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Controlling for biases from measurement errors in health outcomes research: A structural equation modeling approach
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Controlling for biases from measurement errors in health outcomes research: A structural equation modeling approach
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INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. U M I films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send U M I a complete manuscript and there are missing pages, these w ill be noted. Also, if unauthorized copyright material had to be removed, a note w ill indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with smalt overlaps. Photographs included in the original manuscript have been reproduced xerographicaliy in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact U M I directly to order. ProQuest Information and Learning 300 North Zeeb Road. Ann Arbor. M l 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONTROLLING FOR BIASES FROM MEASUREMENT ERRORS IN HEALTH OUTCOMES RESEARCH: A STRUCTURAL EQUATION MODELING APPROACH by Jinhai Shi A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHARMACEUTICAL ECONOMICS AND POLICY) August 2001 Copyright 2001 Jinhai Shi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number 3054804 Copyright 2001 by Shi, Jinhai All rights reserved. ____ ________ (f t UMI UM I Microform 3054804 Copyright 2002 by ProQuest Information and Learning Company. A il rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, M l 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA T he G ra d u a te School U n iv ersity P ark LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, w ritten b y JIN H A I SH I Under th e direction o f ku L . D issertation Com m ittee, and approved b y a ll its m em bers, has been presen ted to and accepted b y The Graduate School in p a rtia l fu lfillm en t o f requirem ents fo r th e degree o f DOCTOR OF PHILOSOPHY Dean o f Graduate Studies D ate August 7 , 2001________ DISSERTATION COMMi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication This dissertation is dedicated to my parents, Pimu Shi and Yuehua Lei, To my wife, Jie Meng, and my daughters, Helen and Catherine Shi For their strength, spirit and love. I am deeply sorry that it only seems possible to write the dissertation during family time: evening and weekends. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements The dissertation is not my lonely venture but is a joint effort. I have been fortunate to be a student and research assistant under the supervision of Professor Jeffrey McCombs. He is not only my academic advisor but also my best friend. I am indebted to Professors Joel W. Hay, Michael Nichol, Chen Hsiao and Chi-ping Chou for their encouragement and valuable advocacy to my proposal and dissertation. I greatly benefited from this research experience. It is a great asset to my whole life. Thanks are also due to Drs. Marisue Cody and Joseph Parker for their data preparation and many insightful discussions. I am very grateful for the enthusiastic support of my colleagues in Amgen Inc., Drs. Haim Erder, Michael Woolley, Joel Kallich, and John Lu. I also want to offer a special thanks to Drs. Mark Danes, Jon Ford, John Issit and Rima Tannous for their valuable comments and tremendous efforts in my English writing. At the top of the list of persons I am indebted to, are my mother, Yuehua Lei and my wife Jie Meng. Their understanding, support and love, keep me smiling throughout. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Dedication................ U Acknowledgements iii Listof Tables...........................................................................................................v Abstract................... vi Chapter 1. Introduction............m .....................................................................l Chapter 2. Literature Review........................................................................4 2.1 Impact of Measurement Error on Linear Regression Model.......................... 6 2.2 Measurement of Perceived Health Status.........................................................9 Chapter 3. Methodology...............................................................................15 3.1 D ata.................................................................................................................. 15 3.2 Measurement of Health Status and Health Outcomes................................... 17 3.3 Analytic Strategy............................................................................................. 19 3.4 Model Specification........................................................................................23 3.4.1 Classical Linear Regression Models......................................................23 Classical Linear Regression Models for Health Care Costs........................... 23 Classical Linear Regression Models for a Single Scale of RAND SF-36.......23 3.4.2 Structural Equation Models with a Latent Health Variable.................25 SEMs for an Observed Single Dependent Variable (SEMSI)............................ 26 SEMSI for Health Care Costs........................................................................26 SEMSI for a Single Scale of the RAND SF-36..............................................29 SEM for Latent Health Outcomes with Observed Multiple Indicators (SEMMI)30 SEMMI with Multiple Scales of RAND SF-36..............................................30 SEM for Both Health Care Costs and Latent Health Outcomes (SEMHCHOMI)31 SEMHCHOMI with Multiple Scales of RAND SF-36..................................32 3.5 Model Evaluation and Estimation.................................................................. 