke Orhto 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Stroke Orhto 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Stroke A mputee 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Stroke A mputee 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Ortho A mputee 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3-2-10123 Person Ability ( ) (logits)Probability of seccess P( ) Ortho A mputee Figure 3-4. Differential item f unctioning plots for FIM-walking (A B, C) and FIM-stair (D, E, F) items based on the ICC DIF method A B C F E D

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101 CHAPTER 4 EVALUATING THE FIM-MDS CROSSW ALK CONVERSION ALGORITHM VIA FUNCTIONAL RELATED GROUP CLASSIFICATION Introduction To develop an effective and efficient mechan ism for evaluating and tracking changes of functional status across the continuum of care, it is important to have a means to integrate information and achieve score comparability acr oss outcomes instruments. While utilizing a single comprehensive outcome assessment instru ment for post acute care would provide the optimal mechanism for the synchronized and seam less monitoring of patient outcomes, the fact that different instruments are firmly entrenched across different post-acute settings has made large-scale reformation extremely difficult. In contrast to adopting a single outcome measure across all post acute setti ngs, another possible solution is to cr eate a crosswalk or statistical link between functional status subscales of different instruments alr eady used in these settings. In inpatient rehabilitation facilities (IRF s) in the U.S., the Functional Independence Measure (FIM) is the most widely used f unctional assessment [64] Through the conjoint efforts by the American Congress of Rehabilitation Medicine (ACRM), the American Academy of Physical Medicine and Rehabilitation (AAPMR) and 11 other national professional organizations, the FIM was developed as a central core measure of the Uniform Data Set for Medical Rehabilitation ( UDSMR) to document the severity of patient disability [65, 124]. In 2002, the FIM was incorporated into the Inpatient Rehabilitation Faciliti es Patient Assessment Instrument (IRF-PAI) and implemented as the national prospective payment system (PPS) for inpatient medical rehabilitation reimbursement [126]. Based on age, functional status (provided by FIM), comorbidities, and rehabilitation impair ment category, patients are classified into discrete case-mix groups (CMGs) for predicting the resources needed to provide patient care [127].

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102 While FIM is extensively used in inpatient rehabilitation; the Minimum Data Set (MDS) must be completed for all resi dents in Medicare/Medicaid nursi ng facilities or licensed only nursing facilities [71, 89, 90, 145]. In respons e to the Omnibus Budget Reconciliation Act of 1987 (OBRA 87), the Health Care Financing Admi nistration (now the Centers for Medicare and Medicaid Services (CMS)) developed a Resident Assessment Instrument (RAI) for use by all certified skilled nursing facilities to assess and plan care for residents. As a central assessment core in the RAI, the MDS documents a variety of residents health information for care planning [146]. By 1998, Medicare/Medicai d nursing facilities were require d by regulation to encode and transmit MDS data to the state. After the prospective payment system was mandated in rehabilitation, SNFs utilized information from the MDS assessment (an activity of daily living (ADL) score, a depression index, and a cognition performance scor e) to classify SNF residents into the Resource Utiliza tion Groups (RUG-III) [147]. In the year 2000, the CMS recommended inpa tient rehabilitation f acilities to use MDSPost Acute Care (MDS-PAC) as uniform instrume nt to integrate the health care information across the post acute care [ 148]. The MDS-PAC was developed by Morris and colleagues [89] who participated in the development of the or iginal MDS. The structure of the MDS-PAC is similar to that of the MDS, but the content was expanded to cover care needs and outcomes across post-acute settings [49]. For instance, fu nctional status section comprises not only the activity of daily living items (e.g., eating, tr ansferring, dressing, and walking), but also instrumental activity of daily living (IADL) items (such as meal preparation, manage finances, and car transfer). Nonetheless, due to consider able resistance, mainly from the rehabilitation field, the CMS currently is no longer consid ering of the use of th e MDS-PAC to monitor outcomes for post-acute care [149, 150].

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103 In 2006, Velozo and colleagues [151] de veloped a FIM-MDS crosswalk conversion algorithm to link the FIM and the MDS. The original intent was to develop an effective and efficient method to track and evaluate veterans functional status cha nges across rehabilitation and skilled nursing facilities. The basis of th e crosswalk methodology was the similarity of the item content of the FIM and MDS. Rasch true sc ore equating method [4] wa s used to develop the FIM-MDS crosswalk. A linked sa mple a sample of Veteran Affairs (VA) patients who had been assessed on both instruments within 5 days was used for data analysis. Following the recoding rating scales to be comparable across the instruments, a met hod used by Linacre (2005) [153] was performed to remove invalid data fo r those patients who obtained dissimilar overall measures between these two instruments. Follow ing elimination of inva lid person measures, the FIM and MDS items and rating-scale calibrations were placed on a common linear scale with the same local origin by including both FIM and MDS items in a concurrent run using the Rasch partial credit model analysis. The combined anal ysis provided co-calibrated item measures and rating-scale measures, which were then used as anchors in separate FIM and MDS analyses. These separate analyses generated two output tabl es which linked expected total raw scores to person ability measures. By matching the raw scores from each instrument to the same linked person measure, a FIM-MDS raw-score crosswal k conversion table was created whereby total FIM raw scores could be translated into total MDS raw scores and total MDS raw scores could be translated into total FIM raw scores. Critical to determining the feas ibility of this crosswalk me thodology for application in the real world is to test its validity. One means is a cross-validation method. For example, Nyein and his colleagues (1999) [39] evaluated their Barthel-FIM conversion system by implementing their conversion system in a prospective st udy of 40 subjects. Nonpa rametric statistical

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104 techniques (spearman rank correlation and Wilco xon signed rank test) were used to evaluate the correlation between the derived Barthel score and the actual Barthel score. Absolute agreement between the converted and actual sc ores ranged from 75 to 100% a nd the kappa statistical values ranged from 0.53 to 1.0 (moderate to substantial strength of agreement). Buchanan et al. (2003) [49] evaluated their FIM-(M DS-PAC) conversion system by implementing their conversion algorithm in a second sample (independent from the sample used to develop the conversion algorithm) and computed the percentage of the sample being classified into similar case-mix groups (CMG) by the actual and converted scor es. The FIM and PAC-to-FIM scales mapped 53% of cases into the same CMG; approximate 84% were classified within 1 CMG and 93% within 2 CMG. To continue to investigate the feasibility of developing a crosswalk between the FIM and the MDS, the purpose of this study was to evaluate the accuracy of FIM-MDS crosswalk conversion algorithm in determining Functional Related Groups (FRGs). A second sample, independent from the sample used to de velop the FIM-MDS crosswal k, was used for this validation analysis. Methods Data Preparation A secondary, retrospective an alysis using the FIM and MD S data from two databases collected by the VAs Austin Automation Cent er (AAC) during June 1, 2003 to Dec 31, 2004 was used for this study. The inclusion criteria were: 1) selecting FI M and MDS assessments within 5 days of each other, 2) selecting impairme nt codes within stroke (code ranges from 1.1 to 1.9), amputation (code ranges from 5.1 to 5.9) or orthopedic impairment s (code ranges from 8.1 to 8.9) [154]; and 3) containing no missi ng values within any of ADL/motor and cognition/communication items of the FIM and the MDS instruments.

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105 The original FIM and MDS data sets were merged using social security numbers. The initial merge resulted in a total of 151,770 records. With the criteria of five or less days apart between administrations of the assessments, the av ailable data decreased to 18,754 records. Next, records of the same subject but with multiple re cords assessed at different dates were further filtered to choose FIM and MDS with the smalle st days apart between administrations. This procedure resulted in a total of 6,363 records. After constraining the assessment date during June 1, 2003 to December 31, 2004 in order to have no overlapping period with the data used to create the FIM-MDS crosswalk, the dataset further shra nk to 2,107 records. Next, we selected three major impairment groups in the rehabilitation (s troke, amputation, and orthopedic impairment), removed probable invalid data entry (such as age at 159 years old or negative coding in functional status items) and only retained reco rds with complete values for all FIM or MDS functional status items. This selection results in a dataset containing 1476 patients: 804 stroke, 268 amputation and 404 orthopedic impairment. This study was approved by the Institutional Review Board at the University of Florida and the VA Subcommittee of Human Studies. Analysis Procedure Table 4-1 and 4-2 present the FIM-MDS cro sswalk conversion tables for the ADL/motor and cognition/communication scale respectively. A detailed description of the conversion methodology is presented elsewhere [151]. (While the constructs are most appropriately labeled ADL/motor and cognition/communication, for simp lification, we will use the terms motor and cognition throughout the paper.) The conversion table enables to tal FIM raw scores to be translated into total MDS raw scores and vice ve rsa via the common logit scale. For example, a MDS motor raw score of 22 will be converted to a FIM motor raw score of 50 because both of these raw scores are associated with the co mmon person ability meas ure of -0.06 logits.

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106 Similarly, a FIM motor raw score of 71 corresp onds to a MDS raw score of 10 since both raw scores are associated with a person ability measure of 0.68 logits. Prior to using the conversion table, several st eps were taken in orde r to use the crosswalk conversion table. First, the MDS ra ting of (activity did not occu r) was recoded to a (total dependence). The rationale underlying this deci sion was that a probable explanation for an activity not occurring du ring the observation period was that th e activity could not be performed [152]. A similar recoding procedures were also performe d by Jette and colleagues [155] and Buchanan (2003) [40]. Next, four recall cogni tion items in the MDS instrument had to be recoded so that all cognition MD S items will have the same rati ng scale direction with a lower score indicating a better performance. Therefor e, a on the MDS recall items was recoded to and a on the MDS recall items was recoded to . Lastly, item ratings from each motor and cognition scale were summed to obtain a total raw motor and cognition score. The conversion algorithm was test ed at three different levels: 1) individual level, 2) classification level, and 3) facility level. For th e individual level analysis, the absolute values of point differences between the actual FIM scor es and the MDS derived FIM scores (|FIMa FIMc|) were computed. The percentage of data with point differences of 5 points or less and 10 points or less was calculated. To compare whethe r the score distributions are similar between the actual and converted scores, pair ed t-test were used to test the equivalence of the score distributions. For the classification level analysis, the F unctional Related Groups (FRGs) classification system was used to examine whether the converted FIM scores would cla ssify the same patient into similar classification level as that derived from the actual FIM scores. The FRGs is a patient classification system being used by the CMS a nd is the basis for computing the Prospective

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107 Payment System (PPS) payment in inpatient re habilitation facilities [156, 157]. Using FRGs, patients are first classified into one of 20 impairment categorie s and further divided by the two FIM subscales, motor and cognition, and by age at admission to the rehabilitation setting. Figures 4-1 to 4-5 provide FRG al gorithms for classifying patients in to one of the FRG levels for each impairment category used in this study (s troke, amputation, orthopedic impairment) [158]. Patients who are assigned to different FRGs ar e expected to have di fferent rehabilitation outcomes and total costs of care. Therefore, wh ether the converted scores could classify the individuals into the same FRGs as actual scor es provides a means to validate the conversion algorithm and indirectly test the accuracy of the conversion algorithm in a pragmatic manner. After classifying patients into one of the FRGs, the percentage of indivi duals being classified into the same FRG category, one category apart ( 1 level), and two categor ies apart ( 2 levels) were calculated. Chi-square statistics were used to test if there is any association between classification results based on the actual and c onverted scores. Meanwhile, kappa statistics was used to quantify the degree of agreement. Kappa statistics is an index that compares the agreement against that which might be expected by chance. The possible values of kappa index range from +1 (perfect agreement) to (com pletely disagreement). Landis and Koch (1977) [159] provided guidelines for the strength of agreement where a ka ppa statistics between 0.21 to 0.40 demonstrate a fair strength of agreemen t; 0.41-0.60 indicate a moderate strength of agreement; and 0.61-0.80 indicate a s ubstantial strength of agreement. Finally, the conversion algorithm wa s evaluated at the facility leve l. After the actual MDS scores were converted to FIM scores (FIMc) via the co nversion algorithm, the score distribution of the FIMc was compared to the actual score distribution of the FIM (FIM a) by facility. Paired t-tests were used to test the equivalence of the means obtained from the actual and the converted FIM

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108 scores. If the mean of the converted score (FIM c) was close to the actu al FIM scores (FIMa), facilities that use different instruments may be co mpared relative to their outcomes locally or nationally by means of a conversion system. Since this data set was collected from facilities throughout the United States, many facilities had two few patients for this analysis. The criterion of selecting facilities with more than 50 patients in this dataset, this selection criterion resulted in only 5 facilities available for this analysis. Results Sample The sample of 1,476 included three major diagnostic groups: 804 stroke, 268 amputation and 404 orthopedic impairment. Table 4-3 presente d the basic demographic information of this sample. Individuals with stroke were fairly equa lly distributed across left and right involvement. The majority of individuals with amputation in volved unilateral lower limb above or below the knee. Most of the individuals with orthopedic im pairment had unilateral hip or knee replacement. The age of sample ranged from 26-97 years with a mean age of 70.19 ( 11.65) years. An average assessment date difference between th e FIM and the MDS was 3.16 ( 1.68 days). Ninety-seven percent of the sample was male, 69 % was White, and 46 % was married. Validation at the Individual Level Score distribution Figure 4-6 (A) and (B) showed the actual MDS score distribution for the motor and cognition scale, respectively. The MDS motor domain had a score range of 0-52, where 0 indicates a person is able to perform every task independently without any assistance. With a mean of 20.7 ( 14.7 S.D.), the motor domain ha s a slightly skewed di stribution toward higher function (skewness = 0.43). The MDS cognition domain (ranging from 0-25), however, showed a severe ceiling effect (skewness =1.84). Appr oximately 42.9 percent of subjects (n = 633)

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109 scored intact on every cogniti on item and nearly 79% of the subjects (n = 1166) obtained a perfect score or a score within 5 points away fr om a perfect score (max imum total independence score, 0-5). Results from Kolm ogorov-Smirnov test of normality indicated that both MDS motor score distribution (p < .001) a nd MDS cognition score distribution (p < .001) deviated from a normal distribution. Figure 4-6 (C) and (D) showed the actual FIM score distribution for the motor and cognition items, respectively. The FIM motor domain has a score range of 13-91, where 91 indicate an individual can perf orm every task independently. The FIM cognition domain has a score range of 5-35, where 35 in dicate an individual is rated intact on every cognition item. Similar to the MDS score distributions, the FI M motor scale has a sli ght skew distribution toward a higher function (skewness = -0.372) and the FIM cognition scale has a severe ceiling effect (skewness = -1.03). Approximately 29.6% of individuals (n = 437 ) obtained the maximum FIM cognition score of 35 and 53.5 % of the indi viduals (n = 791) obtained the score within 5 points away from the maximum score (i.e., 30-3 5). Results from Kolmogorov-Smirnov test of normality rejected the null hypothesis of nor mal distribution for both FIM motor score distribution (p < .001) and FIM cognition scor e distribution (p < .001). The FIM motor and cognition scales correlated with MDS motor and cognition scale at -0.80 and -0.66, respectively. Point difference |FIMa-FIMc| The MDS scores were converted into FIM comp atible scores via the crosswalk conversion algorithm. Figure 4-6 (E) and (F) showed the converted FIM score distribution for the motor and cognition scales, respectively. Compared to the actual FIM score distri butions, Figure 4-6 (C) and (D), the converted FIM sc ores showed a similar distri bution pattern. Results from Kolmogorov-Smirnov test of normality rejected th e null hypothesis of normal distribution for both FIM converted motor score distribution (p < .001) and FIM conve rted cognition score

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110 distribution (p < .001). Non-para metric Wilcoxon signed ranks test, hence, was used to test the equivalence of the score di stributions between the actua l and converted FIM scores. The converted FIM motor scale had a mean of 54.4, which was close to the actual FIM motor score distribution with a m ean of 55.7. While the mean diffe rences of the distributions was only 1.3, the results from Wilcoxon signed ranks test showed a signifi cant difference between these two score distributions (z = -4.11, p < .001). Pearson correlation coefficient was 0.79 between the actual and converted FIM motor scores. Approximate 33.7 percent of the actual and converted scores show a 5 point difference or le ss and 56.9 percent show a 10 point difference or less (see Figure 4-7). The average of point differe nces was 11.6 ( 10.4) points. The converted FIM cognition scale had a mean of 27.1 ( 7.8), which was virtually identical to the actual FIM cognition score distribution with a mean of 27.0 ( 9.0). In spite of the similarity of means, the Wilcoxon signed ranks test also rejected the null hypothesis that these two score distributions are equivalent (z = -2.21, p = 0.027). The converted FIM cogniti on scores correlated moderately (Pearson correlation coefficient r = 0.67) with the actual FIM cognition scores. Sixty-seven percent of the actual and convert ed scores show a 5 point diffe rence or less and 87.7 percent show a 10 point difference or less (see Figure 4-7) The average of point differences was 4.9 ( 4.8) points. Table 4-4 summari zes the validation results at this individual level. Validation at the Classification Level The Functional Related Groups (FRGs) classi fication system requires individuals FIM motor score, FIM cognition score, age, and impair ment code to classify an individual into a specified level. We initially used actual FIM scor es to perform the classification analysis and then used converted FIM scores to perform the sa me procedures. Table 4-5 to 4-7 presents cross tabulations of the results of FRG classifications derived usin g actual FIM scores (FRGa) and converted FIM scores (FRGc).

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111 For the stroke impairment group, the FRGs cl assified individuals into nine categories (Table 4-5). Chi-square statistics showed that there was a significant association between the classification results (chi-s quare = 1232.6; df = 64; p < .001). Kappa analysis demonstrated a fair strength of agreement (0.37). Forty-four percent of patients were classified into the same FRGs, 67.0 % were classified into FRGs within one cl assification level (within plus or minus one FRG level), and 80.5 % were classified into FRGs w ithin two classification levels (within plus or minus two FRG levels). For the amputation impairment group, individu als are classified into one of two FRG categories (Table 4-6). Chi-square statistics sh owed that there was a significant association between the classification results (chi-square = 120.6; df = 1; p < .001). Kappa analysis demonstrated a substantial strength of agreemen t (0.66). Approximate 83.1 percent of subjects were classified into the same FRG. For the orthopedic impairment group, there ar e seven FRG classification levels (Table 47). Chi-square statistics exhibi ted a significant association between the classification results (chisquare = 433.4; df = 36; p < .001) with a fair strength of ag reement (kappa = 0.37). About fiftyfive percent of patients were classified into th e same FRGs, 69.2 % were classified into FRGs within one level apart; and 87.4 % were classi fied into FRGs within two levels apart. Validation at the Facility Level The FIM-MDS crosswalk conversion algorithm wa s evaluated at the facility level by comparing to FIM converted score distributions to FIM actual scor e distributions by facility. The five facilities with more than 50 subjects in th is dataset were selected. Table 4-8 listed the validation results at the facility level. In gene ral, the mean differences between the actual and converted FIM motor scores varied from 1.41 (Faci lity E) to 11.30 (Facility A). Since the score distributions of the actual and c onverted FIM scores also deviated from normal distribution, non-

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112 parametric statistics were used to test the equi valence of the score distri butions. The results from Wilcoxon Signed Rank Test showed that an acceptable equivalence in 3 out of 5 facilities. The correlations between the actual a nd converted motor scores varied from facility to facility (ranging from 0.58 to 0.89). The cognition scale show ed more consistent results with the mean differences between actual and converted FIM c ognition scores ranging from 1.51 to 3.82 points. Nonetheless, the non-parametric Wilcoxon Signed Ra nk Test revealed statistical significance for all facilities. The co rrelations between the actual and converted cognition sc ores also varied from facility to facility (ranging from 0.42 to 0.80). Discussion The purpose of this study was to evaluate the FIM-MDS crosswalk conversion algorithm developed by Velozo and colleagues. An indepe ndent sample of the FIM and the MDS from the existing VA databases was used to validate the crosswalk. The FIM-MDS crosswalk conversion algorithm was examined under 1) individual level, 2) classification level, and 3) facility level. There are mixed findings from the validity testing of the FIM-MDS motor and cognition crosswalks. On one side, several results support ed the feasibility of developing the FIM-MDS crosswalks. The FIM and MDS motor and c ognition raw scores showed similar score distributions. The scales showed moderate-strong correlations at -0 .80 for the motor scales and 0.66 for the cognition scales. The means of MDS derived FIM scores were very close to the actual FIM scores with 1.3 points difference for the motor scale and 0.1 points for the cognition scale. At the classification level, chi-square st atistics showed a significa nt association between the FRG classification results ba sed on actual and MDS derived FI M scores and kappa statistics demonstrated a fair (0.37) to substantial (0.66) st rength of agreement. Furthermore, at the facility level, 4 out of 5 facilities had just 1 to 3 point s differences between means of the actual and MDS derived FIM scores.

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113 While sample distributions were similar, how ever, individual score comparisons fell short of expectations. Only 34 percent of the converted FIM motor scores were within 5 points of the actual FIM scores and 56.9 percen t were within 10 points. For cognition scale, 67 percent of the actual and converted FIM cognition scores showed a 5 point difference or less and 87.7 percent show a 10 point difference or less. The better results of FIM cognition scale may be due to a severe ceiling effect. That is, if individuals are at the ceiling of both instruments, we expect a better conversion result, even though these individuals may di ffer in cognition ability. The results from nonparametric proc edure did not support the hyp othesis that the actual and converted scores have the same score distribut ions for either the motor or cognition scales. Meanwhile, the validation results at the facility level varied. The correlation coefficient between the actual and MDS derived FIM scores varied fr om moderate to strong for the motor scale (0.58 0.89) and cognition scale (0.42 to 0.80). While four of the five facilities demonstrated 1 to 3 points differences between means of the actu al and MDS derived FIM scores, one facility showed 11.30 point difference in the motor scale. The mixed findings from the validity te sting of the FIM-MDS motor and cognition crosswalks leave considerable questions as to the extent to which crosswalks should be implemented. While the relatively strong correla tions between the actual and converted scores support using a crosswalk, the significant differences found be tween the actual and converted score distributions suggest that the crosswalk may not have adequate accuracy for decision making in health care. The almost equivalent means between the actual and MDS derived FIM scores suggest that the crosswalks may dem onstrate population equivalence and may have adequate accuracy for monitoring facility-level outcomes and ad equate accuracy for research involving large sample sizes. Howeve r, the results varied between f acilities and the validation at

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114 the facility level did not complete ly support this conclusi on. It should be noted that the facilitylevel testing was done with sample sizes just above 50 subjects. Larger sample size should be analyzed in future study to inves tigate whether it is feas ible to apply crossw alk at the facility level. Our validation results based on the FRG classifi cation system were slightly less promising than those found by Buchanan and colleagues (2004) in there study of a crosswalk between the FIM and MDS-PAC [49]. They evaluated their FIM-(MDS-PAC) conversion system by classify approximately 3,200 subjects into CMGs using a prospective study. The FIM and PAC-to-FIM scales mapped 53% of cases into the same CMG; approximate 84% were classified within 1 CMG and 93% within 2 CMG, where most of CMGs have 3 to 4 levels. In this study, about 44 % of the stroke was classified into the same FRG; 67 % within 1 FRG level; and 81 % within 2 FRG levels. Since the FRG classification for th e amputation impairment only have 2 levels, a high percentage (83 %) of indi viduals were classified into the same FRG and 100 % within 2 FRG. For the orthopedic impairment group, about 55 % of patients were classified into the same FRG, 69.2 % within 1 FRG, and 87.4 % were with in 2 FRG. They further evaluated the payment implications of substituting the MDS-PAC fo r the FIM. They found the mean payment difference between these two instruments was not significantly different from zero. However, the standard deviation of differences was large ($1,960) and nearly 20 % of the facilities had revenue shifts larger than 10 % of original cost. Similar costs comparisons were not made in the present study due to the unavailabili ty of cost data. Note that the lo wer validity values in the present study as compared to Buchanan and colleague s findings may be a function of different methodologies and sampling (e.g., differences in FRG versus CMG calculations, secondary analysis of VA data versus prospective data collection).

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115 The effectiveness of crosswalks may be depende nt on sources of the e rror associated with FIM and MDS. This sample was selected base d on the criteria of fiv e or less days apart between administrations of the FIM and MDS assessments. Based on the requirement that clinical staff have three days to complete the FIM assessment after patients are admitted or discharged from inpatient rehabilitation and the assessment coordinators have 14 days to finish the MDS evaluation, the five-day criteria used in this study may be c onsidered stringent. This study was based on an assumption that a patient s functional status remains unchanged during this five days period. Obviously, this assumption is unlikely to be supported in clinical practice. However, when criteria of fewer than five days apart, there was a dramatic decrease in available records for analysis. Future studies may be need ed to exam that whether selecting fewer days apart between administrations of the assessmen ts will lead to better validation results. To keep the quality of data, clinicians have to obtain 80 % and above passing score on the FIM mastery test to be qualified for entering FI M data into the VA national database. Moreover, clinicians are retested every 2 years with a diffe rent version of the examination to ensure the rating accuracy of the FIM. A number of studies have shown that the FIM has good interrater or test re-test reliability (> 0.90) [56, 59, 62, 160]. In contrast, for MDS assessments, each units assessment coordinator may obtain information from ot her staff orally or has others actually rate relevant items and charges the final completion of the MDS. The raters do not necessarily receive formal training, and no qua lification exam is required. Th e MDS is much more extensive than the FIM. Assessment burden may result in completing assessments quickly instead of accurately and further introduced rating error. To improve the application of FIM-MDS crosswalk conversion algorithm in the clinical sites, improvement in the quality of test administration and rater training are likely to be required.

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116 There are several limitations in this validation study. First, the data sets did not have sufficient information about assessment type (e.g., admission, discharge, follow-up) and discharge reason. For patients w ho transferred from inpatient reha bilitation to skilled nursing facilities, their condition may be different from those who transferred from skilled nursing facilities to inpatient rehabilitati on. For instance, a transfer from one facility to another might due to a significant change in the patients medi cal or functional status Second, the present validation study only focused on three major reha bilitation impairment groups. More diverse impairment groups and more representative samp les should be explored in terms of developing FIM-MDS crosswalk conversion algorithms. Third, fewer days apart between assessments dates should be explored in the future to rule out the potential functional st atus change during the transfer period. The failure of the FIM-MDS crosswalks in th e present study to de monstrate individual equivalence (i.e., relatively low percentage of actual and converted scor es being within 5 points of each other), suggests that the crosswalks do not have adequate accuracy to monitor individual patients that transfer from facilities which use th e FIM (e.g., inpatient rehabilitation settings) to or from which use the MDS (e.g., skilled nursing f acilities). While these validation results fail to support using the crosswalk to m onitor individuals across the con tinuum of care, we would argue that the variance might be as much a function of the error in global measures per se as it is a function of error in the cr osswalk. That is, there is a possibility that varian ce in use of the same measure (e.g., only the FIM or only the MDS/MDS-PA C), by different raters and across different facilities, could result in different FRG/CMG cla ssifications and differences in revenue shifts similar to those found by Buchannan and coll eagues in their study of the FIM-MDS-PAC crosswalk. That is, while utilizing a single co mprehensive outcome asse ssment instrument for

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117 post acute care may appear to be the best m echanism for the monitoring patient outcomes across post acute settings, inherent error in these measures, may lead to the type of inconsistencies found with using crosswalks. A direct comparison of a single measure to crosswalk conversions may be necessary to determine the best method for monitoring outcomes across the continuum of care. Furthermore, this comparison must be revi ewed relative to the pote ntial costs of converting all post acute care settings to a common outcome measure (e.g., large scale transformation of existing administration procedures and equipments new training for clinicians, therapists, and staffs, and follow-up research studies for validat ing the newly-developed assessment tool). A crosswalk system for monitoring patient outcome s across the continuum of care would not incur these costs since facilities could continue to use there current outcome measures. The effectiveness of a single measure or crosswal k measures may ultimately be dependent on the quality of the data. Effective monitoring of patie nts across the continuum of care, whether it be via a single measure or crosswalks, may ultima tely be dependent on require more rigorous standardization and more extensiv e training of clinical raters.

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118 Table 4-1. FIM-MDS Crosswalk C onversion Table ADL/Motor Scale FIM Logits MDS FIM Logits MDS FIM Logits MDS 13 -3.61 52.0 40 -0.35 28.0 67 0.51 12.5 14 -2.55 51.0 41 -0.32 27.0 68 0.55 12.0 15 -2.02 49.5 42 -0.29 26.5 69 0.59 11.5 16 -1.75 48.0 43 -0.26 26.0 70 0.63 11.0 17 -1.57 47.0 44 -0.23 25.5 71 0.68 10.0 18 -1.44 46.0 45 -0.20 25.0 72 0.73 9.5 19 -1.33 44.5 46 -0.17 24.0 73 0.78 9.0 20 -1.24 43.5 47 -0.14 23.5 74 0.84 8.5 21 -1.16 42.0 48 -0.12 23.0 75 0.89 8.0 22 -1.09 41.0 49 -0.09 22.5 76 0.95 7.5 23 -1.03 40.0 50 -0.06 22.0 77 1.02 6.5 24 -0.97 39.0 51 -0.03 21.5 78 1.09 6.5 25 -0.92 38.5 52 0.00 21.0 79 1.16 6.0 26 -0.87 37.5 53 0.03 20.5 80 1.24 5.0 27 -0.82 37.0 54 0.06 20.0 81 1.33 4.5 28 -0.78 36.0 55 0.09 19.5 82 1.43 4.0 29 -0.73 35.0 56 0.12 19.0 83 1.54 3.5 30 -0.69 34.5 57 0.15 18.5 84 1.67 3.0 31 -0.66 34.0 58 0.19 18.5 85 1.82 2.5 32 -0.62 33.0 59 0.22 17.0 86 2.00 2.0 33 -0.58 32.0 60 0.25 16.5 87 2.22 2.0 34 -0.55 31.5 61 0.28 16.0 88 2.51 1.0 35 -0.51 31.0 62 0.32 15.5 89 2.92 0.5 36 -0.48 30.5 63 0.35 15.0 90 3.63 0.5 37 -0.45 30.0 64 0.39 14.5 91 4.84 0 38 -0.42 29.0 65 0.43 13.5 39 -0.38 28.5 66 0.47 13.0

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119 Table 4-2. FIM-MDS Crosswalk Convers ion Table Cognition/Communication Scale FIM Logits MDS FIM Logits MDS FIM Logits MDS -5.78 29 11 -0.37 13 2.04 3 -5.78 28 12 -0.17 12 26 2.15 -4.5 27 13 0.02 11 27 2.37 5 -3.88 26 14 0.21 10 2.52 2 -3.2 25 0.41 9 28 2.62 -2.82 24 15 0.35 29 2.9 6 -2.58 23 16 0.5 30 3.2 1 -2.22 22 17 0.63 8 31 3.54 -1.97 21 18 0.8 7 32 3.94 7 -1.77 20 19 0.94 33 4.44 -1.53 19 20 1.09 6 4.53 0 8 -1.28 18 21 1.25 34 5.2 -1.13 17 22 1.37 5 35 6.44 9 -0.91 16 23 1.57 -0.75 15 1.67 4 10 -0.62 24 1.75 -0.56 14 25 1.94

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120 Table 4-3. Demographic Baseline Characteristics Characteristic N=1,476 Race, n (%) Age, mean S.D. (y) 70 12 White 1,019 (69.0 %) Gender, n (%) Black 313 (21.2 %) Male 1,434 (97.2 %) Hispanic 56 ( 3.8 %) Female 40 ( 2.7 %) Native American 8 ( 0.5 %) Missing 2 ( 0.1 %) Asia 2 ( 0.1 %) Marital Status Other 40 ( 2.7 %) Married 680 (46.1%) Missing 38 ( 2.6 %) Divorced 348 (23.6%) Impairment Groups, n (%) Stroke (n = 804) Left Body Involvement 343(23.2 %) Right Body Involvement 285(19.3 %) Bilateral Involvement 32(2.2 %) No Paresis 80(5.4 %) Other Stroke 64(4.3 %) Amputation (n = 268) Unilateral Upper Limb Above the Elbow (AE) 1(0.1%) Unilateral Upper Limb Below the Elbow (BE) 1(0.1%) Unilateral Lower Limb Above the Knee (AK) 73(4.9 %) Unilateral Lower Limb Below the Knee (BK) 140(9.5 %) Bilateral Lower Limb Above the Knee (AK/AK) 9(0.6 %) Bilateral Lower Limb Above/Below the Knee (AK/BK) 9(0.6 %) Bilateral Lower Limb Below the Knee (BK/BK) 16(1.1 %) Other Amputation 19 (1.3%) Orthopedic (n = 404) Unilateral Hip Fracture 56(3.8 %) Femur Fracture 3(0.2 %) Pelvic Fracture 4(0.3 %) Major Multiple Fractures 12(0.8 %) Post Hip Replacement 1(0.1%) Unilateral Hip Replacement 106(7.2 %) Bilateral Hip Replacement 1(0.1%) Unilateral Knee Replacement 166(11.2 %) Bilateral Knee Replacement 4(0.3%) Post Knee Replacement 1(0.1%) Other Orthopedic 46(3.1 %)

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121Table 4-4. Summary of the Valid ation Results at Individual Level Point Difference |FIMa-FIMc| Mean Standard Deviation Wilcoxon signed ranks test Corre. Mean ( S.D.) 5 points 10 points FIM actual motor score 55.7 24.23 FIM converted motor score 54.4 23.50 z = -4.11, p <.001 0.79 11.6 ( 10.43) 33.7% 56.9% FIM actual cognition score 27.0 8.98 FIM converted cognition score 27.1 7.84 z = -2.21, p = .027 0.67 4.9 ( 4.83) 67.1% 87.7%

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122 Table 4-5. FRG Classifi cation for Stroke Sample FRGa Total 1 2 3 4 5 6 7 8 9 FRGc 1 88 0 0 13 4 5 1 0 2 113 2 5 65 15 3 2 3 0 0 0 93 3 1 29 39 15 9 1 4 1 0 99 4 14 6 7 32 21 15 14 7 10 126 5 6 1 3 12 13 15 11 6 3 70 6 3 4 1 4 8 6 11 4 10 51 7 3 0 1 9 8 7 51 5 20 104 8 3 0 2 3 5 7 5 7 14 46 9 0 1 1 5 3 6 17 14 55 102 Total 123 106 69 96 73 65 114 44 114 804 Chi-square=1232.6; df = 64; p < 0.001 Kappa =0.368 Classified into the same FRGs (44.28%), 1 level apart (67.04%), 2 levels apart (80.47%) Table 4-6. FRG Classificat ion for Amputation Sample FRGa Total 1 2 FRGc 1 112 33 145 2 12 109 121 Total 124 142 266 Chi-square=120.6; df = 1; p < 0.001 Kappa =0.664 Classified into the same FRGs (83.08%) Table 4-7. FRG Cla ssification for Orthopedic Impairment Sample FRGa Total 1 2 3 4 5 6 7 FRGc 1 2 3 0 0 0 0 0 5 2 1 17 3 4 1 3 6 35 3 0 4 8 3 0 1 17 33 4 1 2 8 40 1 1 4 57 5 0 0 2 0 12 0 34 48 6 0 1 0 0 3 3 16 23 7 0 3 7 1 22 9 114 156 Total 4 30 28 48 39 17 191 357 Chi-square=433.4; df = 36; p < 0.001 Kappa =0.366 Classified into the same FRGs (54.90%), 1 level apart (69.19%), 2 levels apart (87.39%)

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123 Table 4-8. Validation Results at the Facility Level Mean (raw score) ( S.D.) Mean Diff. (FIMa-FIMc) Corr. Wilcoxon Signed Ranks Test Facility A (N=63) FIM actual motor 77.21 ( 13.54) 11.30 r = 0.62 z = -5.64, FIM converted motor 65.91 ( 12.78) p < .001* FIM actual cognition 31.30 ( 5.87) 2.84 r = 0.80 z = 5.07, FIM converted cognition 28.46 ( 6.57) p < .001* Facility B (N=53) FIM actual motor 50.47 ( 18.91) -3.53 r = 0.77 z = -2.14 FIM converted motor 54.00 ( 19.28) p = 0.032* FIM actual cognition 30.30 ( 7.37) 1.51 r = 0.80 z = -3.07 FIM converted cognition 28.79 ( 8.89) p = 0.002* Facility C (N=57) FIM actual motor 70.49 ( 17.42) 2.08 r = 0.70 z = -1.04 FIM converted motor 68.41 ( 18.93) p = 0.299 FIM actual cognition 31.11 ( 6.49) 2.86 r = 0.53 z = -3.97 FIM converted cognition 28.25 ( 4.60) p < .001* Facility D (N=72) FIM actual motor 73.96 ( 15.61) -1.96 r = 0.58 z = -0.54 FIM converted motor 75.92 ( 15.83) p = 0.586 FIM actual cognition 28.90 ( 6.88) -3.82 r = 0.42 z = -4.63 FIM converted cognition 32.72 ( 2.89) p < .001* Facility E (N=71) FIM actual motor 52.07 ( 23.06) 1.41 r = 0.89 z = -1.00 FIM converted motor 50.66 ( 23.31) p = 0.314 FIM actual cognition 24.10 ( 8.97) -1.82 r = 0.66 z = -2.01 FIM converted cognition 25.92 ( 7.38) p = 0.044* indicates statistical significance with p value less than 0.05.

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124 Figure 4-1. FIMFunction Related Groups predicting model for the Stroke population (Impairment code= 1.1 to 1.9) Figure 4-2. FIMFunction Relate d Groups predicting model for the individuals with lower limb amputation (Impairment code= 5.3 to 5.9) 18-35 > 62 RIC: Stroke Stroke Cognitive Age Motor Motor Motor Motor Cognitive Motor 1 2 3 4 5 6 7 8 9 13-48 > 48 13-37 16-74 > 74 5-17 49-55 56-62 49-62 > 30 63-73 74-91 38-62 FRGs RIC: Lower Limb Amputation 13-54 RIC: Other Amputation 1 AM2 1 Motor AM1 2 55-91 FRGs

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125 Figure 4-3. FIMFunction Rela ted Groups predicting model for the individuals with lower extremity fracture (Impairment code= 8.1 to 8.4) Figure 4-4. FIMFunction Rela ted Groups predicting model fo r the individuals with hip replacement (Impairment code= 8.5 to 8.52) LEFx 13-42 5-9 RIC: Lower Extremity Fx (8.1 to 8.4) 1 2 3 4 FRGs > 42 10-35 43-52 53-91 Motor Cognitive Motor SPHR 13-17 > 17 RIC: Status Post Hip Replacement (8.5 to 8.52) FRGs 18-46 > 46 47-56 57-91 5-32 > 80 57-64 65-91 Motor Motor Motor Age Motor 16-80 Cognitive > 32 1 2 3 4 5 6 7

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126 Figure 4-5. FIMFunction Rela ted Groups predicting model fo r the individuals with knee replacement (Impairment code= 8.6 to 8.62) SP K R 13-17 > 17 RIC: Status Post Hip Replacement (8.6 to 8.62) FRGs 18-46 > 46 47-56 57-91 5-32 > 80 57-64 65-91 Motor Motor Motor Age Motor 16-80 Cognitive > 32 1 2 3 4 5 6 7

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127 (A) MDS actual motor score (B) MDS actual cognition score 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0Frequency300 200 100 0 Std. Dev = 14.75 Mean = 20.7 N = 1476.00 25.0 22.5 20.0 17.5 15.0 12.5 10.0 7.5 5.0 2.5 0.0Frequency1000 800 600 400 200 0 Std. Dev = 4.73 Mean = 3.2 N = 1476.00 (C) FIM actual motor score (D ) FIM actual cognition score 90.0 85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0Frequency300 200 100 0 Std. Dev = 24.23 Mean = 55.7 N = 1476.00 35.0 32.5 30.0 27.5 25.0 22.5 20.0 17.5 15.0 12.5 10.0 7.5 5.0Frequency600 500 400 300 200 100 0 Std. Dev = 8.98 Mean = 27.0 N = 1476.00 (E) FIM converted motor score (MDS derived FIM motor score) (F) FIM converted cognition score (MDS derived FIM cognition score) 90.0 85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0Frequency160 140 120 100 80 60 40 20 0 Std. Dev = 23.50 Mean = 54.4 N = 1476.00 32.5 30.0 27.5 25.0 22.5 20.0 17.5 15.0 12.5 10.0 7.5 5.0Frequency700 600 500 400 300 200 100 0 Std. Dev = 7.84 Mean = 27.1 N = 1476.00 Figure 4-6. FIM and MDS Scor e Distribution. A) MDS actual motor score distribution. B) MDS actual cognition score di stribution. C) FIM actual mo tor score distribution. D) FIM actual cognition score distribution. E) FIM converted motor score distribution. F) FIM converted cogni tion score distribution.

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128 (A) (B) Motor |FIMa-FIMc|70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0Frequency500 400 300 200 100 0 Std. Dev = 10.43 Mean = 11.6 N = 1476.00 Cognition |FIMa-FIMc|28.0 26.0 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0Frequency600 500 400 300 200 100 0 Std. Dev = 4.83 Mean = 4.9 N = 1476.00 Figure 4-7. Point Difference Between the Actu al and Converted FIM Score Distribution. A) Point difference between the ac tual and converted FIM motor score distribution. B) Point difference between the actual and converted FIM c ognition score distribution.

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129 CHAPTER 5 CONCLUSION: INTEGRATING THE FINDINGS To develop an effective and efficient mechan ism for evaluating and tracking changes of functional status across the continuum of care, it is necessary to integrate information and achieve score comparability across acute and postacute healthcare facilities. While utilizing a single and comprehensive outcome assessment inst rument across all facilit ies would provide the best mechanism for the synchronized and seamless monitoring of patient outcomes, the fact that different instruments are firmly entrenched in di fferent types of rehabil itation settings has made large-scale reformation extremely difficult. Around 2000, the Center of Medicare and Me dicaid (CMS) attempted to develop a Minimum Data Set for Post Acute Care (MDS-P AC) and used it across th e whole spectrum of post-acute care. Despite the fine concept and fu ll support from the CMS, the movement was no longer considered after 2002. Ther e was considerable of criticism and resistance to adopt a single instrument across all of post acute care. First, for more than a decade, different functional assessment instruments have undergone extensiv e development and are presently adopted in different major rehabilitation settings. For example, the Functional Independence Measure (FIM) is widely used in inpatient rehabilita tion; the Minimum Data Set (MDS) is mandated in skilled nursing facilities; and the Outcomes Assessment Information Set (OASIS) has been adopted by home care agencies. The functional status informa tion provided by the FIM and the MDS has been further incorporated into com puting the prospective pa yment system. Hence, changing existing system faces resistance from ad ministrators who have built structures (e.g., software, risk adjustment algorithms) and processe s (e.g., training, data collection) within their facilities based on existing instruments and health care practitioners who are familiar with their existing assessment procedures. Implementing a ne w assessment tool requires not only a large-

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130 scale transformation in administ rative procedure and staff re-t raining, but also a thorough consideration regarding the c onsequences and impact of rehabilitation services and reimbursement algorithm. The costs of convert ing from existing instruments and adopting to a uniform measure across all of post-acute care is li kely to be in the millions if not billions of dollars (e.g., software/hardware development, retr aining of staff across thousands of facilities). Developing a universal assessm ent tool also requires an adequate item set to cover the whole spectrum of post-acute care with a variety of patients at different di sability levels. This leads to another issue of administrative burden (large item bank) and inappropriate items for different rehabilitation settings. For example, easy mobility items such as rolling in bed might be an essential to assess individuals with severe di sability in skilled nurs ing facilities but provide little information (too easy) to most of the indivi duals in inpatient rehabi litation facilities. More challenging items such as walking outdoors 200 meters may provide useful information for evaluating patients who are thr ee months after discharge (follow-up evaluations) but not a common item for healthcare practioners to evalua te patients who are still stay in inpatient rehabilitation facilities. Lastly, the newly-developed universal assessm ent tools require intensive research studies to determine the reliability a nd validity of the instrument. Without rigorous psychometric research studies, these instrume nts are unlikely to be supported by health service re searchers. All of the above issues add practical issues in de veloping a universal assessm ent tool across the postacute care in rehabilitation. One solution for integrating functional status that requires no change of existing circumstances is to create crosswalks or statis tical links between functi onal status subscales of different instruments. While th e Functional Independence Measure (FIM) is widely used in

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131 inpatient rehabilitation facilities, the Minimum Data Set (MDS) is federally mandated for all residents in skilled nursing facilities. To invest igate the potential of creating measurement links between these two functional outcome instruments, this project comprised four steps: 1) a conceptual paper reviewing linking methodologies and the state of the art of existing linking studies in healthcare; 2) a inspection of the MDS item characteristics using the Rasch model; 3) an investigation of whether the FIM items func tion similarly across different impairment groups using differential item functioni ng analysis (b-difference and ite m characteristic curve methods); and 4) an evaluation of the accuracy of th e crosswalk conversion algorithm by applying Functional Related Groups (FRG s) classification system. The results supported the possibility of crea ting a crosswalk conversion algorithm between the FIM and the MDS. The item difficulty hierar chical order of MDS phys ical functioning and cognitive domains demonstrated si milar pattern to those in previ ous studies related to the FIM. For motor items, climbing stairs and walking tasks, which requires extensive strength and coordination of the whole body, appeared to be the most challenging items. Items such as toileting, dressing, transferring and hygiene represented items around the average difficulty level. Tasks that require more upper extremity function and mild muscle strength, such as eating and grooming are commonly found to be the easiest. For the FIM cognitive items, problem solving and memory function were found to be relativ ely more challenging, while expression and comprehension were the easiest. For the MDS, s hort-term-memory, ability -to-recall, and dailydecision-making items also formed the most challenging items along this construct, while communication items (making-self-understood, sp eech-clarity, and abilit y-to-understand-others) were the next difficult items. Items that indi cated delirium (altered-perception-or-awareness, easily-distracted, disorganized-speech, and lethargy) were the easiest items. The similar patterns

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132 in item difficulty hierarchical order support th at items in the FIM and the MDS are measuring similar underlying constructs along motor and cognitive scales. Several FIM motor and cognitive items were found to have significant DIF across three impairment groups (stroke, amputation, and orth opedic impairment). These inconsistencies in item calibrations led to the development of se parate crosswalk conversion tables for each impairment group. Removing misfit items led to a similar DIF results. However, removing misfit items or adjusting for DIF seemed to have li ttle effect on overall person ability measures estimated by the Rasch model. The 2PL logistic IRT model showed that item discrimination parameters varied across FIM it ems. Although the DIF results based on different models showed a slightly different set of items showing significant DIF, items that exhibited significant DIF appeared to be connected to sp ecific characteristic s of the impairment typically found for each diagnostic group. For example, individuals with st roke tended to have more difficulty with tasks that involved more upper extremity functions (e.g., grooming, and dressing-upper-extremity). Since majority of the amputation and orthopedi c groups involved lower extremity impairment, these individuals tended to have more difficulty with tasks that depend on lower extremity strength and functions (e.g., stair, walk, tr ansfer-to-tub). For cognitive items, two items (expression and problem solving) consistently showed significant DIF across three impairment groups. While individuals with stroke showed greater difficulty in expression item, than amputation and orthopedic groups, the latter two groups did not show cognitive DIF. These inconsistencies in item difficulty calibrations led to the development of separate crosswalk conversion tables for each impairment group. In pilot work (not reported here) we found virtually no differences between a single conversion table acro ss all impairment groups and

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133 impairment-specific crosswalks. Therefore, vali dity testing is based on a single conversion table (one conversion table for the motor scale and one for the cognition scale). The validity testing the FIM-MDS conversion al gorithm resulted in mixed findings at the individual, classification and facility levels. For example, at the individual level, while there were relatively strong correlations across the FI M and the MDS raw scores (0.80 for motor scale and 0.66 for cognitive scale), the actual and conv erted distributions were significantly different. Similarly, at the classification level, while chi sq uare analysis showed that there was a significant association between FRG classi fications derived from actual and converted scores, kappa statistics only showed a fair to substantial strength of agreement. Finally, at the facility level, 4 of the 5 facilities showed onl y 1-3 point mean differences be tween actual and converted FIM scores, correlation coefficient between the ac tual and MDS derived FIM scores varied considerably across facilities. While some of these results challenge the vali dity of the crosswalk, we would argue that the variance observed in this validation study may be as much a function of the error in global measures per se, as it is a functi on of error in the crosswalk. That is, there is a possibility that variance in use of the same measure (e.g., onl y the FIM or only the MDS-PAC), by different raters and across different facilities, may resu lt in similar variance in evaluating and tracking patients functional status across different rehabilitation settings. To improve the application of FIM-MDS cros swalk conversion algori thm in the clinical sites, however, rigorous explor ation of the optimal linking me thodologies is needed. Besides expert panel, item-to-item conversion algorithms or Rasch true score equating methods, other linking methodologies including clas sical test theory and item response theory methods should be explored. In addition, sin ce the factor analysis of th e MDS showed a potential of

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134 multidimensional issue along the functional stat us construct, multidimensional IRT equating methods should be considered in future crosswal k studies. Last and most important of all, since the crosswalk conversion algorithm relies on the accuracy of ratings, improving quality of test administration and additional rate rs training is recommended. While the above results do not totally support the application of cro sswalks, the critical questions is whether or not more valid result s would be obtained usi ng a universal assessment tool across all of post ac ute care. If the crosswalk algorithm between instruments that measuring similar construct is found to be as at least as valid as using a single in strument, it would provide an efficient and economical wa y to compare the outcomes of facilities that use different instruments.