33 Chapter 4. Results............................................................................................36 4.1 Descriptive Statistics.......................................................................................37 4.2 Measurement Model....................................................................................... .40 4.3 Structural Models............................................................................................45 SEMs for an Observed Single Dependent Variable........................................46 SEM for Latent Health Outcomes with Observed Multiple Indicators..........51 SEM for both Health Care Costs and Latent Health Outcomes..................... 52 4.4 Effects of the Interventions and the Health Status........................................ 53 4.5 Model Comparison..........................................................................................57 Chapter 5. Discussion»....................M ..........................................M M ..............M ....66 Bibliography..........................................................................................................76 Appendices...............„........«.....m ........................................................................83 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables Table 1. Correlation Coefficients of the Scores of RAND SF-36 Scales.............................39 Table 2. Goodness-of-Fit Indexes for Measurement Models.............................................. 41 Table 3. Validity & Reliability of the Latent Health with Eight SF-36 Scales.................... 44 Table 4. Goodness-of-Fit Indexes for Structural Equation Models......................................48 Table S. Estimations of Measurement Portions of Structural Equation Models...................49 Table 6. Estimations of Treatment and Health Status of Structural Equation Models..........SS Table 7. Expected Cross-Validation Index (ECVI) of CLRMs and SEMs.......................... 58 Table 8 Comparison of OLS and SEM Models on Health Costs and Health Outcomes.......61 Table 9. Correlation Coefficients Between SEM Health Status Index (SEMHSI) and Other General Health Status Measures................................................................................ 64 Table 10. Mean Scores in SEM Health Status Index (SEMHSI) and Others General Health Status Measures Between the Cardiovascular and Anxiety Drug Users..................... 65 Table 11. Mean Scores in SEM Health Status Index (SEMHSI).Between Drug Users and Non-Users.................................................................................................................65 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract Controlling for Biases from Measurement Errors in Health Outcomes Research: A Structural Equation Modeling Approach By Jinhai Shi Measurement error in an independent variable may lead to attenuated estimate of its effect on dependent variable and may contaminate estimates for other covariates in conventional linear regression models (CLRM). However, if multiple variables are measured with errors, the direction and magnitude of these biases are difficult to determine theoretically. Measurement error is a serious problem in health outcomes research as health status is a latent variable that can only be measured with error using proxy variable. Few studies have addressed the potential biases due to the error in the measurement of health status in a linear regression analysis on health outcomes. This study empirically evaluated the validity of CLRMs for health outcomes research by using structural equation modeling (SEM) to re-evaluate the estimated effects of the pharmaceutical consultations on both health outcomes and costs reported previously. In the SEMs, a patient’s perceived health status at a given time point is modeled as a latent variable measured with the multiple scales of the RAND SF-36 in order to vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. eliminate the bias stemming from the measurement errors in the scales. The SEMs were estimated using data from the Kaiser/USC pharmacist consultation study. The latent health construct and its SEMs for health outcomes and costs are empirically supported by the KP/USC data. SEM estimations of the latent health construct were all statistically significant with expected signs in both the measurement and the structural models. As predicted, CLRM estimates for the SF-36 scales were attenuated by their measurement errors. However, there is no strong evidence that the CLRM estimations of pharmacist consultation effect were contaminated by the measurement errors, and that the simultaneity between health outcomes and costs leads to biased estimates. The results support the hypothesis that the measurement error in the multiple scales of the SF-36 may leads to biased estimation and invalid inference. Careful study design can eliminate the contamination of treatment effect estimates due to errors in measuring health status. Moreover, SEM methods can be used to control both attenuation and contamination biases. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Controlling for Biases from Measurement Errors in Health Outcomes Research: A Structural Equation Modeling Approach By Jinhai Shi Chapter 1. Introduction This study attempted to empirically evaluate the validity of the linear regression model for health outcomes research by using structural equation modeling (SEM) to eliminate the potential bias from measurement errors and simultaneity between health outcomes and health care costs. The patient’s perceived health status or health-related quality of life (HRQOL) at a given time point is modeled as a latent variable measured with the multiple scales of the RAND SF-36. A set of structural equation models (SEM) with the latent health construct was used to examine the consequences of the measurement errors of the perceived health status (or HRQOL) in a linear regression model for health outcomes or health care costs. The estimations of the SEM approach are compared to those of classical linear regression model (CLRM) using data from the Kaiser/USC pharmacist consultation research project (the Kaiser/USC study) (McCombs 1995,1998). The effects of alternative pharmacist consultation models on the patient health outcomes and health costs are re-estimated by using the SEMs. l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Linear regression models are widely