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135 APPENDIX A DATA REQUEST: THE FUNCTIONAL STAT US AND OUTCOMES DATABASE (FSOD) VA and non-VA researchers may access the data stored in the FSOD with approval of Department of Physical Medi cine and Rehabilitation (PM& R) administrative office. Investigators with approval proposals for VA resear ch funding may contact Clifford R. Marshall, a Rehabilitation Planning Special ist, at PM&R Central Office. A formal written and signed request forms include: a) the specific FSOD variables needed, b) the requesting facility submitting VA form 9957 (if the patients social security number is required), c) a Memo of Justification via the local information security office, d) the Privacy Act and Data Security Statement, e) a one page document describing the project, f) a copy of th e letter approval from the VA research office, and g) a copy of the Institutional Review Board approval.

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136 APPENDIX B DATA REQUEST: THE MINIMUM DATA SET (MDS) Researchers who are interested in requesti ng MDS data need to submit a data request packet to the Centers for Medi care & Medicaid Services at Division of Privacy Compliance (DPC), which contains: a) written request letter, outlines the primary purposes for which the data are required, b) study plan or protocol that delineates the objective, background, methods, and importance of the study, c) data use agreement, d) internal review board (IRB) documentation of waiver approval, e) evidence of funding, f) CMS da ta request form, which contains a checklist of all the information submitted in the request pack et, g) privacy board review summary sheet, h) request letter of support from proj ect officer (federally funded pr ojects only, and i) long term care MDS workbench variable sel ection & justification worksheet.

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146 131. Hamilton BB, Deutsch A, Russell C, Fiedler RC, Granger CV. Relation of disability costs to function: Spinal cord injury. Archives of Physical Medicine and Rehabilitation 1999;80(4):385-391. 132. Cater GM, Relles DA, Rigeway GK, Rime s CM. Measuring Function for Medicare Inpatient Rehabilitation Paym ent. Health Care Financing Review 2003;24(3):77-88. 133. Hsueh IP, Lin JH, Jeng JS, Hsieh CL. Compar ison of the psychometric characteristics of the functional independence measure, 5 item Ba rthel index, and 10 item Barthel index in patients with stroke. Journal of Neurology Neurosurgery and Psyc hiatry 2002;73(2):188190. 134. Lundgren-Nilsson A, Grimby G, Ring H, Tesio L, Lawton G, Slade A, et al. Cross-cultural validity of functional independence measure items in stroke: A study using Rasch analysis. Journal of Rehabilitation Medicine 2005;37(1):23-31. 135. Crane PK, van Belle G, Larson EB. Test bias in a cognitive test: differential item functioning in the CASI. Statistics in Medicine 2004;23(2):241-256. 136. Fleishman JA, Spector WD, Altman BM. Impa ct of differential it em functioning on age and gender differences in functional disabi lity. Journals of Gerontology Series BPsychological Sciences and Social Sciences 2002;57(5):S275-S284. 137. Fleishman JA, Lawrence WF. Demographic variation in SF-12 scores: True differences or differential item functioning? Medical Care 2003;41(7):75-86. 138. Marshall SC, Mungas D, Weldon M, Reed B, Haan M. Differential item functioning in the Mini-Mental State Examination in Englishand Spanish-speaking older adults. Psychology and Aging 1997;12(4):718-725. 139. Davis AM, Badley EM, Beaton DE, Kopec J, Wright JG, Young NL, et al. Rasch analysis of the Western Ontario McMaster (WOMAC ) Osteoarthritis Index: results from community and arthroplasty samples. Jour nal of Clinical Epidemiology 2003;56(11):10761083. 140. Haley SM, Coster WJ, Andres PL, Ludlow LH, Ni PS, Bond TLY, et al. Activity outcome measurement for postacute care. Medical Care 2004;42(1):49-61. 141. Groenvold M, Bjorner JB, Klee MC, Kreiner S. Test for Item Bias in a Quality-of-Life Questionnaire. Journal of Clini cal Epidemiology 1995;48(6):805-816. 142. Camilli G, & Shepard, L. A. Methods for identifying biased test items. Thousand Oaks, CA.: Sage Publications; 1994. 143. Wright BD, Stone MH. Best test design. Chicago: MESA Press; 1979. 144. Thissen D, Chen WH, Bock D. MULTILOG 7. In. Lincolnwood, IL: Scientific Software International, Inc.; 2006.

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147 145. Lum TY, Lin WC, Kane RL. Use of proxy respondents and a ccuracy of minimum data set assessments of activities of daily living. Journals of Ge rontology Series a-Biological Sciences and Medical Sc iences 2005;60(5):654-659. 146. Administration HCF. Minimum Data Set, 2. 0. Washington, DC: U.S. Government Printing Office; 1998. 147. Fries BE, Schneider DP, Foley WJ, Gavazzi M, Burke R, Cornelius E. Refining a case-mix measure for nursing homes: Resource Utili zation Groups (RUG-III). Medical Care 1994;32(7):668-685. 148. Rogers JC, Green Gwinn SM, Holm MB. Comp aring activities of daily living assessment instruments: FIM, MDS, OASIS, MDS-PAC. Physical & Occupational Therapy in Geriatrics 2001;18(3):1-25. 149. McMullan M. Re: HCFA-1069-PMedicare Prospective Payment System for Inpatient Rehabilitation Facilities Proposed Rule (65 Federal Register 66304), November 3, 2000. In: Regulatory Comment Letters. Retrieved fr om the World Wide Web on Oct. 15, 2006. (www.aha.org); 2001. 150. Kittredge FI. Comment on HCFAs proposed IRF PPS (January 29, 2001). Retrieved from the World Wide Web on Oct. 15, 2006. (www.aan.com) 151. Velozo CA, Byers KL, Wang YC, Joseph BR. Translating measures across the continuum of care: Using Rasch analysis to create a cr osswalk between the FIM and the MDS. Journal of Rehabilitation Research and Development (in press). 152. Jette AM, Haley, S. M., & Ni, P. Comparison of functional status tools used in post-acute care. Health Care Financ ing Review 2003;24(3):1-12. 153. Linacre JM. WINSTEPS Rasch model com puter program. In. Chicago: Winsteps.com; 2005. 154. Guide for the Uniform Data Set for Medica l Rehabilitation, Versi on 5.1. Buffalo, NY: State University of New York at Buffalo; 1997. 155. Jette AM, Haley SM, Ni P. Comparison of f unctional status tools used in post-acute care. Health Care Financing Review 2003;24(3):1-12. 156. Stineman MG, Goin JE, Granger CV, Fi edler R, Williams SV. Discharge motor FIMFunction Related Groups. Archives of Physical Medicine and Rehabilitation 1997;78(9):980-985. 157. Stineman MG, Escarce JJ, Goin JE, Hamilt on BB, Granger CV, Williams SV. A case-mix classification-system for medical rehabilitation. Me dical Care 1994;32(4):366-379. 158. Stineman MG, Granger CV. A modular ca se-mix classification system for medical rehabilitation illustrated. Health Ca re Financing Review 1997;19(1):87-103.

PAGE 148

148 159. Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics 1977;33(1):159-174. 160. Ottenbacher KJ, Taylor ET, Msall ME, Braun S, Lane SJ, Granger CV, et al. The stability and equivalence reliability of the func tional independence measure for children (WeeFIM)(R). Developmental Medicine and Child Neurology 1996;38(10):907-916.

PAGE 149

149 BIOGRAPHICAL SKETCH Ying-Chih (Inga) Wang received her Bachel or of Science degree with a major in occupational therapy from the National Taiwan Un iversity, Taipei, Taiwan in June 1999. She worked for 2 years as an occupational therapist at the Taipei Medical University Hospital. She currently holds the Certificate of Occupationa l Therapy from the Department of Health, Executive Yuan, R.O.C. (Taiwan). She plans to remains active in both clinical practice and clinical research to improve the f unctional status of indi viduals with disabilities after graduation.


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LINKING THE FUNCTIONAL INDEPENDENCE MEASURE (FIM) AND THE MINIMUM
DATA SET (MDS)




















By

YING-CHIH (INGA) WANG


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

2007































Copyright 2007

by

Ying-Chih (Inga) Wang


































To my parents Sang-Jyi and Ching-Hsian.









ACKNOWLEDGMENTS

Four years of wide goose chasing left me tremendous unforgettable memories and learning

experiences. I still vividly remember of my first question for my advisor was "What is a grant?"

and my first statistics class was talking about normal distribution and how to compute the

standardized Z score. As time went by, along with the cheers of Gator football game, I had

opportunities to expose myself to a variety of interesting topics including neuroanatomy,

outcome measurement, biomechanics, and assistive technology. Till now, I finally feel that I am

equipped with certain tools for use and have some skills to enable me to continue to explore

unknown territory.

I would like to thank for many people who supported me along the way. I would not have

been able to go this far without support and guidance from them. First, I would like to give

thanks to my lovely advisor, Dr. Craig Velozo, a man with great vision and who is fun to work

with. Thanks go to him for his guidance, inspiration, and most important of all, financial support

of the past four years. I also would like to thank my committee members (Dr. Sherrilene Classen,

Dr. John C. Rosenbek, and Dr. James Algina) for their invaluable contribution to make my

dissertation better. I would like to share this joyfulness with my colleagues and friends who

accompanied and cheered me forward all the time. I also wish to thank the rehabilitation science

doctoral program at the University of Florida and the Rehabilitation Outcomes Research Center

(RORC) for their support throughout this process. Finally, I would like to thank my parents who

always gave me unconditional support and encouraged me to pursue what I wanted to be.












TABLE OF CONTENTS


page

ACKNOWLEDGMENTS .............. ...............4.....


LIST OF TABLES ............ ...... ._ ...............8...


LIST OF FIGURES .............. ...............10....


AB S TRAC T ............._. .......... ..............._ 1 1..


CHAPTER


1 THE STATE OF THE ART OF TEST EQUATING IN HEALTHCARE ................... .........13

Introducti on ................. .. ... .. ........ ........ ... ..... ..........1
The History and Concept of Equating in Education ................. ...............14..............
Equating: Education versus Healthcare ................. ...............21................
State of the Art of Equating Studies in Health Care ................. ...............22.............
Expert Panel Equating ................. ...............22................
Equating an Item Bank ................. ...............24........... ...
Rasch Equating Method............... .... ... .......... .......2
Next Critical Studies for Advancing Linking in Healthcare .............. ....................2
Research Question ................. ...............3.. 1..............
Research Question 1 .............. ...............32....
Research Question 2 .............. ...............32....
Research Question 3 .............. ...............32....


2 RASCH ANALYSIS OF THE MINIMUM DATA SET (MDS) ON THE PHYSICAL
FUNCTIONING AND COGNITION DOMAINS .............. ...............39....


Introducti on ..............._ ...............39......_......
M ethods .............. ...............41....

Sam ple ............... ........ ._ .. ...... ......... ............. .......4
Resident Assessment Instrument Minimum Data Set (RAl-MDS) .............. ................42
Administration of the MDS ............ ...... ._ ...............43..
Rasch Analysis .............. ....... ... ................4
Sample Size Requirement for Rasch Analysis .............. ...............45....
Analy si s ............ ... ... ...............45...
Dimensionality .............. ...... ...............45.
How well the data fit the model .............. ...............46....
Item difficulty hierarchy............... ...............4
Person-item match: targeting .............. ...............46....
Separation index ............ .......__ ...............47..
Rating scale structure ................... ...............47.
Differential item functioning (DIF)............... ...............47.
R e sults........._. ...... .. ...............48....












Dimensionality .............. ...............48....
Rasch Analysis .............. .... ...............49
ADL/Physical functioning items ....._ .....___ .........__ ............4
Cognitive item s .............. ...............53....
Discussion ............ .... __ ...............57..


3 DIFFERENTIAL ITEM FUNCTIONING OF THE FUNCTIONAL INDEPENDENCE
MEASURE ACROSS DIFFERENT DIAGNOSTIC GROUPS ................. .....................73


Introducti on ................. ...............73.................
M ethod ................. ...............76.................
Participants .............. ... .. .. .. ............. ...............7
Differential Item Functioning Based on the Rasch Model ................... .......... .............7
Differential Item Functioning Based on Two-Parameter Logistic IRT Model ..............79
Re sults............ .... __ ...............82..

Subj ects ............... .. .... ..__ ...........__ .............8
DIF Analysis Based on Rasch Model ....__ ......_____ .......__ ...........8
DIF Analysis Removing Misfit Items .............. ...............84....
The Impact of DIF Items on Person Ability Measures. ......___ .......__ ..............84
DIF Analysis Based on 2PL IRT Model ....._ .....___ .........__ ..........8
Discussion ............ .... __ ...............87..


4 EVALUATING THE FIM-MDS CROSSWALK CONVERSION ALGORITHM VIA
FUNCTIONAL RELATED GROUP CLAS SIFICATION ................. ................. .... 101


Introducti on ................. ...............101................
M ethods ............... ...............104...
Data Preparation .............. ...............104....
Analysis Procedure ................. ...............105......... ......
Re sults ................ ...............108................

Sam ple .............. ..... ......... ..... ......... ............10
Validation at the Individual Level .............. ...............108....
S core distribution .................. ............... 108.
Point difference |FIMa-FIMc|............... ..............10
Validation at the Classification Level ................. ...............110........... ...
Validation at the Facility Level ................. ...............111.......... ...
Discussion ................. ...............112................


5 CONCLUSION: INTEGRATING THE FINDINGS ................ .............................129


APPENDIX


A DATA REQUEST: THE FUNCTIONAL STATUS AND OUTCOMES DATABASE
(F SOD) .............. ............... 13 5...

B DATA REQUEST: THE MINIMUM DATA SET (MDS)............... ...............136.


LIST OF REFERENCES ................. ...............137................












BIOGRAPHICAL SKETCH ................. ...............149......... ......











LIST OF TABLES


Table page

1-1 Educational Equating Methodologies ................. ...............33................

1-2 Education versus Healthcare Differences in Equating Procedures ................. ...............35

1-3 Review of Linking Studies in Health Care ................. ...............36..............

2-1 Demographic Characteristics ................. ...............61................

2-2 Minimum Data Set (MD S) Physical Functioning and Cognition Items ................... ......62

2-3 Factor Analysis on MDS Items Factor Pattern .............. ...............63....

2-4 Physical Functioning Item Statistics (Listed by Item Difficulty Order).............._._..........64

2-5 Cognition/Communication Item Statistics ....__ ......_____ .......___ ............6

3-1 FIM Instrument ................. ...............92......___ ....

3-2 Participants Descriptive Statistics for Each Diagnostic Group ........._. ...... ............. ...93

3-3 Difficulty Calibrations for FIM Motor Items............... ...............94.

3-4 Item Difficulty Calibrations for FIM Cognition Items .............. ...............94....

3-5 Item Parameter Calibrations for FIM Motor Items ................. ............... ......... ...95

3-6 DIF Analysis for FIM Motor Items .............. ...............95....

3-7 Item Parameter Calibrations for FIM Cognitive Items ................ .......... ...............96

3-8 Item Parameter Calibrations for FIM Cognitive Items ................ .......... ...............96

4-1 FIM-MDS Crosswalk Conversion Table ADL/Motor Scale ................. ................ ..118

4-2 FIM-MDS Crosswalk Conversion Table Cognition/Communication Scale ..............119

4-3 Demographic Baseline Characteristics .............. ...............120....

4-4 Summary of the Validation Results at Individual Level ..........__ ......... ..... .........._121

4-5 FRG Classification for Stroke Sample............... ...............122

4-6 FRG Classification for Amputation Sample ....__ ......_____ .......___ ..........12

4-7 FRG Classification for Orthopedic Impairment Sample .............. .....................2











4-8 Validation Results at the Facility Level ................. ...............123........... ..










LIST OF FIGURES


Figure page

2-1 Person Score Distribution Item Difficulty Hierarchy Map -Physical Functioning ........66

2-2 Frequency Count of Item Rating Scale Physical Functioning Items (A) Rating scale
category from 0 to 2 (B) Rating scale category 3, 4, and 8 .............. .....................6

2-3 Rating Scale Structure of the Physical Functioning Items ................. ........_............_68

2-4 General Keyform Structure of the Physical Functioning Items ................. ................ ...69

2-5 Person Score Distribution Item Difficulty Hierarchy Map Cognition ................... ......70

2-6 Rating Scale Structure of the Cognition/Communication Items. ................ ............... ...71

2-7 General Keyform Structure of the Cognition/Communication Items ............... .... ........._..72

3-1 Examples of DIF A) Uniform DIF and B) Non-uniform DIF .........._._... ......._._......97

3-2 Differential Item Functioning Plots for A) Motor and B) Cognition items across
differential impairment groups (Stroke, Amputation, and Orthopedic Impairment) .........98

3-3 Differential Item Functioning Plots for A) Motor and B) Cognition items across
differential impairment groups after removing misfit items ................. ......................99

3-4 Differential Item Functioning Plots for FIM-walking (A, B, C) and FIM-stair (D, E,
F) items based on the ICC DIF method ..........__ .......... ...............100

4-1 FIM-Function Related Groups predicting model for the Stroke population
(Impairment code= 1.1 to 1.9) .............. ...............124....

4-2 FIM-Function Related Groups predicting model for the individuals with lower limb
amputation (Impairment code= 5.3 to 5.9) .............. ...............124....

4-3 FIM-Function Related Groups predicting model for the individuals with lower
extremity fracture (Impairment code= 8.1 to 8.4) .............. ..... ............... 12

4-4 FIM-Function Related Groups predicting model for the individuals with hip
replacement (Impairment code= 8.5 to 8.52)............... ...............125.

4-5 FIM-Function Related Groups predicting model for the individuals with knee
replacement (Impairment code= 8.6 to 8.62) ....._._.__ ... ....___.. .......... .......12

4-6 FIM and MDS Score Distribution. ........... ....__ ...............127

4-7 Point Difference Between the Actual and Converted FIM Score Distribution.. ............128









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

LINKING THE FUNCTIONAL INDEPENDENCE MEASURE (FIM) AND THE MINIMUM
DATA SET (MDS)

By

Ying-Chih Wang

May 2007

Chair: Craig A. Velozo
Major Department: Rehabilitation Science

To develop an effective and efficient mechanism for evaluating and tracking changes of

functional status across the continuum of care, it is necessary to integrate information and

achieve score comparability across acute and post-acute healthcare facilities. While utilizing a

single and comprehensive outcome assessment instrument across all facilities would provide the

best mechanism for the synchronized and seamless monitoring of patient outcomes, the fact that

different instruments are firmly entrenched in different types of post-acute healthcare settings has

made large-scale reformation extremely difficult. One solution for integrating functional status

that requires minimum cost and effort would be the development of crosswalks or statistical links

between functional status subscales from different instruments. While the Functional

Independence Measure (FIMTM) is widely used in inpatient rehabilitation facilities, the Minimum

Data Set (MDS) is federally mandated for all residents in skilled nursing facilities. To investigate

the feasibility of creating measurement links between these two functional outcome instruments,

this study consisted of four steps: 1) a conceptual paper reviewing linking methodologies and the

state of the art of existing linking studies in healthcare; 2) a inspection of the MDS item

characteristics using the Rasch model; 3) an investigation of whether the FIM items function

similarly across different impairment groups using differential item functioning analysis (b-









difference and item characteristic curve methods); and 4) an evaluation of the accuracy of the

crosswalk conversion algorithm by applying Functional Related Groups (FRGs) classification

system. The item difficulty hierarchical order of MDS physical functioning and cognitive

domains demonstrated similar pattern to those in previous studies related to the FIM. Several

FIM motor and cognitive items were found to have significant DIF across three impairment

groups (stroke, amputation, and orthopedic impairment). These inconsistencies in item

calibrations led to the development of separate crosswalk conversion tables for each impairment

group. The validity testing the FIM-MDS conversion algorithm resulted in mixed findings. The

similarity between the actual and converted score distributions, relatively strong correlations

across the FIM and the MDS raw scores, and a fair to substantial strength of agreement when

using the actual FIM scores and the MDS derived FIM scores to classify individuals into FRGs,

all supported the development of FIM-MDS crosswalk conversion algorithm. However, the

average of point differences between the actual and converted scores were large and results from

Wilcoxon signed ranks test do not support the equivalence of actual and converted score

distributions at both individual and facility level. To improve the application of FIM-MDS

crosswalk conversion algorithm in the clinical sites, rigorous exploration of the optimal linking

methodologies, the needs for quality of test administration, and rater training are recommended.









CHAPTER 1
THE STATE OF THE ART OF TEST EQUATING IN HEALTHCARE

Introduction

A myriad of rehabilitation outcome measures have been developed over the past 50 years.

These assessments typically cover such health domains as physical functioning, cognition, basic

and/or instrumental activity of daily living, depression, pain, and quality of life [1]. Despite the

proliferation of measurement tools, many instruments evaluate similar attributes. For example,

more than 85 instruments currently evaluate basic and instrumental activity of daily living and

more than 75 measures are available to measure quality of life [2]. While these assessments are

designed to measure the same construct, scores from one instrument cannot be compared to

similar scores gathered by another instrument [3]. This lack of "communication" across

assessments seriously hampers healthcare outcomes measurement. As patients transfer from one

setting to another, their information is discontinuous since different instruments are often

specific to particular healthcare settings. The incompatibility of assessment data prohibits post-

acute healthcare services in monitoring and evaluating the effectiveness of intervention through

the continuum of care. Furthermore, facilities that use different instruments cannot be compared

relative to their outcomes locally or nationally.

Recently, several healthcare studies have attempted to confront this measurement

challenge by attempting to achieve score comparability using test equating methodologies.

Equating is a procedure used to adjust scores on test forms so that the score on each form can be

used interchangeably [4]. Despite the availability of numerous, well-developed equating methods

in the field of education, few of these methods have been applied in healthcare. This may be a

function of lack of familiarity with the education literature, and/or the belief that educational

equating methods are not applicable to equate healthcare assessments. To better understand










equating, a literature review comparing the equating techniques used in education to those

presently used in healthcare would provide the critical background for future equating studies.

Therefore, the purpose of this proj ect was to 1) review equating concepts and existing

methodologies in education, 2) discuss the challenges in using these methodologies in healthcare,

3) review the state of the art of equating in healthcare, and 4) propose the next critical studies

necessary to advance equating in healthcare.

The History and Concept of Equating in Education

The history of equating can be traced back to the education field in the 1950s, when the

excessive testing in the schools rendered the need for "comparable" scores between test batteries.

The College Entrance Examination Board and the American College Testing Program provide an

example in which many colleges have to make decisions to enroll students, some of whom have

taken one of the standard tests and some the other (e.g., the Scholastic Aptitude Test (SAT) or

the American College Test (ACT) test battery) [5]. For purposes of fairness in admission

selection, many colleges would like to use the scores from these test batteries interchangeably.

Hence, tables were developed which allow the conversion of scores between tests from different

publishers. As a result, students can take different admission tests. Using conversion tables, each

college's admissions office can be converted to a score that is considered acceptable by that

college [6].

As the development and administration of national-wide test in education became more

and more popular, standardized tests were used and administered throughout the United States

several times throughout the year. This led to another challenge. Students were potentially taking

the same test on multiple occasions and therefore memorizing the answers to test items. In order

to guarantee the fairness of the test and control the exposure rate of test items, sets of test

questions were built according to certain content and statistical test specifications to replace test









items on old forms [7]. Although multiple forms of a test are ideally constructed according to

strict statistical specifications, it is still possible for these different test forms to vary in difficulty.

Therefore, the equating was applied to adjust scores on different versions of test forms such that

scores from these test forms were put onto a common metric and became comparable [7].

In 1964, some of the first studies on equating appeared at the Annual Meeting of the

National Council on Measurement in Education in Chicago and later were published in the first

volume of the Journal of~ducational2\~ea;surement [5, 6, 8, 9]. Over the past few decades, as the

number and variety of testing programs that used multiple test forms increased, the topic of

equating became more and more popular and vital. In 1985, the Standards for Educational and

Psychological Testing, developed j ointly by the American Educational Research Association

(AERA), American Psychological Association (APA), and National Council on Measurement in

Education (NCME), listed equating into its index and dedicated a substantial portion of the

standards to equating issues [7]. To date, various equating issues have emerged in the literature,

such as different equating concepts [10-14], properties of equating [15], comparing different

equating methods [16-18], guidance for evaluating the accuracy of equating [19], investigating

test equating in the presence of differential item functioning [20], and evaluating the effects of

multidimensionality on equating [21, 22]. In 1982, Holland and Rubin published the book Test

Equating [23], which included several important studies from the Educational Testing Services

(ETS). In 1995, Kolen and Brennan published Test Equating2~ethods and'Practices [7], which

provides comprehensive summaries of equating concepts, methodologies, research designs, and

practical issues in conducting equating.