used in the field of health outcomes research, hi a linear regression model, measurement error in an independent variable can cause biased estimation and questionable hypothesis testing. Specifically, the linear regression estimation of a covariate can be attenuated as a result of its measurement error (attenuation). Moreover, measurement error can also contaminate the estimates for other covariates (resonation). For instance, the estimation of treatment effects can be biased by the measurement errors of other covariates, such as health status measures. However, the direction and magnitude of both attenuation and resonation biases are difficult to determine with theoretical reasoning. Patient-reported health status or health-related quality of life is a very important measure of health outcomes, but it is an unobserved latent variable that can only be measured by a variety of proxies. There are few published studies that document the potential bias caused by measurement errors in the multiple scales of an instrument used to measure patient-reported health status or HRQOL, such as the RAND Medical Outcomes Study Short Form 36 (RAND SF-36). Three contributions to the research literature are derived from this dissertation study. First, this study documents the extent of multiple variable measurement errors in the RAND SF-36 HRQOL instrument. Second, this research examines how simultaneity between health outcomes and health care costs, affect the estimations of treatment and health status at the baseline. Finally the study re-estimates the effects of 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pharmacist consultation models and health status at baseline on health outcomes and health care costs. These results will provide insight into whether or not the patient-reported health status or HRQOL (such as the RAND SF-36) is an adequate health risk adjuster for health policy analyses. In addition, this research tested the validity of structural equation models with the latent health construct as a framework for health outcomes research, especially where measurement error, simultaneity and an objective health index will be the concerns or interests of the study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2. Literature Review Assessing outcomes from a health care intervention is crucial to the development of medical science and health care delivery. In such studies, the most important and challenging work is to separate the effects of the health care intervention under study from other confounding factors. The two methods available to control confounding are an experimental study design and multivariate statistical method. In a randomized clinical trial, members of the treatment and control groups are identical except for their treatment status. The measurement of the treatment effect is very straightforward and requires relatively simple statistical methods. More elaborate statistical method are required when carefully experimental research designs are not possible due to concerns for feasibility and costs. In these situations, observational and quasi-experimental study designs are most common study designs used in health care studies. The linear regression model is the most common statistical method used by health care researchers to control those confounding factors, which cannot be balanced a priori across treatment groups. An individual’s health status is a very important explanation variable in any health outcomes study. Health status is an unobservable variable and can only be measured using a variety of proxies, which are subject to measurement errors. Furthermore, the 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurement error in a linear regression model may lead to inconsistent estimation of the relationship between variables and results in potential invalid inference. As the population ages and chronic disease becomes the dominant form of illness, patients’ perceived health status and their health-related quality of life (HRQOL) become major concerns of health care research (Rothenberg 1990). A variety of self- reported health measurements have been developed to measure multiple dimensions of health status (such as physical function, mental health, and social role). As a generic instrument of health-related quality of life, the RAND Medical Outcomes Study Short Form 36 (RAND SF-36) is widely used in health services research to monitor the population health status and to evaluate the impact of alternative treatments and health policies. Although it has been widely acknowledged that the measures of health status are far from perfect, very few studies have addressed the issue of potential biases caused by the measurement errors of health status when used as an independent variable in a linear regression analysis of health outcomes or health care costs. In this Chapter, we will review the previous studies regarding the impact of measurement error on the classical linear regression model, the measurements of perceived health status, and potential problems associated with the measurements of health status. 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.1 Impact of Measurement Error in a Linear Regression Model It is well known that measurement error may lead to biased estimation and questionable hypothesis testing. The regression estimated of the effects of a covariate can be attenuated by its measurement error (attenuation). Specifically, the ordinary linear square (OLS) estimation of the impact of an independent variable with measurement error is asymptotically biased toward zero and thus underestimates the effect of the independent variable on the dependent variable (Levi 1973, Bollen 1989, Plummer 1993). Moreover, measurement errors can also contaminate the estimations of the effect of other covariates that are not subject to measurement errors (resonation). The OLS estimation of the impacts of an explanatory variables that are not subject to measurement error are likely to be inconsistent, if this covariate is correlated with the covariate with measurement error or its effect is equal to zero (Levi 1973). For instance, the estimation of treatment effects may be biased by the measurement errors in other covariates, such as health status (Greenland 1980, Carroll 1989). However, the direction and magnitude of those biases are difficult to determine theoretically (Levi 1973, Garber & Klepper, 1980, Greene 1992) (Appendix I). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Generally, if only one explanatory variable (X2) is subject to measurement error, the attenuation and resonation depend on three factors: (1) the strength of the effect of the explanatory variable on the dependent variable (fc); (2) the magnitude of the measurement error (5U 2 ); and (3) the association between the explanatory variables (X2) and other study variables of interest (Xi) (Judge 1979, Bollen 1989, Maddala 1992, Greene 1992). Morgan (1987) and Carroll (1989) demonstrated that in a randomized study an OLS model could yield valid estimation and inference for the treatment effect when measurement error in another explanatory variable was ignored. However, measurement error resulted in a decrease in the power of the hypothesis tests for the treatment effect. Logistic and probit regression models also results in an attenuated estimation of treatment effect. In a non-randomized and unbalanced study, the OLS estimation and inference could be invalidated by measurement error. The bias of treatment effect estimation resulting from measurement error depends on the degree of imbalance (the difference between the means of the treatment and control groups), the measurement error, and the strength of the covariates measured with errors (Morgan 1987, Carroll 1989). Marshall and Hastrup (1996) examined a simple model in which a confounder and null study variable were both measured with error in three situations: (1) both the 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. outcomes and independent variables were continuous and normally distributed; (2) the outcome was dichotomous and the independent variables are continuous and normally distributed; and (3) both outcome and independent variables were binary. They demonstrated that given a strong true confounding (i.e., a single standard deviation increase in the confounder was associated with 0.8 standard deviation increase in the outcome) and a substantially true correlation between the confounder and the null study variable (e.g., -0.5), a measurement error amounting to 40% of observed variance in a continuous confounder could cause a statistically magnificent estimated impact for the null study variable. In the case of a dichotomous outcome variable, While a measurement error of 15% misclassification could lead the null study variable to appear to alter risk by as much as 50% (Marshall and Hastrup 1996). Yanez et.al. (1998) reported that in a model to estimate change in health outcomes, if the outcome variable (blood vessel wall thickness) is subject to measurement error and the baseline value of the outcome variable is included as a covariate, then the estimated effects of other explanatory variables are also biased (Yanez et.al. 1998). If more than one variable is measured with error, the potential inconsistency of the classical linear regression model becomes more complex. The coefficient of a mis- measured explanatory variable is not always attenuated, but at least one estimated 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coefficient would be attenuated. The attenuation can be reduced by improving the measurement of the explanatory variable. The absolute bias in the coefficient of a correctly measured independent variable is not necessarily improved by reducing the measurement error in a mis-measured regressor or by including one or more proxy variables (Garber and Klepper 1980). However, little empirical evidence is available to document the validity of the classical linear regression model where there are multiple variables subject to measurement error. 2.2 Measurement of Perceived Health Status Though the concepts of health, health status and health outcomes have played an important role in health service research, there is no clear consensus concerning their conceptualization and measurement. The most widely accepted definition of health was proposed by the World Health Organization in 1958. Health is defined as a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity (World Health Organization 1958). Health outcomes are commonly viewed as the health status at the end of a study period or the change in health status over a period of time, especially where a specific treatment was given as an input for a group of patients. The measurement of health status represents a great challenge for health outcomes research. Health researchers diverge greatly as to what are the physical, mental and 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. social dimensions of health status and how to measure them. Health status is a theoretical concept that is a latent variable with dynamic and multiple attributes (McDowell 1996, Hays 1994, Siegrist 1989, Fitzpatrick 1992). We cannot observe or measure it directly. Health status and health outcomes have only been measured and recorded by varieties of proxies for health or health-related factors. Such proxies for health status include pathological measurements of health status and the patient- oriented measures of general health status and health-related quality of life (HRQOL). It is clear that these proxies for health outcomes represent different aspects of health outcomes and are vulnerable to measurement errors, provider manipulation, and subjective interpretation. Therefore, these proxies for health outcomes are useful but limited as comprehensive indicators of health status or health outcomes. Savoca (1995) reported that the measurement error in a self- evaluation of mental health has large variance and leads to a substantial understatement of impact of mental health on earnings (Savoca 1995). Traditionally, health is negatively measured by a variety of “objective” pathological proxies, such as death (mortality and survival), disease diagnosis (morbidity), disability, laboratory values, and health utilization. The more a society advances and its economy progresses, the higher the demand for health care becomes. As the population ages and chrome disease becomes the dominant form of illness, the requirement for the health status measurement becomes more complex and subtle. 