As diverse equating concepts continue to emerge and various equating methods continue to

evolve, the subj ect of equating has become a well-defined analytical procedure. The properties of










equating proposed by Lord (1980) [15] have become an essential key concept in conducting

equating. These properties include the following: 1) the tests to be equated should measure the

same construct; 2) conditional distribution of scores given a true score should be equal (equity

property); 3) the equating relationship should be the same regardless of the group of examinees

(group invariance property); and 4) the equating transformation should be symmetric (symmetry

property) [15]. Based on Lord's equating properties, equating is the processes adjusting the

difficulty of the test forms that measure the same construct. The equating results should be

invariant no matter which sub-samples are used to create the conversion algorithm. The equating

function used to transform a score on Form X to Form Y should be the inverse from Form Y to

Form X (i.e., score 35 on Form X equals to 42 on Form Y and vice versa). This property ruled

out the use of regression to predict scores from another test scores for equating since the

regression of y on x usually differs from the regression of x on y [4].

Equating methods can generally be classified according to the test theory on which they are

based: classic test theory (CTT) and item response theory (IRT). Table 1-1 introduces the most

commonly used statistical equating methods and related data collection designs that usually go

with the equating methods. In CTT, equating methods usually are achieved by making

assumptions about statistical properties of score distribution. Mean equating, linear equating, and

equipercentile equating form the basic equating methods in this category. In mean equating, Test

X is considered to differ in difficulty from Test Y by a constant amount. For example, if the

mean of Test X was 50 and the mean of Test Y was 52, 2 points would need to be added to a

Test X score to transform a score on Test X to the Test Y scale. In linear equating, the linear

conversion is based on the rationale that the same person should occupy identical standardized

deviation scores on the two tests such that x u(x)/a(x) = y u(y)/a(y) (where x is the scores









on form X, and u(x) and cr(x) are the mean and standard deviation of score distribution on form

X). While mean and linear equating only allow linear function, the equipercentile equating

method permits a curvilinear relationship between two test scores and is developed by

identifying scores on Test X that have the same percentile ranks as scores on Test Y. It should be

noted that when two test forms have different psychometric characteristics (e.g., different

reliability) or when data are collected from two non-equivalent groups, more sophisticated

equating methods should be considered such as the Tucker method [24], the Levine method [25],

frequency estimation equipercentile equating [26], Braun-Holland Linear method [26], and

chained equipercentile equating method [27, 28]. Angoff (1982) [29] identified more than 12

scenarios used by the Educational Testing Service, including equating formulas for equal reliable

tests, unequal reliable tests as well as under different research designs. Petersen and colleagues

(1982) [30] summarized 22 equating models including linear and non-linear models, true-score

and observed score models, and described maj or assumptions in each scenario.

Three data collection designs are frequently used with the CTT statistical equating

methods to collect data for equating purpose [29]. In Table 1-1, Text X and Test Y represent two

test forms of a test. Subgroup 1 and 2 represent two samples from one population formed by

random assignment, whereas Group 1 and 2 represent two samples recruited from two different

populations. Dashes (---) within the cells indicate that a specific test form was taken by a

particular group. In Design a (Random Groups, One Form Administered to Each Group), the

entire examinees are randomly assigned into two subgroups and each subgroup takes one of the

test forms. In Design b (Random Groups, Both Forms Administered to Each Group,

Counterbalanced), the same tests are administered to all examinees. If fatigue or practice effects

exist, the tests are given in different order to counterbalance the effect. Lastly, in Design c









(Nonrandom Groups, One Test Administered to Each Group; Common Equating Test

Administered to Both Group), different tests are given to a different group of examinees with an

additional set of items (anchor tests or common items) administered to all examinees. The score

on the set of common items could either contribute to the examinee's score on the test (internal

anchor test) or do not contribute to the examinee's score on the test form (external anchor test).

To avoid different response behavior, common items are supposed to be a mini version of the

total test form, proportionally representative of the total test forms in content and statistical

characteristics, and occupy a similar location in the two forms [4]. For the minimum length of

the anchor test, a rule-of-thumb is either more than 20 items or 20% of the number of items on

any of the tests [13].

Item response theory (IRT) comprises a family of models. Each designed to describe a

functional relationship between person ability measures and item characteristic parameters.

While most CTT methods emphasize equating parallel or alternative test forms, the IRT models

along with the implementation of computerized adaptive testing have facilitated and extended the

implementation of equating process with the ability to equate an item bank (a composition of

questions that develop for an operational definition of a variable/construct [31i]). Because of the

"invariant" property of IRT that the examinee's ability is invariant with respect to the items used

to determine it and item statistics under different groups of examinees remain unchanged [32],

IRT equating methods make it possible to ensure that person performances are comparable even

when each person responds to a unique set of items [31]. Different test forms can be linked as

long as there are common persons (who take both test forms), or common items (which exist

across different test forms) in the dataset. This feature extends the potential of applying linking

beyond equating parallel test forms.










Prior to using IRT for equating, one needs to decide which IRT model to use. Overall, IRT

models can be classified into 1-, 2-, and 3-parameter model based on the number of item

parameters included in the model. The general form of 3-parameter logistic model, which

includes all three parameters, can be expressed in the logistic formula:

Da, (8,-b, )
r (0) = c, + (1+ cl) 1+ea(,b)Where 'a 'is a discrimination parameter (a), which determines


how well the item can discriminate persons with different level of abilities; 'b' is an item

difficulty parameter, which determines the difficulty of the item; and 'c' is a lower asymptote

parameter (c), which is also called the guessing parameter. The higher the 'a' value, the more

sharply the item discriminates between high and low ability examinees. The higher the 'b' value,

the more challenging the item is. The higher the 'c' value, the greater the probability that a

person can get an item correct without any knowledge (e.g., multiple choice). In the 2-parameter

IRT model, the guessing parameter (c) is set to be zero such that there is no guessing factor when

a person takes a test (e.g., Likert scale from disagree to agree). In the 1-parameter IRT model, the

item discrimination (a) is assumed to be equal across all items and there is no guessing factor

within a test. Furthermore, if the unidimensionality assumption is violated, multi-dimensional

IRT models that can handle more than one dominant person trait (6) can be considered. The

equating methods based on the IRT model require iterated computation that is usually achieved

via computer software. After a person responds to a set of items, the person's ability and item

parameters are estimated via an IRT mathematical model.

The IRT true score equating method is one of the most commonly used equating methods

under the IRT model. For the IRT true score equating, the true score from one test associated

with a given person's latent trait is considered to be equivalent to the true score from another test

related to that latent trait. The equating method comprises the following steps: a) specify a true










score (rx ) on Form X, b) find the latent trait (8i) that corresponds to that true score, and c) find

the true score on Form Y, (ry ), that corresponds to that true score (8i), where


zx (8, ) = P,, (8,; anbnhcn~) the test performance on Form X and r,. (8, ) = 1 pe (B,; anbncn)) the
]X ]

test performance on Form Y; p is the probability of passing an item based on a person's ability

level (6) and item parameters (a is the item discrimination parameter; b is the item difficulty

parameter; c is the guessing parameter); and j is a particular item on the test form [4].

An alternative IRT equating method is the IRT observed score equating. After the

probability of a number of correct scores for examinees of a given ability level are computed, the

observed score distributions then are cumulated over a population of examinees across the entire

person ability spectrum. This can be achieved by an integration function to obtain the cumulated

observed score distributions, while some computer programs (e.g., BILOG [33]) output a

discrete distribution on a finite number of equally spaced points. After generating an estimated

distribution of observed score distribution for each form (e.g., Form X and Form Y), both score

distributions then are rescaled and equated using conversional CTT equipercentile equating

methods. Kolen and Brennan (2004) have provided detailed examples for conducting true score

and IRT observed score equating [4].

Two data collection designs commonly use with IRT equating methods include the

common-item equating and the common-person equating (Table 1-1) [34]. In common-item

equating, the two tests share items in common where individuals take tests that include

additional common items to all test forms. For example, McHorney and Cohen (2000) [35] used

common-item equating to equate a survey of functional status items where a set of unique items

was included on each of three forms and a set of common items was administered to all groups.

As for common-person equating, common persons take both tests of different items that are









designed to measure the same construct. For instance, Fisher et al. (1995) [43] created a

statistical link between the Functional Independence Measure (FIMTM) and the Patient

Evaluation Conference System (PECS) )where paired assessments (both FIM and PECS) were

collected within a certain period of time. Since the common items or persons are the only link

between different test forms, choosing of the linking items/persons becomes a critical issue.

Smith (1992) [3 8] suggested to select items that are around average person ability level (i.e.,

avoid too challenging or extremely easy items), and the linking items should spread across a

range of person ability spectrum. Meanwhile, the common items/persons between different test

forms should be evaluated for their response pattern. Misfit items/persons that misrepresent the

response pattern may lead to inappropriate shifting constant for equating and should be removed

from the linking process [38].

Equating: Education versus Healthcare

There are maj or differences between equating studies in education versus that in

healthcare. In education, the common purpose of equating is to develop conversions between

different versions of an examination. At present, many tests administered by ETS today use a

new version of a test at each maj or administration (such as the Graduate Record Examination

(GRE), Test of English as a Foreign Language (TOEFL), and the Scholastic Aptitude Test

(SAT). The alternative forms or different versions of a test are usually developed with the

guidelines to ensure common content and consistent statistical characteristics. These alternate

forms are embedded within the national exams and implemented while students or applicants are

taking the tests. Nation-wide administrations readily provide large sample sizes as well as sample

randomization (which is needed in some equating methods). Lastly, there are follow up studies to

monitor and check the accuracy and stability of the equating algorithm longitudinally.









In contrast to educational tests, healthcare equating has a quite different purpose. In

health care, many functional measures have been developed or are used in healthcare settings.

While those assessment tools are developed to measure the same construct, they are built

differently in many aspects, including the number of items, rating scale categories, item

definitions, or item formats (such as self-report or performance test). Since decisions to equate or

link instruments in healthcare occur after individual instruments have been developed,

psychometricians have to confront the inherent differences that exist between instruments.

Several healthcare studies therefore created item-to-item conversions based on instrument

manuals and subj ectively decided upon by expert panels. Moreover, while "equating" is a

specific term referring to linking scores on alternate forms of an assessment that are built

according to similar content and statistical specifications [11, 12], most of the test equating

studies in healthcare do not belong to this category. Linking, which is defined more broadly as a

scaling method used to achieve comparability of scores from two different tests, may be

considered a better term equating for existing assessments in healthcare. Table 1-2 compares

equating procedures in education and healthcare.

State of the Art of Equating Studies in Health Care

Expert Panel Equating

Linking instruments in healthcare have generally focused on creating a translation between

each item on the instrument. Studies by Williams et al. (1997), Nyein et al. (1999) and Buchanan

et al. (2003) represent examples where the equating of two scales was attempted by matching

and rescaling each item across the two instruments [36, 39, 40]. In 1997, Williams and his

colleague [36] created the crosswalk between the Functional Independence Measure (FIM) and

the Minimum Data Set (MDS) using an expert panel. MDS items were first chosen and rescaled

into "pseudo-FIM items" to correspond to similar FIM items (e.g., eating-FIM to eating-MDS,









bathing-FIM to bathing-MDS). Since pseudo-FIM items could only be defined for 12 of the 18

FIM items, this procedure resulted in 8 motor and 4 cognitive items (out of the original 13 motor

items and 5 cognition items) included in the analysis. Furthermore, the conversion algorithm was

based on item-to-item rating scale category comparison. For example, if the expert panel

suggested that rating 3 (limited assistance) of a 5-level MDS item plausibly corresponded to FIM

rating 4 (minimum assistance) of a 7-level FIM item, the MDS rating 3 was rescored as 4. The

final rating scale was determined by agreement between two or more (out of seven) panel

members. With the criteria of FIM and MDS assessments occurring within 2 weeks, 173

rehabilitation patients with paired FIM and MDS scores were recruited from nursing home

rehabilitation by therapists and nurses. Intraclass correlation coefficients between the FIM and

Pseudo-FIM motor and cognitive sub scales were both .81. The reported correlation coefficients

provide an indication of how well scores of one instrument can be predicted from scores of the

other instrument and indirectly imply how well the conversion algorithm may work.

Using similar strategies, Nyein et al. (1999) [39] investigated the feasibility of whether a

Barthel score can be derived from the motor items of the FIM. Based on examination of both

manuals, conversion criteria were developed by researchers via item-to-item rating scale

conversion. As a result, 7-point rating scale FIM items were converted to corresponding 4-point

rating scale Barthel Index items. Following the development of the conversion algorithm, a

sample of 40 patients was assessed for Barthel and FIM by a multidisciplinary team. The FIM-

based derived Barthel score was compared with the actual Barthel score. Absolute agreement

between the converted and actual scores ranged from 75 to 100% and the kappa statistical values

ranged from 0.53 to 1.0 (moderate to substantial strength of agreement).









Another study using expert panel to create the conversion system item by item is by

Buchanan and colleagues in 2003 [40]. These investigators attempted to develop a translation

between the FIM and the Minimum Data Set for Post-Acute Care (MDS-PAC). The development

of translation began with comparing the mean FIM and MDS-PAC motor scale score differences

and mean FIM and MDS-PAC item score differences. To improve the comparability between the

FIM and the MDS-PAC, the scoring for MDS-PAC ADL items was changed (six-point rating

scale was rescaled to eight-point rating scale) and "FIM-like" items were created. Over 3,200

FIM and MDS-PAC pairs of data were collected from fifty certified rehabilitation facilities by

trained clinicians.

While these initial attempts at linking are encouraging, the methodological and statistical

approaches used had considerable limitations. For example, a drawback of using the expert panel

or reviewing the manual instructions to develop the conversion algorithm is that such an

approach is not statistically based. Although the approach is intuitive, it is subj ective. Different

algorithms could be developed based on the different expert's background and experience.

Furthermore, it is rare to find an exact one-to-one relationship across items from different

instruments. Consequently, researchers must revise, combine or develop supplement items to

equating instruments. These modifications not only invalidate the psychometric properties of the

original instruments but also interfere with the integrity of the instruments. As evidenced in the

educational literature, equating does not require item-to-item relationship but based on the

rationale that both set of items are measuring the same construct.

Equating an Item Bank

Several healthcare studies have used IRT methods to link different test forms [3, 35, 41,

42]. This methodology is founded on the basis that items from different instruments that measure

the same construct can be placed on a common scale. Instead of viewing each instrument as an









independent measure, items from similar questionnaires can be considered part of an item bank

intended to measure the same construct [35].

In 2000, McHorney & Cohen [35] sampled 1, 588 items from different functional status

instruments to assure sufficient items allocated across the continuum of hypothesized construct.

Two hundred and six items were selected and revised to meet standard criteria for question

design. Common-item equating was used with a set of common items administered to all groups

and a set of unique items was embedded in each of the 3 forms. After obtaining item parameter

estimations from a concurrent run (estimating all item parameter simultaneously in a single run)

using a 2-parameter IRT model, a functional status item bank was established with all the items

placing on a common scale. The result was a functional status item bank with items scaled onto a

common metric. The authors provided no conversion tables or evaluation of the accuracy of

equating.

Rasch Equating Method

Currently, there are only few equating studies in the healthcare field that developed the

instrument-to-instrument crosswalks. These equating studies all used the Rasch model (1-

parameter IRT model) to perform the equating procedure [43-45]. Emerged in the early 1960s

through George Rasch's work [46], the Rasch model is a probabilistic mathematical model that

assumes the probability of passing an item depends on the relationship between a person's ability

and an item's difficulty. Being the most parsimonious model in the IRT family (compared to

more complicated 2- and 3-parameter IRT models), early studies in healthcare have tended to

employ the Rasch model rather than other higher-order IRT models (2- and 3-parameter) [47].

Fisher and colleagues (1995) [43] were the first to use Rasch true score equating method to

create a crosswalk between 13 FIM motor items and 22 motor skill items from the PECS. Fifty-

four consecutive patients admitted as inpatients were rated on both the FIM and the PECS by









trained rehabilitation professionals. Items from both instruments were initially co-calibrated,

analytically treating the 35 physical functioning items as one instrument. The co-calibration

placed the items from both instruments onto a common metric with a common origin. Then, each

instrument was analyzed separately, anchoring the item and rating scale calibrations to those

obtained from the co-calibrated analysis. Followed by the separate analyses, converting from

FIM to PECS and vice versa was achieved by connecting FIM raw scores and PECS raw scores

to corresponding person ability measures. A PECS/FIM "rehabits" crosswalk table was

presented. The Pearson correlation of the personal measures produced by the separately anchored

FIM and PECS items was 0.91.

To enhance and further investigate the equating results, Smith & Taylor (2004) [45]

replicated the Fisher' s study with larger sample size and modified research design.

Approximately 500 subj ects were recruited in this study (comparing to 54 subj ects in the Fisher' s

study) with diagnostic groups more representative of the rehabilitation population. Rehabilitation

professionals were trained prior to data collection. To prevent ambiguity, FIM "walking" and

"wheelchair" mobility items were calibrated separately as two separate items. Similar to Fisher' s

study, the conversion crosswalk was achieved using Rasch true score equating with both FIM

and PECS items co-calibrated and anchored in separate analyses. Similar to the findings of

Fisher and colleagues, person ability measures estimated by separate FIM and PECS items

correlated at 0.92.

Fisher and his colleagues further used Rasch true score equating to link other healthcare

instruments. In 1997, Fisher and his colleagues [44] equated 10 items of physical functioning

(PF-10) and 29 items from the Louisiana State University Health Status Instruments (LSU-HSI)

based on a convenience sample of 285 patients. The person ability measures estimated from









these two instruments correlated 0.80. Conversion tables were provided for translating raw

scores from one instrument to the other via a common metric. Furthermore, Fisher (1997) [48]

published a theoretical article which provided a framework for linking physical function

measures by reviewing more than 30 Rasch studies of physical function measures. Fisher

suggested that the difficulty hierarchy of physical functioning tasks was affected by two factors:

1) the extent of involvement of upper and lower extremities in coordinated activity and 2) the

amount of strength needed. Items that require extensive coordination and strength of upper and

lower body, such as walking, usually appear to be the most challenging items. Feeding and

grooming, which only require strictly upper extremity functions, were usually found the easiest

tasks. Transfer activities, involving moderately coordinating both upper and lower extremities,

are of medium difficulty. Besides, bowel and bladder management, which involves an

involuntary muscle control component, usually will fail to fit the Rasch measurement model.

Based on the above consistencies across instruments designed to measure physical functioning,

Fisher further supported that the development and deployment of a universal "rehabits" metric

was a realizable goal.

As for measuring cognitive functioning, Coster and colleague (2004) [42] also supported

the feasibility of constructing a meaningful outcome measure to assess cognitive functioning in

daily life. They found the maj ority of items (46/59) could be located along a single continuum

when performing a Rasch analysis across cognition items from several widely used instruments

including the Activity Measure for Post-Acute Care, the Medical Outcomes Study 8-Item Short-

Form Health Survey, the FIM instrument, the MDS, the MDS-PAC, and the Outcome

Assessment and Information Set (OASIS). Meanwhile, they found about 25% of the convenience

sample (out of 477 patients receiving rehabilitation services) were at ceiling and relatively few










people performing at the low end of the difficulty scale. Table 3 summarizes the equating studies

in healthcare field.

Next Critical Studies for Advancing Linking in Healthcare

To achieve more accurate and consistent equating results and thereby advancing linking

studies in healthcare, more rigorous research designs are needed. Successful linking involves

equating methods selection, and the conversion crosswalk validation. Researchers who intend to

conduct linking studies should examine the psychometrics of the instruments to be linked and be

cognizant of the different test administration procedures. Different equating methods including

CTT and IRT should be examined to obtain optimal equating. Moreover, current linking studies

in healthcare have attempted to develop a single conversion algorithm for all patients. Since

health care includes diverse diagnostic groups, group invariance should be investigated. That is,

a critical question is whether separate conversion tables/algorithms should be created for

different diagnostic groups or whether a universal conversion table/algorithm is adequate. This

could be achieved by investigating whether items function similarly across different diagnostic

groups or by comparing the conversion algorithms created based on each diagnostic group.

A maj or limitation of existing linking studies in healthcare is the lack of investigation of

the accuracy of the linking results and insufficient reporting on how to interpret the converted

scores. Follow-up validation studies would provide valuable information for researchers,

clinicians, administrators (conversion accuracy), and policy-makers (cost-efficiency) an insight

to evaluate the application of linking in clinical sites. Without validation analyses, applications

of the conversion algorithm can be challenged. To date, only two equating studies in healthcare

have investigated the validity of their conversion tables. Nyein and his colleagues (1999) [3 9]

evaluated their Barthel-FIM conversion system in a prospective study of 40 subj ects.

Nonparametric statistical techniques were used to evaluate the correlation between the derived









Barthel score and the actual Barthel score (Spearman rank correlation) and percentage of

absolute agreement (Wilcoxon signed rank test). A high correlation (Spearman's rho= 0.99) and

absolute agreement ranging from 75 to 100% were found to confirm the conversion criteria.

Buchanan et al. (2003) [49] evaluated their FIM-(MDS-PAC) conversion system by using actual

FIM score and converted FIM score from MDS-PAC to classify approximately 3,200 subj ects

into case-mix groups (CMG), a procedure to compute the medical payment. Percentage of cases

that mapped into the same CMGs by actual FIM score and converted FIM score from MDS-PAC

were computed. The FIM and PAC-to-FIM scales mapped 53% of cases into the same CMG;

approximate 84% were classified within 1 CMG and 93% within 2 CMG.

Equating studies in healthcare requires rigorous and systematic follow-up studies to

validate the conversion crosswalks. We propose that crosswalk validation phase should be

investigated at two levels. First, the conversion crosswalk should be validated at the patient level.

For example, one may ask how accurate is the conversion algorithm in terms of predicting a

patient' s score from the other instrument. That is, do the converted and actual scores classify

patients similarly? If the converted scores are found to be accurate within reasonable error,

which require further definition, the conversion algorithm may be used to track and monitor

patient' s status through different healthcare settings. Second, the conversion algorithm could also

be validated at the sample level. For example, how accurate is the conversion algorithm in terms

of group equivalence? Is the mean of the converted score distribution equivalent to the mean of

the actual score distribution? If the conversion crosswalk could reach group equivalence, the

conversion algorithm may be valuable in comparing facility-level outcomes.

Lastly, a limitation in present healthcare linking studies is small sample sizes. Kolen

(1990) notes that less equating error can be anticipated with large sample size (e.g., sample sizes










greater than ***) [50]. Large samples would also imply better representations of the population.

Equating studies in education commonly involve large samples. For example, Kingston et al.

(1986) [5 1] used 4,000 subj ects to equate the Graduate Record Examination (GRE) via both CTT

and IRT methods; Yin et al. (2004) [52] used 8,600 to link the American College Test (ACT)

and ITED (the Iowa Tests of Educational Development) via linear and equipercentile methods;

and Dorans et al. (1997) [53] and Pommerich et al. (2004) [54] used approximately 100,000

subj ects to the equate the ACT and the Scholastic Aptitude Test (SAT)). Sample sizes of 400 are

suggested for Rasch model equating and 1,500 for 3-parameter IRT equipercentile equating [4,

19]. However, a sample size of less than 500 subjects is common for equating studies in

healthcare [36, 43, 44].

Researchers who intend to conduct equating studies may take advantages of existing

healthcare databases. Several instruments related to functional outcomes are either extensively

used or federally mandated across the post-acute healthcare settings, for example, the FIM for

inpatient and sub-acute rehabilitation facilities, the MDS for skilled nursing facilities, and the

OASIS for home health care. Using existing databases, researchers may be able to obtain large

sample sizes across diverse diagnostic patients. Moreover, a critical question is whether

prospective studies are the best means of creating and validating crosswalks. Prospective studies

may not produce the type of data that will be used in real-world applications of equating in

healthcare. That is, the quality of healthcare data is likely to be influenced by the context of the

demands and challenges of day-to-day rehabilitation services. Existing clinical and

administrative databases may provide the data that are most relevant to everyday applications of

crosswalks in healthcare.










A key to improve clinical care in healthcare is to develop an effective and efficient

mechanism to evaluate and track changes of patient' s status across the continuum of care. While

utilizing a single outcome assessment instrument would provide the optimal mechanism for the

synchronized and seamless monitoring of patient outcomes, the use of different instruments is

already firmly entrenched across these rehabilitation settings. Using rigorous equating

methodologies, researchers may overcome the challenges inherent in comparing patients and

facilities that use different outcomes measures. The establishment of the crosswalk conversion

algorithms may provide an economical means of monitoring patient progress and comparing

facility outcomes across the continuum of care.

Research Question

The proposed study was funded by Dr. Velozo's VA Rehabilitation Research and

Development Proj ect, 03282R, Linking Measures across the Continuum of Care (October 2003

to March 2006). The main purpose of the proj ect was to develop crosswalk tables/algorithms that

link scores and measures from the FIM and the MDS. It is based on the hypothesis that the

functional status items of the FIM and the MDS are subsets of items along two constructs: an

ADL/motor construct and a cognition/communication construct.

Many studies have provided evidence that FIM has good psychometric properties in terms

of reliability [55-64] and validity [65-69]. While not as extensively studied as FIM, evidence

suggests that the MDS has adequate psychometric properties for use in research purposes [70-

74]. Several studies have used Rasch analysis to investigate the FIM at the item level [48, 75-

78]. However, MDS instrument lacks such studies. To the author's knowledge, there has been

only one published study, by Williams and his colleagues [36], that has attempted to create the

FIM and MDS crosswalk by expert panel. Instead of using non-statistical based expert panel

method to build the FIM-MDS crosswalk, Dr. Velozo applied the Rasch true score equating to









develop the crosswalk conversion algorithm between these two instruments. Two conversion

tables, each for one construct (ADL/motor and cognition/communication), were created. In 2004,

Dr. Byers, a former student of Dr. Velozo, performed a cross-validation study to evaluate the

accuracy of the conversion tables at the patient level. Point differences between the actual and

converted FIM/MDS scores were computed and the score distributions between the actual and

converted scores were compared. In this chapter, several equating/linking methodologies

commonly used to conduct equating/linking and the state of the art of existing test equating

studies in healthcare were reviewed. The proposed studies are a logical extension of this review

and Dr. Velozo and Byers FIM-MDS linking research.

Research Question 1

What are the item-level psychometrics of the MDS in terms of physical functioning and

cognitive domains (e.g., dimensionality, item difficulty hierarchical order, rating scale structure,

item-person targeting, and other item statistical properties)?

Research Question 2

Do the items statistically function consistently across different diagnostic groups so that

only one crosswalk is required or do inconsistencies in item calibrations mandate developing

separate crosswalks (e.g., one for each impairment group)?

Research Question 3

What is the accuracy of the crosswalk? How accurate is the crosswalk at individual level

in measuring individual patients, at classification level in classifying patients into the same

classification system, and at sample level in comparing the facility outcomes?







































::~:: :::I:: 1_1


Table 1-1. Educational Equating Methodologies
A-1 Common Equating Methods Based on CTT
Equating Methods

I. Mean Equating



II. Linear Equating




III. Equipercentile Equating


Description of Equating Methods

Under the mean equating, Test X is considered to differ in difficulty from Test Y by
a constant amount along the score scale.
Under equal reliable tests: x u(x) = y u(y)

In linear equating, the linear conversion is defined by setting standardized deviation
scores (z-scores) on the two forms to be equal.
x-u(x) y-u(y)
o-(x) o-(y)

For the equipercentile equating, the equating function is developed by identifying
scores on Test X that have the same percentile ranks as scores on Test Y.


A-2 Common Data Collection Design Usually Accompany with CTT Equating Methods


(a) Random Groups, One Form
Administered to Each Group


Design A Test X Test Y

Subgroup1l -------

Subgroup2 ----


(b) Random Groups, Both Forms
Administered to Each Group,
Counterbalanced

Design B Test Test
Test X Test Y
Subgroup1 ---- ----

Test Y Test X
Subgroup2


(c) Nonrandom Groups, One Test to Each
Group; Common Equating Test
Administered to Both Groups

Design C Test X Test Y Test V


Nonrandom
Group 1
Nonrandom
Group2











Table 1-1. Continued
B-1 Common Equating Methods Based on IRT
Equating Methods

I. True Score Equating







II. Observed Score Equating


Description of Equating Methods


Under the true score equating, the true score on one form associated with a
given person latent trait (6) is considered to be equivalent to the true score on
another form correspond to that latent trait. The equating procedure involves
specifying a person's true score on Test X, finding the 6 corresponding to
that true score, and finding the true score on Test Y via the same 6.

IRT observed score equating uses the IRT model to produce an estimated
distribution of observed number-correct scores on each form, which then are
equated using equipercentile methods.


B-2 Common Data Collection Desinn Usually Accompany with IRT Ealuatinn Methods


(a) Common Items Design
Test items



Test A Items '






ITest B Items I!!


(b) Common Person Design
Test items

-|-----------------------------| o m nPro

STest AItemS I--||-----------------------------| Common Person
---|-----------------------------| o m nPro
|-----------------------------||-----------------------------| Common Person



Test B Items


Persons
Persons
Persons3
Persons4
Persons









Persons n









Table 1-2. Education versus Healthcare Differences in Equating Procedures


Education


Healthcare


1) The decision of equating or linking
usually occurred before developing
different test forms

2) Tests being equated had the same
question format, length, and rating
scale (usually multiple choice)

3) Data collection is embedded in
national-wised exam while applicants
take the real test

4) Conduct one or more statistical
equating methods and compared the
results

5) Evaluate the results of equating
including the accuracy and stability


1) The decision of equating or linking
occurred after individual instruments
were developed and implemented in
clinical settings
2) Assessments being equated often have
different question format, length, and
rating scales (such as Likert scale)

3) Data collection usually is conducted via
perspective studies from a convenient
sample

4) Many studies use subjective expert
panel for item-to-item conversion and
usually only one equating method is
used
5) Often no follow up studies evaluating
the accuracy and/or stability of
equating











Table 1-3. Review of Linking Studies in Health Care

First Author Procedure to Create Conversion
Instruments Data Source
Year Tables/Algorithm


Conversion Validation/
Algorithm Evaluating


Results


Fisher (1995)
[43]


FIM-PECS Free-standing
rehabilitation
hospital
N=54


Rasch true score common-person
equating


The correlation (Pearson's
R) of the measures
produced by the
separately anchored FIM
and PECS items was 0.91


FIM motor [Reliability]:
Cronbach'a = 0.89
[Correlations between
actual and converted
scores]
Spearman Brown
intraclass correlation r
=0.81
Pearson's correlation r
=0.728

The correlation (Pearson's
R) of the measures
produced by the
separately anchored FIM
and LSU-HIS items was
0.80.
PF-10: Item separation
reliability= 0.99
LSU HIS: Item separation
reliability = 0.90
Support the quantitative
stability of physical
functioning construct
across instruments and
samples


PECS/FIM
Rehabits
conversion
table



Item-to-item
conversion
criteria


None


Williams (1997)
[36]


FIM MDS


Six nursing
homes
By trained
clinicians
N= 173


Expert Panel these experts were
asked which items (or groups of
items) from the MDS were most
comparable to each of the 18 FIM
items
One-way conversion algorithm:
derive a MDS score from the FIM


None


Fisher (1997)
[79]









Fisher (1997)
[48]


SF10 (LSU-
HSI)









Review more
than 30 articles
of physical
functioning
scale


A convenient
sample in a
public hospital
medicine
clinic
N=285





N/A
Review
articles


Rasch true score common-person
equating









Rasch pseudo-common item
equating


Two true score
conversion
table (i.e., raw
score to person
measure to raw
score on the
other
instrument)


N/A


None


None











Table 1-3. Continued
Nyein (1999) FIM Barthel
[39]


N/A
Review
Manuals





Survey of
outpatient
clinics of
VAMC
N=3,358
Secondary
data analysis
N=4,655






Patients drawn
from six health
provider
network in
Boston area
N=485
50 rehab
facilities
By trained
clinicians
N> 3000


[Manual] The conversion criteria
were established by careful
examination of the Barthel Index
and FIM manual
One-way conversion algorithm:
derive a Barthel score from the
FIM
2-parameter IRT conunon-item
equating



2-parameter IRT conunon-item
equating







Concurrent run via Rasch model






Study Team The conversion
algoritinn was decided by the study
team item-by-item. Additionally,
rating scales were modified and
supplement items were added.
One-way conversion algorithm:
from the MDS-PAC items to FIM-
like items


Spearman's rho =0.99







Put all items onto a
conunon metric



Put all items onto a
conunon metric







Put all items onto a
conunon metric





Mean difference between
actual and converted
score for each item ranges
from 0.5 to 1.5 points


Item-to-item
conversion
criteria





Equating items
parameters



Equating items
parameters







None






Item-to-item
conversion
criteria with
modified
rating scale
and
supplement
items


Prospective
study with
40 brain
injury
subjects


None





None








None






Factor
Analysis
Regression
Analysis


McHorney
(2000) [35]



McHorney
(2002) [3]







Jette (2003) [41]






Buchanan (2003)
[401


Item bank with
206 ADL and
IADL items


Nineteen
conunon items
and 2 sets of
supplemental
item that
measure
functional
status
FIM, MDS,
PF-10, and
OASIS




FIM (MDS-
PAC)









































FIM, MDS,
MDS-PAC,
and OASIS


Table 1-3. Continued
Buchanan (21 1 14) FIM (MDS- 50 rehab
[49] PAC) facilities
By trained
clinicians
N=3200











Smith (21 r14) [451 FIM-PECS Free-


The same as previous study
(Buchanan, 2003)


The mean difference
between the FIM and
MDS-PAC motor scales
translations were 2.4 with
scale correlations of .85.
Payment cell
classification using FIM
data agreed with that
using MDS-PAC data
only 56% of the time.
Twenty percent of the
facilities experienced
revenue shifts largertha
10%
Person interval measure
correlation is 0.92







Put all items onto a
common metric


The same as
previous study
(Buchanan ,
2003)












Score
conversion
tables






None


CMG and
payment
comparison













None








None


standing equating
rehabilitation
n hospital
By usual
and trained
clinicians
N=500
Convenience Concurrent run via Rasch model
sample of
patients
receiving
rehabilitation
services
N=477


Rasch true score common-persl


on


Coster (2l1~14) [2]









CHAPTER 2
RASCH ANALYSIS OF THE MINIMUM DATA SET (MDS) ON THE PHYSICAL
FUNCTIONING AND COGNITION DOMAINS

Introduction

According to the U.S. Census Bureau, there are more than 36.6 million individuals in the

United States at age 65 and over, and this population is proj ected to be more than three times as

many in 2050 as today [80]. The increasing age of the population is accompanied by a greater

number of people living with chronic disease including functional limitations and disabilities

[81, 82]. Based on the Center for Disease Control's health statistics report, 34 percent of the

elderly population have activity limitations caused by chronic conditions and 6.3 percent need

help with personal care [83]. Cognitive impairment, which is also common among the elderly

people, was associated with a higher risk of functional decline and with a poor functional

recovery [84]. Cognitive impairment also has an impact on the ability to perform activities of

daily living (ADLs) and is associated with increased cost of care for elderly people [85].

Nursing homes are a critical environment for tracking the health care status of the elderly

population. Individuals who cannot take care of themselves because of physical, emotional, or

mental problems may choose or be placed in skilled nursing facilities (SNFs). Currently, there

are 1.6 million residents living in nursing homes and their average length of stay is approximate

892 days [86]. More than 90 percent of current residents are 65 years of age or older and most

residents require assistance in multiple activities of daily living [87]. Reports estimate that about

40 percent of nursing home residents need help with eating and more than 90 percent require

assistance with bathing [88].

To improve the quality of care in the SNFs, the Centers for Medicare & Medicaid Services

(CMS) developed a resident assessment instrument (RAI) in 1990 to assess and plan care for

residents in long term care facilities [89]. In 1998, with the regulations and the introduction of a









prospective payment system, skilled nursing facilities are required to complete and transmit RAI

data to the state for all residents whose stay is covered by Medicare. As a central assessment core

in the RAI, the Minimum Data Set (MDS) covers 18 clinically important domains. With

approximately 450 items in a fully comprehensive assessment and about half of items needed to

be completed during a quarterly assessment, the MDS gathers abundant resident background

information for designing care plans, evaluating quality of care, and further monitoring the

impact of policy changes [71, 89].

Numerous studies have investigated the psychometric properties of the MDS. Several

reliability and validity properties of the MDS including the inter-rater reliability [71, 72], test-

retest reliability [90], rater agreement [71, 91], concurrent validity [92, 93], responsiveness [93],

and dimensionality [71] have appeared in the literature. Many studies support the reliability and

clinical utility of the MDS items and suggest MDS data should be used for research purposes

[70-73]. Hawes (1995) [74] reported that MDS items met a standard for excellent reliability in

areas of functional status such as ADLs, continence, cognition, and diagnoses with intraclass

correlation of 0.7 or higher. Casten and colleagues (1998) [71] found high correlations between

the raters for each index (Cognition r = 0.80; ADL r = 0.99). Snowden et al. (1999) [93] showed

that the MDS cognition scale correlated with the Mini Mental State Examination (r = 0.45) and

the ADLs scale correlated with the Dementia Rating scale (r = 0.59). However, the MDS has

been criticized for being semi-structured rather than having standardized interview procedures

and for having multiple fields requiring information [74, 94].

Through the Nursing Home Quality Initiative (NHQI) in November 2002, the CMS

continues to work with measurement experts to improve the quality of measures for nursing

home facilities. For better understanding of healthcare instruments, it is central to document the










psychometric properties of these assessments. Findings from these analyses may be suggestive of

revision of the instrument, which is consistent with the commitment from the CMS to continue to

revise and improve the RAI for care planning. Above-mentioned psychometrics analyses all

focus on reliability and validity at the total-score level of the MDS. An alternative approach is to

inspect the rating scale structure and examine underlying psychometrics of the MDS at the item

level .

A myriad of studies have used Rasch analysis to examine and refine instruments in the

health related field [95-101]. However, there are no published studies that have applied Rasch

analysis to explore the psychometric properties of MDS items. As a step to continue to build on

the existing psychometrics studies related to the MDS instrument, the purpose of this study was

to assess the physical functioning and cognitive domains of the MDS using Rasch analysis.

Methods

Sample

A secondary, retrospective analysis using MDS data from a database collected by the

Veteran Affairs (VA)'s Austin Automation Center (AAC) from June 1, 2002 to May 31, 2003

were used for this study. This is also the data set used in the VA Rehabilitation Research and

Development Proj ect, 03282R, Linking Measures across the Continuum of Care. The main

purpose of that proj ect was to develop crosswalk tables/algorithms that link scores and measures

from the Functional Independence Measure (FIMTM) and the Minimum Data Set (MDS). VA

FIM and MDS data reside in two databases at the VA' s Austin Automation Center (AAC). Data

from both databases (the Functional Status and Outcomes Database (FSOD) and the Resident

Assessment Instrument Minimum Data Set (RAl-MDS)) were downloaded and merged on the

basis of social security numbers. In order to minimize the impact that change in a patient' s

condition could have on FIM and MDS scores, data were restricted to those that involved those










subj ects whose FIM and MDS assessment dates were within 5 days of each other. Data with any

missing values in FIM and MDS items were excluded. Individuals with stroke, amputation or

orthopedic impairments were selected for analysis. The dataset comprised a total sample of 654

records (302 stroke, 113 amputation, and 239 orthopedic impairment). The average age of this

sample was 68 + 12 years, 96.6% were male, 74.2% were white, and 46.7% were married. The

average difference between FIM and MDS assessment dates was approximately 2.85 days. Table

2-1 provides the demographic baseline characteristics and information on impairment categories.

This study was approved by the Institutional Review Board at the University of Florida and the

VA Subcommittee of Human Studies. Access to VA MDS data was approved by Department of

Veterans Affairs, Veterans Health Administration.

Resident Assessment Instrument Minimum Data Set (RAl-MDS)

The RAl-MDS database contains a core set of clinical and functional status elements

(MDS), triggers, and 18 Resident Assessment Protocols (RAPs). State Veterans' Homes (SVH),

which are funded by the VA and also participate in the Medicare and Medicaid, are required to

collect residents' information for care planning and transmit MDS data to the Centers of

Medicare and Medicaid Services (CMS).

The physical functioning items are embedded in section G of Physical Functioning and

Structural Problems section of the MDS. It consists of items intended to measure residents'

activity of daily living such as bed mobility, transferring, dressing, locomotion, eating, hygiene

and bathing. All items have a 5-point rating scale ranging from "O" (independent) to "4" (total

dependence) with lower scores representing higher level of performance. If the activity did not

occur during the entire 7 days, the rater is instructed to score an "8" (activity did not occur). In

this study, instead of treating the MDS rating scale category of "8" as missing values, this










category was recorded to a "4" (total dependence). It is based on the rationale that the most likely

explanation of an activity not being observed during the entire observation period is due to

incapability of performing such tasks [40, 41].

The cognition/communication items are embedded within section B (Cognitive Patterns)

and section C (Communication/Hearing Patterns). These items are used for evaluating residents'

memory, perception/awareness, cognitive skills for daily decision making, and communication

performance. The rating scale structure of the cognition/communication domain varies across

items, which include dichotomous to polytomous rating scales with four rating scale categories.

Table 2-2 presents all the items and rating scales of MDS items used in the analysis.

Administration of the MDS

When the resident is admitted to a facility, the Registered Nurse Assessment Coordinator

and the interdisciplinary team (e.g., physician, nursing assistant, social worker, and therapist)

have a 14 day observation period to complete the admission assessment. After the MDS

assessment is completed, the Resident Assessment Protocol is reviewed to identify the resident' s

strengths, problems, and needs for future care plan. Followed by an initial comprehensive

assessment, a quarterly assessment is mandated 90 days after the initial assessment and an annual

assessment is required to be completed no more than 366 days from the date of the prior

comprehensive assessment. Furthermore, the staff must complete additional assessments when a

resident is discharged or has significant change. Due to the large amount of paperwork, some

facilities hire MDS contract nurses to complete the records based on information provided in the

residents' charts [93].

Rasch Analysis

Rasch analysis (partial credit model) using the Winsteps program [version 3.16] [102] was

used to evaluate the MDS physical functioning and cognition/communication items. The Rasch









model (also called a one-parameter logistic item response theory model) is a probabilistic,

mathematical model that assumes the probability of passing an item depending on the

relationship between a person's ability and an item's difficulty. It is based on the concept that

data must conform to some reasonable hierarchy of less than/more than on a single continuum of

interest [34]. By inspecting persons' responses in which items are relatively more difficult or

easier to endorse, the Rasch model derives persons' ability measures. Similarly, the Rasch model

establishes the item difficulty hierarchical order by maximizing the likelihood of persons'

responses on a set of items. Persons will have a higher probability (> 50%) of succeeding on

easier items; and a lower probability (< 50%) of succeeding on harder items.

The basic form of the Rasch model can be explained by a probability equation

In (Pnik / Pni(k-1)) = Bn Di Fk [34]

The left side of the equation is the logarithm function (In is the natural logarithm which uses e =

2.718 as the base). Pnlk is the probability that person n, encountering item i would be observed in

category k. By taking the probability of passing rating category k (Pnlk) divided by the probability

of passing one less rating category k-1 (Pnze-y), it computes the odds ratio of passing the rating

category from k related to k-1 level. The log transformation then turns ordinal-level data into

interval-level data where the probability of passing the rating scale at the next higher level can be

a conj oint measurement of the person ability (Bn), item difficulty (Di) and the step category

between the rating categories (Fk). The unit of measurement that results when the Rasch model is

used to transform raw scores into log odds ratios on a common interval scale is called the "logit"

[34].

The Rasch model has several advantages over the traditional classical test theory. First,

besides exploring the data at the test level (e.g., reliability and validity), the Rasch model can










inspect the data at the item level, including item difficulty, rating scale structure and whether

response patterns fit the expected measurement model. Second, the item parameters are invariant

no matter which subgroups of sample are used (sample-free). Third, the person ability is

estimated independently of the particular set of items that are administered to the examinee

(scale-free). Lastly, items in the instrument are reported on the same scale as ability scores,

which enable an investigation of how well the item difficulties match with the sample abilities.

Sample Size Requirement for Rasch Analysis

One advantage of using the Rasch model is that relatively small sample sizes are required.

Hambleton (1989) [103] suggested that a sample size of approximately 200 is adequate for

studies of health-related quality of life using the Rasch model, whereas larger sample sizes

greater than 500 may be required to obtain stable item parameter estimates with the two-

parameter item response theory model. For polytomous rating scale questionnaires, Linacre

(1999) [104] recommends sample sizes that result in at least 10 observations per rating-scale

category to ensure certain accuracy and different levels of precision.

Analysis

Dimensionality

Many measurement experts believe that meaningful "obj ective" measurement can only be

achieved if each item contributes to measurement of a single attribute [105]. Therefore, factor

analysis (FA) was used to examine the dimensionality of the instrument. FA is a technique that

can be used for dimension deduction [106]. The common factor model assumes that the observed

variance is attributable to common factors and a single specific factor. A determination of

whether the scale is unidimensional is investigated by interpreting the factor loading matrix (the

correlations between the original variables and the common factors), and the percent of variance

explained by each factor. After initial factor analysis without rotation, FA Varimax orthogonall









transformation) and FA Promax (oblique transformation) were used as follow-up analyses for

better interpretability of the results.

How well the data fit the model

Fit statistics were performed to investigate whether the response patterns on the physical

functioning and cognition scales fit the Rasch measurement model. A fit statistic index calculates

the ratio of the observed variance divided by the expected variance with an expected value of I

and a range from 0 to positive infinity. An infit mean square value of 1+ X indicates the

observed variance contains 100*X% more variation than the model predicted [34]. Wright and

Linacre (1994) [107] suggested a reasonable item mean-square (MNSQ) fit statistics ranges from

0.5 to 1.7 for clinical observations. MNSQs higher than 1.7 indicate that the response pattern of

items have more variance than the model expected.

Item difficulty hierarchy

The empirical item difficulty hierarchical order produced by the Rasch analysis can be

used as evidence of construct validity and support or challenge to the theoretical base of the

instrument [101]. Item difficulty hierarchical order was inspected via the estimated item

difficulty calibrations, which are expressed in logits with higher positive values indicating a

more challenging task.

Person-item match: targeting

In Rasch analysis, both person ability and item difficulty are expressed on a common

metric. The extent to whether the items are of appropriate difficulty for the sample can be

examined by comparing the sample ability distribution to the item difficulty distribution. Ceiling

effects can be depicted by a lack of items for persons of high ability and floor effects can be

depicted by a lack of items matching persons of low ability. Furthermore, clusters of items or









gaps between items (no items within a range of a person ability level) may indicate a redundancy

of items or the need to add items within an instrument.

Separation index

The precision of measurement depends on how well the item of an instrument separate

individuals of different ability levels. The person separation index is an estimate of how well the

instrument can differentiate persons on the measured variable. A separation index above 2 is

required to attain the desired level of reliability of at least 0.8 [108]. The person separation index

(G) can be further computed into the number of statistically distinct person strata identified by

the formula [(4G+1)/3]i [34]. This value indicates how many distinct levels of person ability can

be statistically differentiated in ability strata with centers three measurement errors apart [109].

Rating scale structure

The rating scale structure will be examined initially by inspecting the frequency count for

each response option, as well as the rating scale structures summarized by the Rasch model.

Categories with low frequencies indicate that the performance level/rating scale can be assigned

to the respondent only in rare situations or with a narrowly defined scope. Furthermore, Rasch

analysis explores the relationship between the probabilities of obtaining a particular rating scale

score to person ability measures. Linacre (2002) [110] provided three essential guidelines to

optimize rating scale categories via the Rasch model: 1) at least 10 observations should be in

each rating scale category; 2) average measures should advance monotonically within the

category; and 3) outfit mean-squares should be less than 2.0.

Differential item functioning (DIF)

DIF analysis can be used to examine whether the items function similarly across different

groups and identify items that appear to be too easy or difficult after controlling for the ability

levels of the compared groups. In this study, DIF method based on Wright and Stone (1979)










[111] was used to explore whether items on the MDS perform similarly across three different

diagnostic groups (individuals with stroke, amputation, and orthopedic impairment). Items with

DIF t-statistics beyond two standard deviations were indicated as having significant DIF [111].

Results

Dimensionality

Within a conj oint run of all functional items together, the results of factor analysis showed

that 5 factors had eigenvalues greater than 1. The first Hyve factors had eigenvalue equal to 11.9,

3.7, 1.9, 1.3, and 1.0, respectively, which explained approximate 41%, 13%, 7%, 4%, and 4% of

the total variance. Table 2-3 presented the factor patterns from factor analysis. Initially, factor

analysis without rotation was performed. Results from the factor pattern revealed that, for the

first component, all items had positive loadings ranging from 0.41 to 0.80, which indicated a

general construct measuring functional status. For the second factor, all cognitive items had

positive loadings (0. 11 to 0.47) and all physical functioning items had negative loadings (-0.05 to

-0.51), indicating two separate subconstructs were underlie the overall functional status domain.

The third factor had relatively high factor loadings (> 0.35) on six items that were indicators of

delirium (i.e., easily distracted, periods of altered perception, restlessness, lethargy, and mental

function varies over the course of the day). Lastly, while three communication items showed

high factor loadings on the fourth factor (0.37 to 0.52), two walking items demonstrated relative

high factor loadings on the fifth factor (0.53 and 0.54).