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The patients’ perceived health status and their health-related quality of life (HRQOL) become the major concerns of health care research (Rothenberg 1990). A variety of patient-oriented, self-reported health measurements have been developed to measure multiple dimensions of health status (such as mental health, functional status, and social role). As a generic instrument of health-related quality of life, the RAND Medical Outcomes Study Short Form 36 (RAND SF-36) is widely used in health services research to monitor the population health status and to evaluate health policies. It is also used in clinical practice and research as part of a health outcome instrument in conjunction with disease-specific measurements to gauge subtle changes in health status (Ware 1992, 1993, McDowell 1996). This comprehensive short form with only 36 questions yields an 8-scale health profile as well as summary measures of health-related quality of life. As documented in more than 750 publications, the RAND SF-36 has proven useful in monitoring general and specific populations, comparing the burdens of different diseases, differentiating between the health benefits produced by different treatments, and screening individual patients (Health Assessment Lab, 1999). Studies have shown that the RAND SF-36 is a responsive outcome measure to important clinical changes in clinical trials (Croog 1986, Bombardier 1986, Canadian Erythropoietin Study Group 1990, Cleary 1991) and a significant determinant of health outcomes & costs U Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Hombrook 1995). It has become one of the standard HRQOL measures and a core module of major public health surveys and randomized clinical trials (Health Assessment Lab 1999). At least 2 million forms are administrated every year (New England Health Institute, 1992). The number of articles published using the RAND SF-36 has grown each year, from the Erst publication in 1988 to 179 articles in 1996. To date, the RAND SF-36 data have been published for over 130 diseases and conditions in 100 journals and a variety of other sources. Of those conditions, 15 have had over 10 articles and 26 have had over 5 articles using the RAND SF-36 to measure and evaluate patients’ health status (Manocchia 1999). Like other questionnaire-based health measurements, the RAND SF-36 is subject to both systematic and random measurement errors. The criticisms include absence of measures of cognitive function, distress and coordinated actions (Hays 1992, Anderson 1993, Stewart, 1988). Studies have shown the reliability of some scales to be problematic (Ware, 1992,1993). Although it has been widely acknowledged that the measurement of health status is far from perfect (McHomey 1992,1993,1994), the current literature is very limited with respect to the consequences of measurement error in health status measures (RAND SF-36) on the outcomes evaluation of alternative health care interventions. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the current practice, health outcomes (health status at the end of survey used as a dependent variable) are modeled by using a single indicator (i.e., physical function...); the health status at the baseline (used as independent variables) is modeled by using a group of single indicator. Therefore, in terms of modeling, health status represents some unique challenges: it is measured using multiple dimensions, each with measurement errors. Health status measures appear as both dependent and independent variables in a regression model. The correlations among the health measures, and with other covariates and dependent variables (such as health costs) make the situation even more complex. How to adjust for measurement error, multicollinearity, and simultaneity/endogeneity is a core issue in health-related studies. Although it has been widely acknowledged that measurements of health status, such as the RAND SF-36, are far from perfect and that measurement error will lead to biased estimation and problematic hypotheses testing, the impact of multiple variable measurement errors on the classical linear regression models of health outcomes and health care costs are still unclear. In this study, a latent health construct measured with multiple scales of the RAND SF-36 will be introduced. A set of structural equation models (SEM) for health outcomes and health costs research will be used to examine the potential biases due to both measurement errors in the multiple scales of the RAND SF-36 and simultaneity of health outcomes and health care costs in the 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. linear regression model. The following research questions will be answered in this study. 1. Are latent health construct measured with the multiple scales of the RAND SF-36 and the set of SEMs supported by the empirical data? 2. Are the linear regression estimations of the multiple scales of the RAND SF-36 attenuated by their measurement errors? 3. Are the regression estimations of the treatment variables s contaminated by the measurement errors in the multiple scales of the RAND SF-36? 4. Is there simultaneity between health outcomes and health care costs? Before we formally step into the research topic, some important concepts and terminology will be introduced. Since the general perceived health status or HRQOL is the focus of this study, health status is defined as a patient perceived health status or HRQOL at a given time point. Health outcomes are defined as the patient perceived health status or HRQOL at the end of each survey period. Both health status and outcomes are measured by the scores of a generic, patient self-reported questionnaire, the RAND SF-36, at a time point. Health care costs are defined and measured by accumulating all health expenditures during a time period. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3. Methodology 3.1 Data The data used in this analysis were collected for the Kaiser Permanente/University of Southern California Pharmacist Consultation Study (KP/USC Study) (McCombs 1995,1998, Cody & McCombs 1998). On November 1, 1992, the State of California introduced a new law that requires all new prescriptions to be accompanied by a pharmacist consultation. The KP/USC study was designed to assess the effects of both the new state policy (State Model) and an alternative model of pharmacist consultations in outpatient settings (KP Model). KP Model requires pharmacists to provide more procedure consultation for high-risk patients or for high-risk drugs. The baseline for comparison, the Control Model, is the standard practice pattern that was in place prior to the new law (pharmacist consultation were requested or when professional judgment dictated base). A prospective study design was used to examine the difference in patient satisfaction, quality of life, and the use of outpatient physician office visits, prescription drug utilization and hospital services across the alternative models of pharmacist consultation. In the Southern California Region of the Kaiser Permanente Medical Care Program, which provides prepaid comprehensive health care to 2.2 million voluntarily enrolled members, two parallel studies were conducted based on the randomization of over 6,000 patients in three Kaiser Permanente service areas 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Random Assignment design) and a geographic implementation for the three consultation models in six Kaiser Permanente service areas (Area-wide Design). However, only the data from the “Area-wide Design” are used in this study due to treatment contamination in the data of the Random Assignment Design. The area- wide study collected patient interview data for 3,569 patients. Figure 1. Time-Events of KP/USC Pharmacist Consultation Study | Health Costs, Year_o| 1 1 | Health Costs, Year_l | Health Costs. Year_21 1 1 1 1/1/92 1/1/93 A HRQOL YearJ) 4/1/93 4/1/94 4/1/95 A A HRQOL Year_I HRQOL Year_2 The observations for the Kaiser/USC study were selected from Kaiser members who were over 18 years of age and who had a pharmacy benefit. Approximately 75% of enrolled members have outpatient drug benefit coverage. Data collection for the KP/USC study began April 1,1993 and ended March 31,1995. The final patient- level data of the KP/USC study was derived from two sources, a patient survey and the Kaiser computerized database. The surveys for general health status, measured with the RAND SF-36, the Health Utility Index (HUI) and the Visual Analog Scale, were conducted at the end of each 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. one-year observation period (Figure 1). The health care costs were estimated by pricing the services consumed over one year by using other available data (Figure I). There are a total of 68 independent variables included in all analysis of the KP/USC study. They are intervention variables, demographics variables (including social and economic variables), health behavior variables, prior health care utilization, and patients’ health status variables as well as the variables used to control for treatment contamination and severity of illness. A complete-case dataset from the “Area-wide Design” of the KP/USC Study is used in this study to simplify the research questions. This study will focus on the intervention variables (KP Model and State Model), the patient’s perceived health status, health care costs, and outcomes as measured with the multiple scales of the RAND SF-36. 3.2 Measurement of Health Status and Health Outcomes General health status and health outcomes were measured by the RAND Medical Outcomes Study Short Form 36 (RAND SF-36), a well-known generic instrument for measuring general health status or health-related quality of life. It is widely used in health services studies, clinical practice, and policy implementation and evaluation. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The RAND SF-36 questionnaire consists of 36 questions (called items) to measure the eight major health concepts (called domains or scales): 1) Physical functioning (10 items) 2) Role limitations due to physical health problems (4 items) 3) Bodily pain (2 items) 4) Vitality (4 items) 5) General health perceptions (S items) 6) Social functioning (2 items) 7) Role limitations due to emotional problems (3 items) 8) General mental health (S items) and patients’ perception about change in health status over the past year (Ware & Sherboume, 1992; Hays & Shapiro, 1992; Hays, Sherboume & Mazel 1993). The RAND SF-36 can be easily self-administrated by patients or filled out by an interviewer. The ordinal ranking scores of 36 items will be summarized into the raw scores of eight scales; these will be further transformed into the 0-to-100 positive scores and normalized into the T-scores (Ware et al 1993). The T-scores of the RAND SF-36 were used in this study. 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.3 Analytic Strategy In addition to improving the measurement of health status and data collection methods, a rational remedy for measurement error is to use an advanced modeling method. In this study, a set of structural equation models (SEM) for health outcomes and health care costs are developed to assess the validity of linear regression analysis in a health outcomes study and to re-evaluate the effects of pharmaceutical consultation on both health outcomes and health care costs in a large health maintenance organization (HMO). Modeling health status and health outcomes presents a great challenge due to the difficulty inherent in health status measurement. A patient's health status is a dynamic, unobserved latent variable consisting of multiple dimensions and multiple levels, subject to measurement error (Butler 1987, Dwyer 1999). Self-reported patient health status is widely used as a measure for perceived health status, the major outcomes in health-related studies. The instruments used to measure patient- reported health status