Orthogonal transformation was then performed, followed by oblique transformation where

factors are allowed to be correlated with each other. Factor patterns obtaining from orthogonal

and oblique transformation were similar. All physical functioning items (except two walking

items) highly correlated with the first factor (0.56 to 1.00). Severn cognitive items including two

memory items, four recall items, and one cognitive-skill s-for-daily-deci sion-making item had










high correlations with the second factor (0.41 to 1.00). For the third factor, six cognitive items

(indicators of delirium) had relative high factor loadings (0.80 to 1.00). For the fourth factor,

three communication items highly correlated with the fourth factor (0.56 to 1.00). Lastly, two

walking items demonstrated relative high factor loadings on the fifth factor (0.97 to 1.00). While

there were multiple factor loadings, we separated the instrument into 2 factors, physical and

cogntive, as a conservative interpretation.

Rasch Analysis

ADL/Physical functioning items

Rasch analysis (partial credit model) was performed using the WINSTEPS software

program. Overall, the physical functioning items showed good psychometric properties. Person

reliability, analogous to Cronbach's alpha, was 0.89. With all infit MNSQ statistics (0.56 to 1.51)

less than 1.7, no physical functioning items misfit the Rasch model.

The physical functioning item difficulty calibrations were presented in Table 2-4. The item

difficulty calibrations ranged from -1.37 to 1.49 logits with an average of 0.05 logits error

associated with parameter estimations. Two walking items (walking-in-corridor and walking-in-

room) and one bathing item were the most challenging items along this construct. Alternatively,

eating, bed mobility, bladder, and bower, were the easiest items. Items such as toileting,

dressing, transferring and hygiene represent items around the average difficulty level. In general,

the score correlations (point-biserial correlation) between the individual item response and the

total test score were moderate to high (r = 0.62 to 0.82).

The analysis placed persons and items on the common linear scale with the same local

origin. Figure 2-1 illustrated the relationship of the sample score distribution (left) with the

hierarchical order of the physical functioning items (right). Linear measures, in logits, were

represented along the central axis. The distribution of person ability estimations (higher values









representing high ability and lower values representing lower ability) was normally distributed

with a slight ceiling effect with 6. 1 % of the sample receiving a maximum measure. The sample

ability level (M on the left) of 0.58 & 1.76 logits matched well with item difficulties of the MDS

items with the mean item difficulty (M on the right) of 0.00 + 0.87 logits. With person separation

index (G) equaled to 2.89, these physical functioning items statistically defined person ability

into 4. 19 [(4G+1)/3] statistically distinct strata.

The rating scale structure was initially examined by inspecting the frequency count for

each response category. Figure 2-2 showed the frequency count of responses from "O"

(independent) to "4" (total dependence) and the additional rating scale category of "8" for

activity did not occur during the entire 7 days. Three rating scale categories are presented on

each graph to simplify the presentation. On the x-axis, 13 physical functioning items were listed

and ordered from the easiest (eating) to the most challenging item (walk-in-corridor) (from left to

right). The y-axis was the frequency count of rating scale category. As items increased in

challenge, the frequency counts of "O" (independence -+-) decreased as expected. In general, the

frequency count of "1" (supervision -) maintained a relatively low frequency count

independent of the difficulty of the item. Items at the average difficulty level had a relatively

high frequency count for being scored with "2" (limited assistance -A-) or "3" (extensive

assistance-x-). There was a relatively high frequency count for limited assistance with the

dressing item and a particularly high frequency count for extensive assistance with the bathing

item. However, the trend of the frequency count of "4" (total dependence -*-) did not

monotonously increase as the difficulty of the task increased. Instead, the frequency count of

total dependence had a relatively high frequency count for bathing and locomotion-off-unit and

had a very low frequency count for the two most challenging items, walk-in-room and walk-in-









corridor. For the special rating scale of "8" (activity did not occur during the entire 7 days) (-a-),

the frequency count was low across all items except the two walking items and two locomotion

items.

Most of the physical functioning items met Linacre' s (2002) criteria for optimizing rating

scale categories. All the rating scale categories had at least 10 observations in each rating scale

category. The average measures for each rating scale structure advanced monotonically within

the category. Four items (eat, bladder, bowel, walk-in-corridor) had one rating scale category

that showed misfit (outfit mean-square greater than the criteria of 2). The locomotion-off-unit

item had two rating scale categories that showed misfit.

To determine whether the rating scale for each MDS item was being used in an expected

manner, we examined the probability of each rating (0-4) based on the residents' overall

performance on the MDS. We expected that as the function of the residents improves, there

should be increasing probability of obtaining a higher rating scale category. That is, we expected

that individuals of lower ability would use lower parts of the rating scale (e.g., 4 or 3) and

individuals of higher ability would use higher parts of the rating scale (e.g., 2, 1, and 0).

Figure 2-3 showed the rating scale pattern for physical functioning items. The y-axis was

the probability of endorsing a particular rating scale category and the x-axis equaled the value of

the person ability minus item difficulty. Figure 2-3 (a) (eating item) for example, as person

ability is much lower than item difficulty; there is a high probability of getting a rating category

of "4" (total dependence). As person ability increases, a rating category of "2" (limited

assistance) becomes the next most probable rating. Finally, as person ability is much higher than

the item difficulty, a rating category of "O" (independent) becomes the most probable rating.










Hence, three rating categories provide adequate information for evaluating the eating

performance.

Overall, the rating scale pattern showed that the rating scale of "1" (supervision) rarely

appeared to have a higher probability of endorsement than other rating scale categories. While

the four-point rating scale structure may provide adequate information for several items such as

toileting, transferring, dressing, hygiene and bed-mobility, some items (bladder, bowel, walk-in-

corridor, and walk-in-room) appear to use only two rating scale categories to distinguish

resident' s status.

The partial credit model enables each item to have its own rating scale structure. The

"keyform" output allows a connection between the item difficulty hierarchy and person ability

measures. In addition, the keyform provides a method to interpret and report a person's expected

performance pattern. Figure 2-4 presents the keyform structure of the 13 physical functioning

items in the MDS. Items were arranged by item difficulty calibrations with the easiest item on

the bottom of the y-axis to the most difficult item on the top. The x-axis indicates person ability

measures (in logits) estimated by the Rasch model. For a resident at the average function level

(dashed vertical line at 0.4 logits), he/she is expected to be independent (score 0) with eating,

bladder and bowel; supervised (score 1) on locomotion-in-unit and bed-mobility; independent or

needs limited assistance on hygiene (score 1 or 2); needs limited assistance (score 2) on dressing,

toileting, and transferring; requires limited to extensive assistance (score 2 or 3) on locomotion-

off-unit; needs extensive assistance or total dependent (score 3 or 4) on walking tasks (walk-in-

room and walk-in-corridor. As a resident improves to 1 standard deviation above the average

(approximate 1.73 logits), the resident is expected to have the functional level of being










supervised on walking activities and locomotion-off-unit; need supervision or limited assistance

on bathing; and be independent on all other physical functioning items.

After performing the differential item functioning analysis across three impairment groups,

several items were found to have significant DIF. In comparing stroke with amputation, subj ects

with amputation had more difficulty walking (walking-in-room and walk-in-corridor) and

subj ects with stroke had more difficulty in locomotor-off-unit, tasks which involved upper

extremity function (hygiene and eating) and continence (bladder and bowel). In comparing

stroke with orthopedic impairment, subj ects with orthopedic impairments had more difficulty in

walk-in-corridor, transferring, dressing, and bed-mobility. Similar to the stroke-amputation

comparison, subjects with stroke had more difficulty in some tasks which involved upper

extremity function (hygiene, eating) and continence (bladder and bowel). Lastly, when

comparing amputation with orthopedic impairment, where both the maj ority of individuals have

lower extremity deficits, subj ects with amputation experienced more challenges in walking

(walk-in-room and walk-in-corridor) and subj ects with orthopedic impairment had more

difficulty with locomotor-off-unit, transferring, bed mobility, bathing and dressing.

Cognitive items

The psychometric characteristics of the MDS cognition/communication items were good

but slightly less sound as those characteristics of the physical functioning items. Person

reliability, analogues to Cronbach's alpha) was 0.68. No cognition/communication items showed

infit statistics that exceeded the critical value of 1.7.

Table 2-5 presents the item difficulty estimates of cognition/communication items. The

item difficulty calibrations ranged from -1.71 to 2.20 logits with an average of 0. 14 logits error

associated with parameter estimations. Short-term-memory, ability-to-recall, and daily-decision-

making items formed the most challenging items along this construct. Communication items










(making-self-understood, speech-clarity, and ability-to-understand-others) were the next difficult

items. Items that indicated delirium (altered-perception-or-awareness, easily-distracted,

disorganized-speech, and lethargy) were the easiest items. In general, the score correlations

(point-biserial correlation) between the individual item response and the total test score were

moderate to high (r = 0.54 to 0.75). However, the score correlations were low (r = 0.32 to 0.49)

for those items associated with periodic disordered thinking/awareness and communication items

(except the making-self-understood item).

Figure 2-5 showed a map of the person cognitive measures to the left, and MDS item

measures to the right. The Rasch analysis placed persons and items onto the same linear scale

with the same local origin. In contrast to the physical functioning measure, which showed a good

match between person measures and item measures, the cognition/communication measure was

"easy" for this sample. The average item difficulty (0.00 & 1.26 logits, M to the right) was much

lower than the average ability of the sample (3.49 & 1.74 logits). If excluding extreme persons

who obtained the total maximum score, the average ability of the sample was about 2. 13 A 1.3 5

logits (M to the left in the figure). In contrast to the physical functioning map which showed a

normal distribution of person measures, the cognition/communication was highly skewed with

47.4 percent of the sample showing perfect scores. With person separation index equaled to 1.46,

the cognition/communication items distinguished persons into 2.28 statistically distinct strata.

The observations that cognition/communication items were found too easy for most of

residents were also shown on the rating scale patterns. The maj ority of residents (68-96%) were

rated independent/ablea/beahavi or-not-present for their cognitive status on multiple cognitive

items. Several items (8 out of 16 items) had very low frequency count (< 10) in the rating scale










category that indicates the severe impaired cognition/communication status (i.e., severe

impaired, or have problem).

To determine whether the rating scale structure for each MDS item was being used in an

expected manner, we examined the prob ability of each rating in the cogniti on/communi cati on

items. Figure 2-6 showed the probability of responses for each item as a function of the overall

performance on the MDS cognitive measure. Since two memory items and four recall items were

dichotomously rated, the rating scale structure simply showed that the probability of passing an

item increases when person ability is higher than the item difficulty (Figure 2-6 [A]). Several

items (e.g., easily-distracted, lethargy, mental-function-varies-over-the-course-oftedy and

speech-clarity items) had a well-functioning rating scale structure meaning that when a person's

ability increased, the probability of getting a higher rating increased gradually and distinctly for

each rating category (Figure 2-6 [B]). In comparing Figure 2-6 (C) (restless, altered-

perception/awareness) with Figure 2-6 (B), the middle rating scale category (i.e., "1" behavior

present, not recent onset) out of the 3-point rating scale covered a slightly smaller range of

person ability. As for disorganized-speech item (Figure 2-6 (D)), the probability of getting the

middle rating scale of "1" (behavior present, not resent onset) was lower than the other rating

categories. Lastly, the 4-point rating scale structure in Figure 2-6 (E), the probability of getting a

rating move from "3" to "O" increased as a person's ability increases, though the probability of

getting a "2" became more probable than other rating categories only for a small range of person

abilities.

Most of the cognitive/communication items met Linacre's (2002) criteria for optimizing

rating scale categories. In general, the average measures for each rating scale structure advanced









monotonically. Three items (speech-clarity, restlessness, disorganized-speech) had one rating

scale category misfit with outfit mean-square statistics slightly greater than the criteria of 2.

Figure 2-7 presents the keyform output for the cognition/communication items. This output

provided a means to interpret and report a resident' s performance and progress. Since the

cognition/communication domain had a severe ceiling effect, we recalibrated the average

function level of the residents by removing those data with perfect scores. This procedure

resulted in an average ability level at of 2. 13 (logits) for non-extreme persons. For a resident at

this cognitive level (dashed vertical line), he/she is expected to have no indicators of delirium

(periodic disordered thinking/awareness), be able to make self understood, speech clarity, and

able to understand others (score 0). Meanwhile, he/she should be able to have good long-term

memory (score 0), able to recall that he/she is in a nursing home, location of their own room, and

current season (score 1), but probably will have problems recalling staff' s names or faces (score

1). The individual's short-term memory also would probably be challenged (score 1 or 0).

Cognitive skills for daily decision making probably will not be totally independent and might

have some difficulty when confronting new situations (score 1).

Differential item functioning analysis showed that few cognitive items exhibited

significant DIF. When comparing stroke with amputation, only two items demonstrated

marginally significant DIF (t-statistics just above 2). While cognitive-skills-for-daily-decision-

making was more difficult for subj ects with stroke, and recall-that he/she-i s-in-a-nursing-home

was relatively more challenging for subj ects with amputation. For stroke versus orthopedic

impairment, two items (recall-current-season and cognitive-skill s-for-daily-deci sion-making)

were more difficult for subj ects with stroke and one item (periods-of-lethargy) was more

challenging for subj ects with orthopedic impairments. Lastly, while comparing amputation with









orthopedic impairment, only one item (recall-current season) was more difficult for subj ects with

amputation. But this DIF effect showed only marginal significance.

Discussion

Rasch analysis has been widely used for the evaluation and revision of functional outcome

measures [47, 112]. This study used Rasch (partial credit model) to assess the physical

functioning and cognition/communication items of the Minimum Data Set (MDS) [1 13].

Because few studies have investigated those functional status items of the MDS at the item-level,

this study provides further insight into its item-level psychometrics.

Overall, the physical functioning items demonstrated better psychometric properties than

the cognition/communication items. The average difficulty of physical functioning items

matched well to the mean of sample ability. The physical functioning items also cover a wide

range of the resident' s functioning change with the spread of items efficiently discriminating

resident' s performance into approximate 4 statistically distinct strata. The findings of the

empirical item difficulty hierarchical order are supported by Fisher (1997) [48], who

demonstrated a similar item difficulty hierarchy based on a review of more than 30 Rasch studies

related to physical functioning construct. Fisher proposed a theory of physical disability based on

task difficulty that feeding and grooming tasks, which only require upper extremity functioning,

are usually the easiest tasks; transferring activities, which are more physically demanding and

involve coordinating both upper and lower extremities, are of medium difficulty; and walking

activities, which are the most physically demanding are the most difficult tasks. As in the present

study, this item difficulty hierarchical order also replicates findings of Rasch analysis studies of

the motor scale in the FIM, which is widely used in the inpatient rehabilitation facilities [41, 77,

78, 114, 115].









In contrast to the physical functioning measure, which showed a good match between

person measures and item measures, the MDS cognition/communication items are easy for most

of the residents. Similar ceiling effects have been reported for the in the FIM cognitive scale in

studies of rehabilitation patients even at admission [77]. Coster (2004) co-calibrated

cognition/communication items from several widely used functional outcome assessment

(including the FIM, MDS, the Outcome and Assessment Information Set (OASIS), the Minimum

Data Set for Post-Acute Care (MDS-PAC) and the newly developed Activity Measure for Post-

Acute Care (AM-PAC)) using the Rasch partial credit model [42]. Based on a sample of 477

adults who were receiving rehabilitation services ranging from inpatient acute rehabilitation to

home care services, the results showed a severe ceiling effect with approximately a quarter of the

sample receiving maximum scores across all items. Hence, these findings suggest that more

challenging items should be included on these instruments or that the cognitive/communication

scales should only be applied to diagnostic groups likely to have cognitive or communication

deficits.

The item difficulty hierarchical order of the MDS cognition/communication items seems to

have a pattern illustrating that memory, recall and daily-deci sion-making items are more

challenging than communication items. Similar findings also appeared in Rasch analysis studies

of the cognitive scale in the FIM, which demonstrated that memory and problem solving items in

the FIM are more difficult than comprehension, social interaction, and expression items [41, 77].

The MDS physical functioning items have an additional rating scale category of "8"

activity did not occur. Several researchers have indicated that this scoring level was used when

individuals were unable to perform a task and hence converted these codes to the lowest score

for that item, namely total dependence [40, 41]. It is possible that the raters score this category









because they did not observe the residents performing the action during the entire observation

period. Since these items are activities that the maj ority of people perform on daily basis,

however, the most likely explanation may be that residents are incapable of performing such

task. In a preliminary analysis, we found that the results of item difficulty calibrations for two

walking items (walk-in-room and walk-in-corridor) changed dramatically when we treated the

score "8" as missing values. As previous mentioned, frequency count analysis revealed that

walking items have relatively much higher percentage being recorded in this category comparing

to the rest of items, followed by the locomotion items. One plausible explanation for this

observation is that walking and locomotion items are not routine activities for nursing staff to

assist the residents as compared to other activities of daily living such as eating, dressing, or

bathing. Nonetheless, if a resident does not walk within the nursing facility for the entire

observation period, a likely reason is that the resident is incapable of walking on his own.

To be Medicare and Medicaid compliance, the skilled nursing facilities have to follow

regulations to complete the RAI assessment for residents. Besides comprehensive assessments,

nursing facilities have to perform quarterly assessments and annually assessments. Furthermore,

a significant change form needs to be completed when a resident has significant change. With

approximately 450 items for a comprehensive assessment, and 250 items for quarterly

assessment, the massive amounts of paperwork and staff time committed to the MDS raises the

concern of administrative burden [116]. The burden of assessment loadings and rules such as the

requirement of 21 times observations to obtain ADL data might cause nursing home staff to Eind

it difficult to follow the protocol. This may result in the assessment being completed hastily

which might further compromise the validity of the MDS data [90]. Moreover, the MDS has

been criticized for having different fields of clinicians providing information and inadequate









evaluation training for nursing home staff [90]. With a semi-structured assessment procedure,

different procedures for completing the MDS have been reported: a) the Registered Nurse

Assessment Coordinator asks questions of other staff orally; b) all members of the team have to

complete their portions of the assessment; c) all members are asked for their ratings, but the

Assessment Coordinator provides the final judgments; d) use a combination of chart review,

direct observation, or asking other information resources; e.) hire an MDS nurse to perform MDS

assessments [71, 90]. Therefore, studies using data from MDS clinical databases may contain

inestimable noise and error.

There are several limitations of this study. The sample only represented individuals with

stroke, amputation, and orthopedic impairment groups. The data selection was connected to an

existing proj ect' s criteria. Although the MDS demonstrated multiple factors, we analyzed all

functional status items as physical functioning and cognitive subconstructs. More representative

samples and dividing the cognitive construct further should be considered in future studies.

Over the past few years, the CMS had continued to revise the MDS version 2.0 and had

updated technical information on the website. Recently, the CMS has been working on the MDS

version 3.0 with the purpose of reducing burden, updating sections, and increasing the

responsiveness of the scale for measuring of health conditions [1 17]. While CMS continues to

develop additional menu items, it is critical to continue to evaluate and monitor the psychometric

properties of existing and new items to ensure that the MDS not only is clinical relevant but also

can be used for research purposes. This study provided an alternative perspective other than

traditional reliability and validity test of the MDS domains.









Table 2-1. Demographic Characteristics
Characteri sti c
Mean age & SD (y)
Median age (y)
Gender, n (%)
Male
Female
Race, n (%)
White
Black
Hispanic
Native American
Asia
Other
Missing
Impairment Groups, n (%)
Stroke
Left Body Involvement
Right Body Involvement
Bilateral Involvement
No Paresis
Other Stroke


N=654
68 & 12
69


630 (96.6 %)
22 ( 3.4 %)

485 (74.2 %)
120 (18.3 %)
26 ( 4.0 %)
8 ( 1.2 %)
2 ( 0.3 %)
5 ( 0.8 %)
8 ( 1.2 %)


140
134
7
8
13
302

30
71
1
2
9
113

31
1
5
3
6
74
84
2
33
239


(21.4 %)
(20.5 %)
(1.1 %)
(2.0 %)
(46.2%)

(4.6 %)
(10.9 %)
(0.2 %)
(0.3 %)
(1.4 %)
(17.4%)

(4.7 %)
(0.2 %)
(0.8 %)
(0.5 %)
(0.9 %)
(11.3 %)
(12.8 %)
(0.3 %)
(5.0 %)
(36.5%)


Amputation
Unilateral Lower Limb Above the Knee (AK)
Unilateral Lower Limb Below the Knee (BK)
Bilateral Lower Limb Above the Knee (AK/AK)
Bilateral Lower Limb Above/Below the Knee (AK/BK)
Bilateral Lower Limb Below the Knee (BK/BK)

Orthopedic
Unilateral Hip Fracture
Bilateral Hip Fractures
Femur Fracture
Pelvic Fracture
Maj or Multiple Fractures
Unilateral Hip Replacement
Unilateral Knee Replacement
Bilateral Knee Replacement
Other Orthopedic



































Rating Scale Physical Functioning

0 Independent
1 Supervision
2 Limited Assistance
3 Extensive Assistance
4 Total Dependence

8 Activity did not occur during the
entire 7- day period


Rating Scale Cognition


Table 2-2. Minimum Data Set (MDS)


Physical Functioning and Connition Items


Physical Functioning Items


Cognition items


Bed Mobility
Transfer
Walk in Room
Walk in Corridor
Locomotion on Unit
Locomotion off Unit
Dressing
Eating
Toilet Use
Personal Hygiene
Bathing
Bladder Continence
Bowel Continence


Ability to understand others
Making self understood
Speech clarity
Cognitive skills for daily decision making
Short-term memory
Long-term memory
Recall-Current season
Recall-Location of own room
Recall-Staff names/faces
Recall-that he/she is in a nursing home
Easily distracted
Periods of altered perception or awareness of
surroundings
Episodes of disorganized speech
Periods of restlessness
Periods of lethargy
Mental function varies over the course of the day


Communication:
0-Ok,
1 -Usually/sometimes,
2-Rarely/never understand/understood
Speech clarity: 0-Clear, 1-Unclear, 2-No speech
Cognitive decision making:
0-Independent
1-Modified independence
2-Moderately impaired
3-Severy impaired
Memory: 0-Ok, 1-Problem
Recall: 1-Able, 0-Disable
Awareness:
0-Behabvior not present
1-Behavior present, not recent onset
2-Behavior present, over last 7 days










Table 2-3. Factor Analysis on MIS Items Factor Patternr
Without Rotation Oblique Rotation
Items Factor 1 2 3 4 5 1 2 3 4 5
Short-Tern Menaory 0.64 0.29 -0.28 -0.29 0.08 0.03 0.90 0.00 0.00 -0.00
Long-Terna Memory 0.68 0.36 -o.24 -0.19 0.13 0.02 0.80 0.02 0.01 0.00
Recall-Season 0.68 0.30 -o.21 -0.21 0.14 0.03 0.79 0.02 0.00 0.00
Recall-Location of ROOD 0.70 0.26 -0.23 -0.24 0.08 0.06 0.77 0.01 0.00 0.00
Recall -Staff Nanies/Faces 0.51 0.29 -0.25 -0.24 0.18 0.00 1.00 0.00 0.00 0.00
Recall-Nursing Home 0.41 0.32 0.06 -0.08 0.19 0.00 0.41 0.27 0.00 0.02
Cognitive Skills for Daily Decision Making 0.77 0.32 -0.21 -0.15 0.03 0.06 0.61 0.04 0.02 -0.00
Easily ]Distracted 0.41 0.45 0.46 0.02 -0.14 0.00 0.00 1.00 0.00 -0.00
Periods of Altered Perception or Avvaremess 0.49 0.47 0.43 0.04 0.00 0.00 0.02 0.92 0.00 0.00
Episodes of D~isorganized Speech 0.45 0.45 0.35 0.19 -0.02 0.00 0.00 0.86 0.03 0.00
Periods of restlessness 0.45 0.42 0.43 0.00 -0.15 0.00 0.00 0.94 0.00 -0.00
Periods of Lethargy 0.so o.3s o.3s 0.07 0.03 0.01 0.02 0.80 0.00 0.00
Mental Function Varies Over the Course of the Day 0.47 0.41 0.40 -0.04 0.00 0.00 0.03 0.88 0.00 0.00
Making Self Understood 0.63 0.27 -0.34 0.52 0.10 0.01 0.06 0.00 0.81 0.00
Speech Clarity 0.so 0.11 -o.32 0.61 -0.03 0.03 0.00 0.00 1.00 -0.00
Ability to Understand Others o.6s 0.33 -o.27 0.37 0.13 0.01 0.15 0.02 0.56 0.00
Bed Mobility 0.71 -0.36 0.02 0.07 -0.14 1.00 0.00 0.00 0.01 0.00
Transfer 0.75 -0.49 0.12 0.04 -0.02 0.93 0.00 0.00 0.00 0.05
Walk inf DOD1 0.51 -0.51 0.25 0.04 0.53 0.17 0.00 0.00 0.00 0.97
11'alk in Corridor 0.so -o.so 0.25 0.02 0.54 0.16 0.00 0.00 0.00 1.00
Locomotion on Unit 0.75 -0.28 0.06 -0.04 -0.12 0.92 0.02 0.00 0.00 0.00
Locomotion ofE Unit 0.66 -0.31 0.10 -o.oe -o.04 0.90 0.01 0.00 0.00 0.02
Dressing 0.77 -o.40 0.08 0.04 -0.11 0.98 0.00 0.00 0.00 0.01
Eating 0.76 -o.11 -o.12 0.06 -0.20 0.67 0.06 0.00 0.04 -0.00
Toilet Use 0.79 -0.43 0.06 0.00 -0.08 0.97 0.00 0.00 0.00 0.01
Personal Hygiene o.so -o.31 0.oo -o.oo -o.14 0.93 0.02 0.00 0.00 0.00
Bathing 0.71 -o.39 0.06 -0.02 -0.04 0.95 0.00 0.00 0.00 0.02
Bovvel 0.74 -0.14 -0.14 -0.08 -0.24 0.73 0.09 0.00 0.00 -0.00
Bladder 0.66 -o.os -o.1s -o.21 -0.26 0.56 0.19 0.00 0.00 -0.01










Table 2-4. Physical Functioning Item Statistics (Listed by Item Difficulty Order)


INFIT


OUTFIT


SCORE


ITEM


MEASURE


ERROR MNSQ


ZSTD MNSQ ZSTD CORR.


Walk-corridor
Walk-room
Bathing
Loco-off-unit
Dressing
Toileting
Transfer
Hygiene
Loco-in-unit
Bowel
Bladder
Bed-mobility
Eating


1.49
1.22
1.11
0.61
0.14
0.12
-0.07
-0.27
-0.35
-0.78
-0.82
-1.03
-1.37


0.04
0.04
0.05
0.04
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.06


1.28
1.28
0.91
1.51
0.82
0.56
0.72
0.78
1.24
0.98
1.63
1.12
0.99

1.06
0.30


3.9
3.9
-1.5
7.3
-3.5
-9.5
-5.7
-4.2
3.4
-0.2
6.5
1.8
-0.2


2.16
2.01
0.85
1.77
0.84
0.53
0.69
0.78
1.23
1.70
2.29
1.04
1.05


2.6
3.5
- 2.1
5.8
- 2.8
- 8.6
- 5.5
- 3.5
1.9
2.7
5.1
0.3
0.4


0.68
0.69
0.77
0.67
0.79
0.82
0.80
0.78
0.69
0.68
0.62
0.70
0.70


Mean 0.00 0.05
S.D. 0.87 0.00
MEASURE: item difficulty calibration
MNSQ: mean square fit statistics
ZSTD: standardized fit statistics


0.1 1.30
4.8 0.58










Table 2- 5. C ogniti on/Communi cati on Item Stati stick s
(Listed by Item Difficulty Order)
INFIT OUTFIT SCORE
ITEM MEASURE ERROR MNSQ ZSTD MNSQ ZSTD CORR.

Short-term memory 2.20 0.13 0.88 -2.0 0.81 -2.3 0.75
Recall staff names/faces 1.54 0.13 1.18 2.7 1.23 2.3 0.61
Recall location of own room 1.24 0.14 0.88 -1.8 0.83 -1.7 0.67
Daily decision making 1.23 0.08 0.74 -3.7 0.74 -3.3 0.85
Recall current season 1.15 0.14 0.81 -3.0 0.71 -2.9 0.69
Long-term memory 0.96 0.14 0.77 -3.4 0.69 -2.8 0.68
Recall in a nursing home 0.86 0.14 1.09 1.3 1.58 3.8 0.54
Making self understood -0.11 0.09 1.26 2.6 1.09 0.6 0.64
Speech clarity -0.33 0.12 1.31 2.9 1.78 3.7 0.47
Ability to understand others -0.41 0.10 0.98 -0.2 0.99 0.0 0.64
Mental function varies -1.02 0.15 0.97 -0.2 0.68 -1.4 0.49
Altered percept/awareness -1.19 0.16 1.18 1.3 0.83 -0.6 0.43
Restlessness -1.29 0.16 1.05 0.4 0.97 0.0 0.43
Easily distracted -1.43 0.17 0.98 -.1 0.73 -0.9 0.43
Disorganized speech -1.68 0.18 1.25 1.5 0.96 0.0 0.36
Lethargy -1.71 0.19 1.11 0.7 1.74 1.9 0.32

Mean 0.00 0.14 1.03 -0.1 1.02 -0.2
S.D. 1.26 0.03 0.17 2.1 0.36 2.2












Item (item
calibration ~
enrro)



















walk-corridor (
walk-room (1.22
bathing (1.11 +



1 i-of-unit(.


dressing (.14 +
I transfer (-.07

hygiene (-.27 +


bowel (-.78 t
bladder (-.82 +
bed-mobility(-


Harder tc Perform




















19 + .04)
.04)
,15



+ .04)


,15 toilet .ng (.12
.05)

)15 loco-in-unit (-.:



)15
,3 + .05)


36)




















Easier to Perform


+2 SA.D


.mm











.55






.HM


+1 SA. .



















-1 S.D-


-2 SA.D


Note: Each 'll' indicates 4 persons.
M represents the mean of person ability
Figure 2-1. Person Score Distribution


measures (left) and item difficulty calibrations (right
- Item Difficulty Hierarchy Map -Physical Functioning


SMore Able


Sample


SLess Able
























Ab -s -4-0 Ipndepednt

20 -1 --=-1 Supervision
~L 2 Linited Assistance
150-

100 -. Items have been ordered
by item difficulty
1050 *----z


0 1 2 3 4 5 6 7 8 910 1112 13
500

450 -1 B.

400-

350-

~300-

6 250-

0- 200 -1 -x-3 Extensive Assistance

E~~ ~ 15 %4 Total Dependence

100~~~\ x .... -g- 8 Activity Did Not Occur

50 xItems have been ordered
x------ by item difficulty


0 1 2 3 4 5 6 7 8 9 10 11 12 13





Figure 2-2. Frequency Count of Item Rating Scale Physical Functioning Items (A) Rating scale
category from 0 to 2 (B) Rating scale category 3, 4, and 8






































^^^^^^^^^^^^^^^^^^^^^^()()()()() L/L/L/L/L/^^^^^^^^^^^^^^^


(E) Walk-corridor; Walk-room


FERSO A I ILITY MIIIIT ITEII HER TLE


(F) Loco-in-unit; Loco-off-unit


(C) Toileting; Transfer;

Dressing; Hygiene; Bed-mobility


4444 000
444 000
444 00
14 O
1 O
44 00
4 O
44 O
1 O
1 22222222 O
33*333333*2 2 O
33 44 2 33 *2
333 422 33 O 2
33 224 3 00 2
33 2 44 33*111111**11
333 22 44 11*33 221111
'*100 33 22 11111
3 222222 1111*00*4444 33333 22222 1
*************************"""" nnnnnnnn************


n~^rnr ^


(A) Eating


(D) Bladder; Bowel


(B) Bathing


Note: v-axis is the probability of endorsing a particular rating scale category; x-axis equals the value of

the person ability minus item difficulty: independent: supervision: 2=1imited assistance:
3=extensive assistance: 4=total dependence



Figure 2-3. Rating Scale Str-ucture of the Physical Functioning Items














Walk-corridor 4 :1 3 :2 : i
Walk-room 4 : 3 : 2 : 1i
Bathing 4 : 3 :2 p 1
Loco-off-unit : 3 :1 2 : 1 i
Dressing 4 : 3i :2 2 i
Toileting 4 : i3 : 2 :
Transfer 4 : 3i : 2
Hygiene 4 i: 3 : 2 :
Loco-in-unit4: :2:1
Bowel 4 :3i 2: 1 : 10
Bladder : 3 2: 1 : 0
Bed-mobility 4 : 3 : 2 : 1 O
Eating 4 : 31 : 2 : 1 I
-4 -3 -2 -1 0 1 2 3
Person Ability Measure (logits)
Note:(":" indicates half-score point)
The mean and standard deviation is computed after removing persons with maximum or minimum scores.
Figure 2-4. General Keyform Structure of the Physical Functioning Items

















































69





SSamule Item (item calibration + error) Harder to Perform


Remory (2.20 + .13)






name (1.54 + .13)

(1.24+.14); Daily-Decisic
int season (1.15+.14)
emory (0.96+.14)
Irsing (0.86+.14)








Iderstood (-0.11+.09)

ty (-0.33+ .12); Understan




ion varies (-1.02+.15)

:ep/awareness (-1.19+.16);
acted (-1.43+ .17)


g (1.23+.08)






















;s (-1.29+.16)


(-1.68 + .18)


(-1.71 + .19)


Note: Each 'll' in the person column is 11 persons; each '.' is 1 to 10
M represents the mean of person ability measures (left) and item difficulty calibrati

Figure 2-5. Person Score Distribution Item Difficulty Hierarchy Map Cognition


Less Able



























.O I nnnnnnnnn LLLLLL
S2-1012I
PERSON ABILITY MINLS ITEM MEASME

(E) Understand-others, Daily-Decision-
Making, Make-self-understood


(B) Easily-distracted, Lethargy, Mental-
function varies, Speech-clarity


(A) Short-term memory, Long-term
memory, Recall-current season, Recall-
room, Recall-face/name, Recall-in-nursing
l.0 I I


(D) Disorganized-speech


(C) Restl es s, Altered-percepti on/awarenes s


Figure 2-6. Rating Scale Structure of the Cognition/Communication Items















S11

3 :1


1 o:
o 1




3:i 2:1:
2 : 1 : 0




2: 1 i


Person Ability Measure (logits)
Note: ( ": indicates half-score point)
The mean and standard deviation is computed after removing persons with maximum or minimum scores.
Figure 2-7. General Keyform Structure of the Cognition/Communication Items









CHAPTER 3
DIFFERENTIAL ITEM FUNCTIONING OF THE FUNCTIONAL INDEPENDENCE
MEASURE ACROSS DIFFERENT DIAGNOSTIC GROUPS

Introduction

Measuring functional status is important in both patient care and clinical research for

evaluating the net impact of rehabilitation intervention and healthcare services. Information

pertaining to functional status enables clinicians and therapists to plan interventions for their

patients [1 18]. Without functional status information, the effectiveness of these rehabilitation

interventions in fulfilling proposed goals toward independence is unknown [119, 120]. Currently,

functional status information is not only one of the most critical health data in rehabilitation

settings, but also directly related to resource utilization [121] and outcomes prediction [122,

123].

In inpatient rehabilitation, the Functional Independence Measure (FIMTM) is the most

widely used functional assessment [64]. Through the conjoint efforts of several maj or

organizations in rehabilitation, the FIM was developed as a central core measure of the Uniform

Data Set for Medical Rehabilitation (UDSMR) to document the functional level [65, 124]. To

date, more than 60% of comprehensive rehabilitation programs in the U.S. use the FIM [125].

Since 2002, the FIM has been added to the Inpatient Rehabilitation Facilities Patient Assessment

Instrument (IRF-PAI) for inpatient medical rehabilitation prospective payment system [126].

Based on age, functional status (provided by FIM), comorbidities (the presence of disorders or

diseases in addition to a primary diagnosis), and rehabilitation impairment categories, patients

are classified into discrete case-mix groups (CMGs). These classifications are used to determine

the financial resources Medicare provides for a particular patient' s care [127].

The FIM instrument was designed to assess functional independence and predict burden of

care. It consists of 18 items that are rated from a minimum score of 1 (total assistance) to a









maximum score of 7 (complete independence). Previous studies demonstrate that the FIM

represents two statistically and clinically distinct constructs with 13 items that define an

ADL/motor function domain and five items that define a cognition/communication domain [69,

115, 128-130]. A myriad of studies provide evidence that FIM has good psychometric properties

in terms of reliability and validity [57-60, 62]. Ottenbacher (1996) [64] performed a meta

analysis on the basis of 11 published studies and concluded that the FIM demonstrated sound

reliability across a wide variety of settings, raters, and patients (median interrater reliability and

test-retest reliability values both are .95). Stineman and her colleagues (1996) [129] found good

internal consistency in the motor scale (0.86-0.97) and the cognitive scale (0.86-0.95) across 20

impairment groups. Additionally, the total summed FIM measure has been shown to be

correlated with minutes of care therefore providing a measure of burden of care [66, 67, 131i,

132]. Granger et al. (1990) found a change of one point in FIM total score represented 3.8

minutes of care per day [66]. For detecting changes in performance during the hospital stay,

Hsueh et al. (2002) [133] found an effect size of 1.3 for FIM motor scale (effect size greater than

0.8 demonstrate a large responsiveness to detect change over time).

Several studies have examined the psychometric properties of the FIM using the Rasch

model [48, 75-78]. Stairs, which requires extensive strength and coordination of the whole body,

usually appears to be the most challenging item. Walking and transfer-to-tub are usually the next

most difficult items. Transferring activities are usually at average difficulty. Tasks that require

upper extremity function and mild muscle strength, such as eating and grooming are commonly

found to be the easiest. While bowel and bladder management involve an involuntary muscle

control component, these two items often misfit in the Rasch model. For cognitive items,

problem solving and memory function were found to be relatively more challenging than social









interaction, expression, and comprehension [41, 75, 134]. However, cognitive items have been

found to be easy for most of rehabilitation patients even at admission [77].

To compare outcomes, item characteristics should be consistent across different patient

groups. Granger and his colleagues (1993) [75] investigated the patterns of difficulty in

performing FIM items according to types of impairment. By plotting item difficulty calibrations

estimated by the Rasch model for each domain and inspecting the difference, they concluded that

"the patterns were consistent across impairment groups, although not identical" [75]. Using

similar analytical procedure, Heinemann et al (1993) [76] also demonstrated the similarity of

scaled measures across impairment groups for the FIM instrument. While these studies support

the consistency of item performance across different impairment group, the analytical procedure

was not based on statistical tests.

Differential item functioning (DIF) has been utilized in the health-related measurement

field to compare response patterns across gender, ethnicity, educational level, age, countries,

severity groups, and different diagnostic groups [135-141]. DIF analysis is a statistical methods

used to identify items that appear to be have difficulty levels that are dependent on membership

to a particular group (e.g., male/female, Caucasian/Black) after controlling for the ability levels

of the compared groups [142]. It is based on the rationale that persons at a given level of the

attribute being measured (e.g., obtain the same total scores) should have an equal probability of

passing an item regardless of their group membership. In 2005, Dallmeij er et al. [130] applied

DIF analysis of FIM in higher performing neurological patients. They found that almost all the

items showed significant DIF and suggested that adjustments may be required when FIM data is

compared between groups [130]. Nonetheless, Dallmeij er' s study is based a Dutch version of the

FIM. The results may not generalize to the original English version of the FIM.









The focus of this study is to investigate whether FIM items function similarly across

different impairment groups. To some extent, this is an extension of Dallmeij er' s study, but has

several methodological differences. In this study, the original English version of the FIM was

used. Instead of focusing on patient groups with different neurological disorders, three maj or

impairment groups in rehabilitation: stroke, amputation, and orthopedic impairment were

compared. Furthermore, while Dallmeij er and colleagues removed two items that misfit the

Rasch model, this study performed DIF analysis under two different scenarios. The DIF analysis

was conducted with 1) all items and 2) misfit items removed to explore whether misfit items

have an effect on DIF results. While Dallmeijer and colleagues collapsed the FIM 7-point rating

scale into 3-category scale, we chose to keep the original 7-point rating scale to investigate its

properties in the form that it is most frequently used. In addition, instead of using a trend line to

construct the 95% confidence interval, separate j oint measurement errors associated with each

item calibrations were used to improve accuracy [111]. Lastly, while previous studies merely

focus on the Rasch model (also called the one-parameter logistic item response theory model),

another DIF method based on a higher order two-parameter logistic model was used. The DIF

results based on different models were then compared.

Method

Participants

A secondary, retrospective analysis using Veteran Affairs (VA) data from the Functional

Status and Outcomes Database (FSOD) collected by the VA's Austin Automation Center (AAC)

during June 1, 2002 to May 31, 2003 were used for this study. This database contains all VA

rehabilitation records previously stored at the UDSMR. VA and non-VA researchers may access

the data stored in the FSOD with approval of Department of Physical Medicine and

Rehabilitation (PM&R) administrative office. See Appendix A for data request information.









This is also the data set used in the VA Rehabilitation Research and Development Proj ect,

03282R, Linking Measures across the Continuum of Care. The main purpose of that proj ect was

to develop crosswalk tables/algorithms that link scores and measures from the Functional

Independence Measure (FIMTM) and the Minimum Data Set (MDS). VA FIM and MDS data

reside in two databases at the VA' s Austin Automation Center (AAC). Data from both databases

(the Functional Status and Outcomes Database (FSOD) and the Resident Assessment Instrument

- Minimum Data Set (RAl-MDS)) were downloaded and merged on the basis of social security

numbers. In order to minimize the impact that change in a patient' s condition could have on FIM

and MDS scores, data were restricted to those that involved those subj ects whose FIM and MDS

assessment dates were within 5 days of each other. Data with any missing values in FIM and

MDS items were excluded. Individuals with stroke, amputation or orthopedic impairments were

selected for analysis. The dataset comprised a total sample of 654 records (302 stroke, 1 13

amputation, and 239 orthopedic impairment). The average age of this sample was 68 + 12 years,

96.6% were male, 74.2% were white, and 46.7% were married. The average difference between

FIM and MDS assessment dates was approximately 2.85 days. Table 2-1 provides the

demographic baseline characteristics and information on impairment categories. This study was

approved by the Institutional Review Board at the University of Florida and the VA

Subcommittee of Human Studies. Access to VA MDS data was approved by Department of

Veterans Affairs, Veterans Health Administration.

Differential item functioning based on the Rasch model

In this study, the DIF method based on Wright and Stone (1979) [143] was used to explore

whether items on the FIM perform similarly across three different diagnostic groups (individuals

with stroke, amputation, and orthopedic impairment). This method is based on the differences










between two parameters calibrated on the same item from two subpopulations of interest. Given

the pairs of item calibrations and the associated estimates of the standard error of estimate from

the Rasch model, a t-statistic can be constructed for each item using the formula:

d,, -d~,
t=
(s,2 + s12 )1/

where d,, and d,, are the item difficulty of item i in the calibration based on subpopulation 1 and


2, s,, is the standard error of estimate for d,,, and s,, is the standard error of estimate ford,,. A

graphical representation method equivalent to the t-statistic method was also proposed. After

obtaining initial item parameter calibrations and estimated errors associated with each item

calibration, paired item difficulty parameters from compared groups are cross-plotted. A pair of

95% confidence interval lines based on the conj oint error estimates is constructed. Points outside

the 95% confident interval are flagged as potential DIF items.

The motor and cognitive scales were analyzed separately. Rasch analysis (partial credit

model) using Winsteps program [version 3.16] [102] was used to obtain the FIM item difficulty

calibrations. Fit statistics were performed first to examine whether the response pattern fits the

Rasch measurement model. Fit statistics with a mean square (MNSQ) greater than 1.7 indicate

the response pattern of items are more unusual than the model predicted [107]. If the data fits the

Rasch model, Rasch analysis allows for the detection of differences in item difficulties between

groups. Some studies exclude misfit items from further analysis based on the rationale that items

have to fit the Rasch model to investigate DIF. However, removing items from a standardized

measurement instrument may damage the integrity of the instrument. To explore the influence of

misfit items on a DIF analysis, the DIF analytic procedure was performed using all items from









the motor and cognitive scale, the same procedures was performed with misfit items removed

from each scale.

Furthermore, to investigate the effects of the DIF items on estimated person ability measures,

person ability measures for the motor and cognitive scales were estimated for each group by the

Rasch model under the following scenarios. First, the person ability measures were estimated

using all items in the motor and cognitive scales. Second, the person ability measures were

estimated using all motor and cognitive items with misfit items removed. Third, the person

ability measures were estimated with all items adjusted for DIF, by splitting the items that

showed significant DIF into impairment-specific items. For example, if a walking item exhibited

significant DIF across all 3 diagnostic groups, data was encoded into 3 variables by their

impairments (walking-stroke, walking-amputation, and walking-orthoppedic). Correlation

coefficients between person ability measures under each scenario were computed to investigate

the impact of DIF items on person ability measures estimated by the Rasch model.

Differential Item Functioning Based on Two-Parameter Logistic IRT Model

The Rasch model has a strong assumption that item discrimination parameters are equal

across all items. This assumption makes Rasch model only allows to detect uniform DIF where

there is a relative advantage for one group over the other group through the entire ability range

(low to high ability level). Compared to the one-parameter Rasch model, the two-parameter

logistic (2PL) IRT model, a higher-order item response theory (IRT) model, allows item

discrimination parameters to vary across items. Non-uniform DIF thus can be detected, where

one group has a relative advantage over the other group at certain person ability range but has a

relative disadvantage at other person ability range.









Uniform and non-uniform DIF can be further illustrated via item characteristic curve

(ICC). The ICC curve illustrates the relationship between person ability (6) and the probability of

passing an item P(6) within the IRT model. In Figure 3-1, the x-axis is the person ability (6)

(logits is the measurement unit), and the y-axis is the probability of passing an item P(6). Figure

3-1 (A) provides an example of uniform DIF where a) persons at the same ability level (6) but

from different groups do not have equal opportunity of passing an item and b) one group has

relative advantage through the entire person ability range. The magnitude of DIF, thus, could be

expressed as a summation of differences between probabilities of passing an item from two

groups across the entire person ability range and can be defined mathematically as the integration

of the area/space between the two ICCs (i.e., signed area index = [P, (0) P2 (0)]dB) [142]. The

size of the area index value indicates the magnitude of DIF.

When two ICCs cross at some point on the person ability scale, non-uniform DIF indicates

a) persons at the same ability level (6) but from different groups do not have equal opportunity of

passing an item and b) one group has relative advantage at a certain person ability range but has

disadvantage at other person ability range (Figure 3-1 (B)). When non-uniform DIF occurs, the

signed area index (mentioned above) will confront a situation where positive and negative areas

in different regions of the graph canceling each other out to some extent. In this scenario, an

alternative method using the squared probability differences is useful


(unsigned area index = [IP, () P2 2 dO ) [142]. When the unsigned area index is much

higher than the signed area index, it indicates that non-uniform DIF occurs. The DIF method

based on computing the area between two ICCs, however, does not provide significant test.

Therefore, there is no clear-cut method of determining whether a particular item exhibits

significant DIF.









In this study, the two-parameter (2PL) logistic IRT model (graded response model) was

used to analyze the FIM items with the Multilog program [version 7.0] [144]. Again, the motor

and cognitive scales were analyzed separately. After obtaining item parameters from the 2PL

model, the parameters from separate runs were rescaled onto the same scale. This is due to the

property of indeterminacy of scale location and spread within the IRT model. To convert the

parameters for each item from scale I to scale J, for example, the item parameters on the two

scales are rescaled as follows:



J4 A'

b, = A b, + B,


u(al )
A=
u(a )'

B = u(b, ) Au(b, ),

where a~ and b~ are the item discrimination (a) and item difficult (b) parameters for item j

on scale J; az and b, are the item parameters for item j on scale I; u(al),u(ay), u(b ) ,

andu(b,) are the means of item discrimination parameter and item difficulty parameter on each

scale.

After the parameter transformation, the item characteristic curves can be constructed based

on item parameters obtained from each group. The DIF analysis was then performed by

calculating the area/space between two item characteristic curves (singed and unsigned area

index). With three impairment groups, three comparisons were conducted (stroke-amputation,

stroke-orthopedic, and amputation-orthopedic). Areas between two item characteristic curves

were summed across the-3 to +3 logits person ability range.












Subj ects

This sample comprised a total of 654 subjects, with 302 (46%) stroke, 113 (17%)

amputation, and 239 (37%) orthopedic impairment. Among individuals with stroke, the majority

had either right-brain involvement (n=140) or left-brain involvement (n=134). For individuals

with amputation, most of the subj ects had unilateral below the knee amputation (n=71) or

unilateral above the knee amputation (n=30). For subj ects with orthopedic impairment, most

subj ects involve lower extremity impairment (unilateral j oint replacement at knee (n=84);

unilateral joint replacement at hip (n=74); unilateral hip fracture (n=31)). Overall, 96.6% were

male, 74.2% were White, and 46.0% were married. The average FIM motor score was 54.3 and

the average FIM cognitive score was 27.7. In general, individuals with orthopedic impairment

had higher FIM-motor and cognitive scores than individuals with amputation and stroke. Ceiling

effects were found in FIM-cognition subscale across three impairment groups; 12.6% stroke,

37.5% amputation, and 45.2% orthopedic impairment received maximum scores in the cognitive

scale. Table 3-2 summarizes the demographics information and average FIM scores for this

sample.