have multiple scales that are all subject to measurement errors. The multiple scales measurement error of health status in a linear regression model can cause invalid estimation and inference. In addition, endogeneity or “simultaneous equation problems” that may exist between health outcomes and health care costs is a potential concern for any health- 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. related study. Theoretically, health status and health resources utilization are both the input and output of health care. Intuitively, a healthy person should consume fewer health care resources; a patient with a serious disease should consume more health services. An effective treatment or health care program could improve the patient’s health status. If health resources are more expensive, fewer health services may be used, thus the health outcomes may suffer. Therefore, health outcomes and health costs are jointly distributed and should be modeled simultaneously (Greene 1992, Judge 1979). Although the presence of endogeneity bias can be tested using the Durbin-Wu-Hausman test, the test will be inappropriate in this case since there is measurement error (Wu 1973, Hausman 1978). The proposed models could assess the combination of both factors, the inconsistency due to the measurement errors of the multiple scales, and the endogeneity between health outcomes and health care costs. SEM is particularly well suited to model health status and health outcomes, and takes full advantage of the association among the multiple measures of a patient’s health status to identify possible latent variable(s) for the patient’s health status. By using the latent health variable(s), advanced modeling and integrating different kinds of measures, we can use SEM to eliminate the bias stemming from both random and systematic errors among measured variables (Judd et. al., 1986, Lu, M.S., 1998); simultaneously assess multiple dependent variables in a single model; and examine 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. causality between different variables (Bender, 1990). In addition, it can systematically evaluate alternative models for given data with comprehensive indices of the overall fit and can test complex hypotheses (Hays & DiMatteo 1987). To control and evaluate the potential inconsistency caused by the measurement error of health status and the simultaneity (endogeneity) between health outcomes and health care costs, the following structural equation models are proposed. The classical linear regression models are used as the baseline for the comparison. Based on the endogeneity between health care costs and health outcomes, and the method of modeling the dependent variables (the health outcomes), the proposed SEMs can be grouped under three heads, the SEMs with a latent health variable for an observed single dependent variable, including health care costs or health outcomes (SEMSI), the SEM for a latent dependent variable with observed multiple indicators (SEMMI) and the SEMs with a latent health variable for health care costs and a latent health outcomes variable with multiple indicators (SEMHCHOMI). If exogeneity between the health care costs and health outcomes is statistically accepted, then the SEMSIs and SEMMI can be used to estimate health outcomes and health care costs separately. Structural equation modeling allows us to model health outcomes as a latent variable measured with the multiple scales of a HRQOL instrument. Furthermore, if endogeneity exists between the health outcomes and 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. health care costs, then the structural equation model, SEMHCHOMI, can estimate the health outcomes and health care costs simultaneously. The proposed structural equation models are summarized as follows: I. Basic Models • Classical Linear Regression Models (CLRM) - Classical Linear Regression Model for Health Care Costs - Classical Linear Regression Models for a Single Scales of the RAND SF-36 n. Structural Equation Models with a Latent Health Variable • SEM for an observed single indicator dependent variable (SEMSI) - SEM with a Latent Health Variable for Health Care Costs - SEM with a Latent Health Variable for a Single Scale of the RAND SF-36 • SEM for a latent dependent variable with observed multiple indicators (SEMMI) - SEM with a Latent Health Variable for Health Outcomes Measured with the Multiple Scales of the RAND SF-36 • SEM for both health care costs and latent health outcomes with observed multiple indicators (SEMHCHOMI) 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SEM with a Latent Health Variable for Health Care Costs and a Latent Health Outcomes Variable Measured with Multiple Scales of RAND SF-36 In the following section, the model specifications for the proposed structural equation models will be discussed in detail. 3.4 Model Specification 3.4.1 Classical Linear Regression Models (CLRM) CLRM for Health Care Costs H C 2 =<XcT + X ’ Pc + Y c H C o + S Jtc jS F 3 6 J,a + C c (1) 1*1 1*2 2 *1 1*14 14*1 1*1 1*1 1*8 8*1 1*1 - iid N (0, 52 ;c) Where. HC:: LTCl2, LVC,2, or LRXC,2. T: Treatments X = (AGE* SEX . R A C E, M ARRIAGE* EDUCATION* W O R K * SM OK* ALCOHOL* CO M PLIA N CE* N EW D RG * VISIT* H O SPIT A L o. LRA TIO ,, R X o )’ 1 j^j SF36j,o = j^ioPFo+Jt^RPo+HjBPo+n^VTo+UdGHo+t^rtSFo+r^TREffM^s MHq; CLRM for a Single Scale of RAND SF-36 SF36i r , 2 = ( X q k T + X’ P q k + Y q k HCq + £ 7 t q f c j SF36j,o + £qk (2) 1*1 1*2 2*1 1*14 14*1 1*1 1*1 1*8 8*1 1*1 k = 1 ,2 ,3 ,...8 . ^qk ~ iid N (0, S2gc) Where. SF36U: PFj, R P 2 , B P 2 , VT2 , G H 2 , SF2 , RE* or M H 2 T: Treatments X = (AGE* SEX , R A C E, M ARRIAGE* EDUCATION* W ORK* SM OK* ALCOHOL* C O M PLIA N CE* NEW DRG * VISIT* H O SPIT A L o. LRA TIO ,, R X o )’ E T t c j SF36 j .o — J^o P F o + H ^R P o + H aB P o + H rtV T o + ^sG H o + n rtS F arM tT R E o + Jiig M H q ; 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The classical linear regression models (CLRM) are exactly the same as the previous analysis of the Kaiser/USC pharmacy consultation study and serve as a baseline for further analyses. These models ignore measurement