DIF Analysis Based on Rasch Model

Table 3-3 presents the FIM-motor item difficulty calibrations for the entire sample and

each impairment group. The results of Rasch analysis showed 4 out of 13 motor items (bladder,

bowel, walk, and stairs) had high infit statistics (mean-square fit statistics (MNSQ) greater than

1.7) for at least one impairment group. Climbing stairs was the most challenging items on the

motor scale. Walking and transferring-to-tub items were the next most difficult items for this

sample. Several items such as bathing, toileting, dressing-lower-extremity, transferring-to-toilet

and transferring-to-chair were near the average item difficulty. Dressing-upper-extremity, bowel,


Results









bladder, and grooming were shown to be the easier items. Among all motor items, the eating

item was the easiest.

Table 3-4 lists the FIM-cognition item difficulty calibrations for the entire sample and each

impairment group. None FIM-cognition items had high fit statistics. Problem solving item was

the most challenging item among five cognitive items followed by the memory item.

Comprehension was at the average difficultly. Expression and social interaction items were the

easier items along this scale.

Figure 3-2 shows the DIF plots for both motor and cognitive items. Items demonstrated

significant DIF were labeled with item numbers as presented in Table 3-3 for the motor items

and Table 3-4 for cognitive items. For motor scale, 9 out of the 13 motor items were found to

have significant DIF when comparing stroke with amputation group. The amputation group had

more difficultly transferring and walking and the stroke group had more difficulty with eating,

grooming, dressing-upper-extremity, and bladder. When comparing the stroke and the orthopedic

impairment groups, 10 out of 13 motor items showed significant DIF. Similar to what had found

in stroke versus amputation comparison, items with higher item calibrations (more difficult

items) turned out to be more difficult for orthopedic group and items with lower item calibrations

(easier items) were more challenging for stroke group. When we compared item calibrations

between amputation and orthopedic impairment groups, only four items showed significant DIF.

The results revealed that bathing and dressing-lower-extremity were more challenging for

individuals with orthopedic impairment, while individual with amputation had more difficulty

climbing stairs and eating.

For the FIM-cognition items, 2 out of the 5 cognition items exhibited significant DIF.

Compared to the amputation group, the stroke group showed more difficultly with expression.










Compared to orthopedic impairment group, the stroke sample demonstrated more difficultly with

problem solving. When comparing item calibrations between the amputation and orthopedic

impairment groups, problem solving was shown to be more challenging for the orthopedic

impairment group and expression was relatively more difficult for amputation group.

DIF Analysis Removing Misfit Items

After the DIF analytic procedure was performed using all items from the motor and

cognitive scale, the same procedure was performed with misfit items removed from each scale.

Since there were no misfit items among the cognitive scale, this procedure only applied to the

motor scale. Therefore, four misfit items (item number "7" bladder, "8" bowel, "12" walk, and

"13" stairs) were removed. Figure 3-3 shows the DIF plots for the motor items after removing

misfit items.

In general, the DIF findings were similar to those found when including the misfit items.

When comparing amputation and stroke groups, individuals with amputation had more difficulty

with transferring task and individuals with stroke had more difficulty grooming and dressing

their upper extremity. When comparing orthopedic impairment and stroke groups, individuals

with orthopedic impairments had more difficulty transferring and dressing lower extremity and

individuals with stroke again had more difficulty with grooming and dressing their upper

extremity. The DIF results changed when comparing the amputation with orthopedic impairment

groups after removing misfit items. Three transfer items were more difficult for individuals with

amputations, while the dressing lower extremity item was more challenging for individuals with

orthopedic impairments.

The Impact of DIF Items on Person Ability Measures

To investigate the effects of DIF items on estimated person ability measures, person ability

measures estimated 1) using all items, 2) with misfit items removed, and 3) adjusting for effects










of DIF by splitting significant DIF items into impairment-specific items, were compared. For

motor scale items, the estimated person ability measures were highly correlated with each other.

The estimated person ability measures correlated at 0.97 between using all items and with misfit

items removed. The estimated person ability measures correlated at perfectly (r = 1.0) between

using all items with and without adjusting for DIF. Since the cognition scale did not have any

misfit items, person ability measures were compared between using all items and adjusting for

DIF. The estimated person ability measure was also found to have a perfect correlation

coefficient of 1.0.

DIF Analysis Based on 2PL IRT Model

Table 3-5 presents the item parameter calibrations for 13 FIM motor items based on two-

parameter logistic IRT model. Initially, each item contained one item discrimination parameter

and six item difficulty parameters (category threshold) due to a 7-point rating scale structure.

The category thresholds were then divided by 6 to obtain the average item difficulty parameter

(b) for easier comparison.

The results demonstrated that item discrimination parameters varied across items. Among

them, several items such as bath, dress-upper-extremity, dress-lower-extremity, toilet, and

transfer-to-toilet showed relatively higher discrimination than other motor items. Item difficulty

calibrations revealed a similar difficulty hierarchical order as those results shown in the Rasch

model. Stairs appeared to be the most challenging item, followed by the walking item. Transfer

activities were at average difficulty. Eating and grooming were found to be the least difficult

items.

Table 3-6 provides results of DIF analysis for FIM motor items including the signed area

index and unsigned area index. For the signed area index, positive values indicate the specific

item is more challenging for the second group comparing the first group and negative values









indicates the first group has more difficult performing such tasks. For purposes of comparison,

items that have greater than 0.4 for signed area index and 0.3 for unsigned area index are

considered as potential items showing differential item functioning

In comparing stroke versus amputation group, items that involved more upper extremity

function (e.g., eat, groom, and dress-upper-extremity) were found to be more difficult for stroke

and items that depends mostly on lower extremity functions (e.g., stair, walk, transfer-to-tub)

were found to be more difficult for subj ects with amputation. While comparing stroke with

orthopedic impairment group, stroke group had more difficulty in eating and bowel tasks and

orthopedic impairment group had more difficulty with several tasks requiring lower extremity

functions (e.g., dress-lower-extremity, transfer-to-tub, and walk). When comparing amputation

with orthopedic impairment group, two items (bath and dress-lower-extremity) were found to be

more difficult for subj ects with orthopedic impairment, and the other two items (bowel and

stairs) were found to be more challenging for subj ects with amputation. It should be noted that

the above-mentioned results were not consistent through the entire person ability range (i.e., non-

uniform DIF). If the relative advantage changes the direction toward the other group (i.e., when

two ICCs cross at some point along the person ability range), the signed index will reveal a

smaller value.

The results from unsigned area index were similar to that from the signed area index. For

most items, when the signed area index revealed larger values than other items, the unsigned area

index was also greater within the same comparison. The FIM-walk items (amputation versus

orthopedic) revealed to be a non-uniform DIF where the unsigned area index (0.32) was much

higher than the signed area index (-0.20) within the same comparison. Figure 3-4 presents the

ICC DIF plots of two FIM items (FIM-walking and FIM-stairs) as an example. Figure 3-4 (C)









showed the ICC plots for walking item (amputation versus orthopedic) in which the two ICCs

crossed at about 0 (logits) person ability range. At lower person ability level (< 0 logits), subj ects

with amputation had relative advantage of performing the walking task. At higher person ability

level (> 0 logits), however, subj ects with orthopedic impairment had advantages over the

amputation group.

Table 3-7 presents the item parameter calibrations for 5 FIM cognitive items. Again, the

category thresholds were divided by 6 to obtain the average item difficulty parameter (b). Similar

to the motor items, the results demonstrated that item discrimination parameters varied across

items. For cognitive items, problem solving and memory function were found to be relatively

more discriminating than social interaction, expression, and comprehension. Table 3-8 provides

results of DIF analysis for FIM cognitive items including the signed area index and unsigned

area index. When comparing stroke with amputation group, expression was found to be more

challenging to the stroke and problem solving was more difficult for subjects with amputation.

Expression was also found to be more challenging when comparing stroke to orthopedic

impairment group. When comparing amputation with orthopedic impairment group, no items

revealed potential DIF. The unsigned area index revealed a pattern similar to the signed index.

Discussion

This study used DIF analysis to investigate whether items in the FIM instrument function

similarly across three maj or impairment groups in rehabilitation (stroke, amputation, and

orthopedic impairment). If items exhibited significant DIF across groups, adjusting for

differential item functioning may be required when data is compared between groups or when

used in a pooled analysis [130]. It has also been stated that "If items with DIF are retained in test

equating, they not only increase the errors of test equating or parameter estimates, but also could

cause bias towards some examinees. [20]" Therefore, some investigators suggest that DIF items









be removed when conducting test equating to avoid potential biases that might result against a

particular subpopulation [20].

Dallmeij er and colleagues' study of DIF in the Dutch version of the FIM was based on a

DIF method (b-difference) using Rasch (rating scale) model. Similar to their results, our DIF

analysis showed several items demonstrated significant DIF. In Dallmeij er' s study, 4 of 11 motor

items and 4 of 5 cognition items showed statistically significant DIF across stroke, multiple

sclerosis, and traumatic brain injury. In our study, 4 to 9 of 13 motor items and 2 of 5 cognition

items exhibited significant DIF. Removing misfit items revealed slightly different DIF results in

certain groups. However, removing misfit items or adjusting for DIF had little impact on overall

person ability measures (r > 0.97). Dallmeij er and colleagues (2005) also had similar findings in

regards to correlations between the adjusted and unadjusted person ability measures under the

Rasch model (r = 0.99).

DIF results seemed to reflect the characteristics of the impairment typically found for each

diagnostic group. For example, tasks which involved upper extremity function (such as groom

and dress-upper-extremity) were more challenging for individuals with stroke (possibly due to

the result of unilateral paresis of upper extremity limb). On the other hand, since most

amputation and orthopedic impairment in this sample involved lower extremity impairment (e.g.,

hip and knee j oint replacement, lower extremity amputation, or hip fracture), individuals with

amputation or orthopedic impairment had more difficulty with tasks that involved lower

extremity function (such as transfer and dress-lower-extremity). Some of the findings were

unexpected.

Tennant et al. (2004) [114] used DIF analysis to investigate the item difficulty hierarchical

order of FIM motor scale items with respect to age, gender, and country (translated FIM). They










found that 7 out of 9 items having significant DIF by country, but no items were found to have

DIF by gender or age. The item difficulty hierarchical order in Dallmeij er' s Dutch study also

showed a slightly different pattern than previous studies using the FIM in the original English

version [48, 75-78]. For example, their results showed the eating item was at the average item

difficulty and was more challenging than transfer, toilet, dress-upper-extremity, and groom

items. Another inconsistency between English and Dutch studies is that the Dutch translated

problem-solving item was not consistently the most difficult item. For individuals with multiple

sclerosis, the problem solving was shown to be the easiest item.

In general, DIF results were consistent across different methods. Individuals with stroke

consistently had more difficulty grooming and dressing upper extremity while the other two

groups (amputation and orthopedic impairment group) had more difficulty with several tasks

involving lower extremities (e.g., dress-lower-extremity, transfer-to-tub, and walk).

There were some differences found across the different IRT and DIF methods. The b-

difference DIF method based on the Rasch model assumed that item discrimination parameters

are equal across different test items. In this study, the two-parameter model showed items had

different item discrimination. When items exhibited similar discrimination across different

impairment groups (e.g., bathing item showed relatively high discrimination across different

impairment group: stroke (a = 3.59); amputation (a = 3.00), orthopedic (a = 3.46)), uniform DIF

method may be adequate. However, when items exhibited dissimilar discrimination across

different impairment groups (e.g., walking item showed relatively high discrimination for stroke

(a = 1.62) and orthopedic (a = 1.99) groups, but relatively low discrimination for amputation

group (a = 0.92)), non-uniform DIF may occur, a finding that is not possible when using the

Rasch model.









DIF results may also depend on how group membership is defined. Some variables are

clearly defined (such as gender), while other variables are more subj ectively defined (such as age

and severity). DIF results may be dependent on how a particular variable is defined. In this

study, we classified patients into three impairment groups. The results may show different

patterns when patients are divided into more specific diagnostic groups (e.g., when dividing

stroke into left and right body involvement or dividing orthopedic impairment into upper and

lower limb involvement). In future studies, more diverse and comprehensive impairment groups

should be further examined.

In conclusion, the purpose of this study was to investigate whether FIM motor and

cognitive items function similarly across different impairment groups (stroke, amputation, and

orthopedic impairment). These inconsistencies in item calibrations led to the development of

separate crosswalk conversion tables for each impairment group. Removing misfit items led to a

similar DIF results. However, removing misfit items or adjusting for DIF seemed to have little

effect on overall person ability measures estimated by the Rasch model. The 2PL logistic IRT

model showed that item discrimination parameters varied across FIM items. Although the DIF

results based on different models showed a slightly different set of items showing significant

DIF, items that exhibited significant DIF appeared to be connected to specific characteristics of

the impairment typically found for each diagnostic group. For example, individuals with stroke

tended to have more difficulty with tasks that involved more upper extremity functions (e.g.,

grooming, and dressing-upper-extremity) Since maj ority of the amputation and orthopedic

groups involved lower extremity impairment, these individuals tended to have more difficulty

with tasks that depend on lower extremity strength and functions (e.g., stair, walk, transfer-to-

tub). For cognitive items, two items (expression and problem solving) consistently showed










significant DIF across three impairment groups. While individuals with stroke showed greater

difficulty in expression item, than amputation and orthopedic groups, the latter two groups did

not show cognitive DIF. These inconsistencies in item difficulty calibrations led to the

development of separate crosswalk conversion tables for each impairment group.









Table 3-1. FIM Instrument
The Functional Independence Measure (FIM)


Motor Items
Eating
Grooming
Bathing
Dressing-Upper Body
Dressing-Lower Body
Toileting
Bladder Management
Bowel Management
Transfer to B ed/Chair/Wheelchair
Transfer to Toilet
Transfer to Tub/Shower
Walk/Wheelchair
Stairs


Cognition Items
Comprehension
Expression
Social Interaction
Problem Solving
Memory


Rating Scale
7 Complete Independence (Timely, Safely)
6 Modified Dependence
5 Supervision (Subject=100%)
4 Minimum Assist (Subj ect=75%+)
3 Moderate Assist (Subj ect=50%+)
2 Maximal Assist (Subj ect=25%+)
1 Total Assist (Subject=1ess than 25%)









Table 3-2. Participants Descriptive Statistics for Each Diagnostic Group
Stroke Amputation Orthopedic All
Characteri sti c (N=3 02) (N= 1 13) (N=239) (N=654)
Age (year)
Mean (a SD) 69.40 (12.0) 67.70 (11.0) 66.36 (12.2) 67.99 (12.0)
Range 37-100 46-90 20-93 20-100
Males (%) 97.7% 99.1% 93.3% 96.6%
Race, n (%)
White 211 (69.9 %) 75 (66.4 %) 199 (83.3 %) 485 (74.2 %)
Black 67 (22.2 %) 24 (21.2 %) 29 (12.1 %) 120 (18.3 %)
Hispanic 15 (5.0 %) 4 (3.5 %) 7 (2.9 %) 26 ( 4.0 %)

FIM-motor
Mean (+SD) 46.77 (A 24.6) 53.14 (A 21.6) 64.44 (18.2) 54.33 (123.4)
Range 13-91 13-86 15-89 13-91
Median 44.00 56.00 67.00 57.00
Maximal Score N (%) 4 (1.3%) 0 (0%) 0 (0%) 4 (1.3%)

FIM-cognition
Mean (+SD) 23.29 (A 8.8) 29.7 (A 6.9) 32.16 (A 4.9) 27.72 (A 8.3)
Range 3-35 5-35 7-35 3-35
Median 25.00 32.50 34.00 31.00
Maximal Score N (%) 37 (12.6%) 45 (37.5%) 108 (45.2%) 190 (29.1%)



































Table 3-4. Item Difficulty Calibrations for FIM Cognition Items
Cognition Entire Sample Stroke Amputation Ortho
# Item Item Difficulty Infit Item Difficulty Infit Item Difficulty Infit Item Difficulty Infit
& Error & Error & Error & Error
1 Comprehension 0.15 & 0.07 0.99 0.05 & 0.08 0.91 -0.14 & 0.17 1.20 0.14 & 0.15 1.05
2 Expression -0.55 & 0.06 1.12 -0.33 & 0.07 1.23 -0.88 & 0.19 0.88 -0.31 & 0.16 0.64
3 Social Interaction -0.64 & 0.06 1.10 -0.86 & 0.08 0.97 -0.50 + 0.16 1.13 -0.71 & 0.15 1.44
4 Problem Solving 0.72 & 0.06 0.74 0.81 & 0.08 0.87 0.99 & 0.15 0.64 0.22 & 0.12 0.58
5 Memory 0.33 & 0.06 0.86 0.34 & 0.08 0.88 0.52 & 0.15 0.65 0.67 & 0.13 1.14


Table 3-3. Difficulty Calibrations for FIM Motor Items


Motor
# Item


Entire Sample
Item Difficulty


Stroke
Item Difficulty
& Error
-1.20 + 0.06
-0.53 & 0.06
0.30 + 0.06
-0.22 & 0.06
0.21 & 0.06
0.24 & 0.06
-0.33 & 0.06
-0.47 & 0.06
-0.27 & 0.06
-0.04 & 0.06
0.29 & 0.06
0.45 & 0.06
1.57 & 0.07


Amputation
Item Difficulty
& Error
-1.60 + 0. 11
-0.95 & 0.09
0.13 & 0.08
-0.62 & 0.08
-0.03 & 0.08
0.03 & 0.08
-0.65 & 0.08
-0.70 + 0.08
0.05 & 0.08
0.30 + 0.08
0.80 + 0.08
0.76 & 0.08
2.47 & 0.13


Ortho
Item Difficulty
& Error
-2.22 & 0. 11
-1.00 + 0.08
0.50 + 0.06
-0.671 0.07
0.671 0.06
0.141 0.06
-0.551 0.07
-0.901 0.08
-0.011 0.06
0.261 0.06
0.821 0.06
0.981 0.06
1.981 0.07


Init

1.38
0.88
0.71
0.81
0.77
0.59
1.39
1.14
0.77
0.74
1.32
1.89
1.71


Infit

1.37
0.82
0.61
0.61
0.57
0.66
1.86
1.66
0.74
0.60
1.02
1.71
1.74


Init

1.38
0.84
0.85
0.76
0.76
0.58
1.56
1.28
0.66
0.69
1.04
2.47
1.58


Infit

1.36
1.02
0.64
1.32
0.68
0.55
2.31
1.72
0.56
0.62
1.40
1.50
1.22


& Error
-1.58 & 0.05
-0.90 + 0.04
0.33 & 0.04
-0.58 & 0.04
0.27 & 0.04
0.08 & 0.04
-0.48 & 0.03
-0.62 & 0.04
-0.19 & 0.04
0.26 & 0.04
0.73 & 0.04
0.83 & 0.04
1.84 & 0.04


Eat
Groom
Bath
Dress-up
Dress-low
Toilet
Bladder
Bowel
Transfer-chair
Transfer-toilet
Transfer-tub
Walk
Stairs











Table 3-5. Item Parameter Calibrations for FIM Motor Items
Item Discrimination Average Item Difficulty
Items Parameter (a) Parameter(b
Stroke Ampuaton Ortho Stroke Amputation Ortho
Eat 1.76 2.22 1.16 -1.59 -2.11 -2.81
Groom 2.68 2.50 2.68 -1.01 -1.53 -1.19
Bath 3.59 3.00 3.46 -0.35 -0.53 -0.12
Dress-up 3.71 3.51 2.70 -0.76 -1.16 -1.01
Dress-low 3.70 3.87 3.29 -0.42 -0.66 0.04
Toilet 3.47 4.33 4.28 -0.41 -0.61 -0.32
Bladder 1.83 1.89 1.63 -0.86 -1.15 -0.96
Bowel 2.02 1.96 1.03 -0.96 -1.20 -1.85
Transfer-chair 2.60 2.82 3.90 -0.76 -0.57 -0.50
Transfer-toilet 3.03 3.18 4.27 -0.56 -0.34 -0.24
Transfer-tub 2.48 2.11 2.76 -0.32 0.11 0.13
Walk 1.62 0.92 1.99 -0.09 0.63 0.35
Stairs 1.98 2.14 1.31 0.63 1.60 0.99



Table 3-6. DIF Analysis for FIM Motor Items
Signed Area Unsigned Area
Stroke vs Stroke vs Amput. Stroke vs Stroke vs Amput.
Items Amput. Ortho vs Ortho Amput. Ortho vs Ortho
Eat -0.51 -0.76 -0.25 0.30 0.51 0.29
Groom -0.51 -0.18 0.33 0.34 0.12 0.22
Bath -0.18 0.23 0.41 0.14 0.18 0.30
Dress-up -0.40 -0.25 0.15 0.31 0.20 0.13
Dress-low -0.24 0.46 0.70 0.19 0.34 0.52
Toilet -0.20 0.09 0.29 0.17 0.09 0.24
Bladder -0.29 -0.09 0.20 0.16 0.07 0.12
Bowel -0.23 -0.65 -0.41 0.14 0.46 0.35
Transfer-chair 0.19 0.26 0.07 0.13 0.21 0.10
Transfer-toilet 0.22 0.32 0.10 0.16 0.26 0.11
Transfer-tub 0.43 0.45 0.02 0.27 0.30 0.08
Walk 0.64 0.44 -0.20 0.38 0.25 0.32
Stairs 0.95 0.32 -0.64 0.55 0.23 0.36
Note :
Positive values indicated that item is more challenging to the second group
Negative values indicated that item is more challenging to the first group











Table 3-7. Item Parameter Calibrations for FIM Cognitive Items
Item Discrimination Average Item Difficulty Parameter
Parameter (a) b
Stroke Amputation Ortho Stroke Amputation Ortho
Comprehension 4.55 2.11 3.54 -1.70 -1.96 -1.96
Expression 3.59 2.52 5.92 -1.56 -2.17 -1.94
Social Interaction 4.49 2.60 3.03 -1.71 -1.55 -1.53
Problem Solving 5.40 10.00 6.42 -1.24 -0.83 -1.00
Memory 5.57 6.36 4.69 -1.34 -1.04 -1.12


Table 3-8. Item Parameter Calibrations for FIM Cognitive Items
Signed area Unsigned area
Stroke vs Stroke Amput. Stroke vs Stroke Amput.
Amput. vs Ortho vs Ortho Amput. vs Ortho vs Ortho
Comprehension -0.21 -0.25 -0.04 0.26 0.22 0.14
Expression -0.57 -0.38 0.18 0.42 0.34 0.26
Social Interaction 0.17 0.18 0.02 0.18 0.17 0.04
Problem Solving 0.41 0.24 -0.17 0.43 0.24 0.20
Memory 0.30 0.22 -0.08 0.29 0.20 0.10












(A) Uniform DIF


.4
C' '


Groupl.'


P,(0)


-3 -2 -1 0 1

Pe rs on Ability (0) (log its)


2 3


(B) Non-uniform DIF


Groupl.


-3 -2 -1 0 1

Pe rs on Ability (0) (log its)


2 3


Figure 3-1. Examples of DIF A) Uniform DIF and B) Non-uniform DIF





-2 -1 0 1
Stroke (Logits)




















-2 -1 0 1
Stroke (Logits)


-2 -1 0 1 2 3

Stroke (Logits)



13

12
51
10


'~~ 4


~1


-3 -2 -1 0 1 2 3
Stroke (Logits)


A. ADL/Motor Items


B. Cognition/Communication Items


2




1






2 1


-L


1


-s












3

2


p






-2

-3


11 12


2-






11



S-3 2 -1 0 1



Amputation (Logits)


0 o





-2


4


-2 -1 0
Amputation (Logits)


1 2


2 3


Figure 3-2. Differential item functioning plots for A) Motor and B) Cognition items across
differential impairment groups (Stroke, Amputation, and Orthopedic Impairment)


























































10

9


ADL/Motor Items


3


e
o O
p

C
E -1


-1 0 1 2


Stroke (Logits)


2


1






-1


-2


-1 0 1


Stroke (Logits)


-3 -2 -1 0

Amputation(Logits)


1 2


Note :
Misfit items in the motor scale: bladder, bowel, walk, and stair
Misfit items in the cognition scale: none
Figure 3-3. Differential item functioning plots for A) Motor and B) Cognition items across
differential impairment groups after removing misfit items


















"FIM-walking" item









Stroke *'



.' Orhto


"FIM-stair" item


09
S08
~07
S06
$05


S03

01


09
608
~07
S06



S03
S02

01


101
Person Ability (9) (logits)


2 3


-3 -2 -1 0 1 2
Person Ability (6) (logits)


09
S08
u,07
S06
V~05
S04
~03

02


09
608
~07
u806


S04
~03
S02

01


-3 -2 -1 0 1
Person Ability (9) (logits)


-3 -2 -1 0 1 2
Person Ability (6) (logits)


09
S08
~07
S06
05
S04
~03

02


09
S08
~07
S06


S04
~03
S02

01


Ortho


-3 -2 -1 0 1
Person Ability (9) (logits)


-3 -2 -1 0 1
Person Ability (6) (logits)


2 3


Figure 3-4. Differential item functioning plots for FIM-walking

F) iteas based on the ICC I)IF method


(A, B, C) and FIM-stair (D, E,