error and use observable health proxies instead of health status as both dependent and independent variables. They can estimate only one dependent variable in a single model. There are two kinds of linear regression model, CLRMs for health care costs and for health outcomes. The classical linear regression models can be viewed as a special case of the structural equation model. They can be evaluated and estimated by either the ordinary linear square method (OLS) or the Maximum Likelihood estimation (ML). In the CLRM equations, “t” is a given time when an event happens. Here we consider only two time points, the baseline (Time 0) and the end of survey (Time 2). HC2, including LTC12, LVC12, and LRXC12, represents health care costs during the last two years and is used as a dependent variable in each of the three linear regression models for health care costs. LTC12 is the log total health care costs during the last two years. LVC12 is the log physician office visit costs during the last two years. LRXC12 is the log prescription drug costs during the last two years. SF36 j,2 is the jth scale of the eight RAND SF-36 scales at the end of Year 2 and is used as a dependent variable in each of the eight linear regression models for health outcomes. PF2 is the score of the physical function scale at the end of Year 2. RP2 is the score of the role limitation due to physical function at the end of Year 2. BP2 is the score of the body pain scale at the end of Year 2. VT2 is the score of the energy 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. scale at the end of Year 2. GH2 is the score of the general health scale at the end of Year 2. SF2 is the score of the social function scale at the end of Year 2. RE2 is the score of the role limitation due to emotional function at the end of Year 2. MH2 is the score of the mental health scale at the end of Year 2. £ (zeta) is a vector of disturbance for the dependent variables (HC2 and SF36 2), with an independently, identically normal distribution, i.e., £ is unrelated to the independent variables in the model and has a zero mean and identical variance. Of the 68 independent variables, three kinds of variables were given special attention, health outcomes (SF36 2), health status at the baseline (SF36o), and the treatment variable (T). For detailed information about these variables, please refer to the previous analysis (McCombs 1995, 1998, Johnson & McCombs 1998, Cody & McCombs 1998). 3.4.2 Structural Equation Models with a Latent Health Variable The Structural equation model consists of two components, the measurement model and the structural model. A latent variable is the key for structural equation modeling. It is a (or a group of) random variable(s) for true score or unobservable concepts, such as health status, preference, policy, etc. A latent variable is measured by a group of observed variables or reference indicators. In the measurement model the observed measures can be modeled as functions of the latent variable and separated into true score and measurement errors. The structural model represents the associations between the latent variable(s) and other dependent or independent 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. variables (Judd 1986, Fuller 1987, Bollen 1989). In the proposed models, a patient’s perceived health status at a given time point is modeled as a latent variable measured with the multiple scales of the RAND SF-36. SEMs for an Observed Single Indicator Dependent Variable (SEMSI) If exogeneity exists between health care costs and health outcomes, health costs and health outcomes can be separately estimated without worrying about “simultaneous equation problem”. SEMSI for Health Care Costs HC2 = c x cT +X ’ pc + Y c HC. 4 TfcHQt + G e (3) 1*1 1*1 2*1 1*14 14*1 1*1 1*1 1*1 1*1 1*1 SF36o = X *HQo 4 - £ (4) 9 * 1 9 * 1 1*1 9 * 1 Where, HC2 : LTCi2, LVC,* or LRXC1 2 , S F 3 6 o = (PF* RP* BP* VT* GH* SF* RE* M H* H T 0 )\ E (’H Q o ) = 0, E(Z e ’HQo) = 0 . E(e * H Q b ) = 0, E (£ J =0. E (5 c C J = • E(Ci £ c) = 0, £ i is the i-ih column of e. E (e ) = 0, e is homescedastic & nonautocorrelated across observations. Since the measurement errors of explanatory variables are the major concern of the validity of the linear regression model, the patient’s perceived health status at the baseline (*HQo) is modeled as a latent variable with multiple indicators first. On the basis of previous theoretical and empirical studies, one latent health variable 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measured by eight scales and the health transition item of the RAND SF-36 is a reasonable starting point for the measurement model (McDowell 1996; Hays & Stewart 1990; Ware & Sherboume 1992; Hays & Shapiro 1992; Hays, Sherboume & Mazel 1993). Three versions of SEMSI Models are used to estimate total health care costs (LTC12), physician office visit costs (LVC12), and prescription drug costs (LRXC12) during the last two years. In these models, the most important modification to the classical linear regression models above is that a patient’s perceived health status is modeled as an unobservable latent concept (*HQo) with multiple indicators (the multiple scales of the RAND SF-36 at the baseline). Equation 3 is the structural model. The general health status at the baseline (Time 0), *HQo, is a random variable for latent health which is measured with errors, E (epsilon). The scales of the RAND SF-36 at the same time point (SF-36o) are used as reference indicators for the latent health variable. We assume that the latent health variable is a random variable with expectation equal to zero and unrelated to either disturbance term, £c (zeta), or random measurement error, e (epsilon). Disturbance term, (zeta), is assumed with a standard assumption, i.e., zero expectation and consistent variance. 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Equation 4: Measurement Model for the Latent Health Variable SF36. = X ’HQ. • •i • • i i*i + e 9 *1 (4) i.e., PF. = X, ’HQ. + £i RP. = x2 ’h q . + 62 BP. = X 3 ’HQ. + 63 VT. = ’HQ. + 64 GHo = X S *HQ. + 65 SF0 = X * ‘HQ. + 6. RE. = X 7 ’HQ. + 67 MH0 = x8 ’h q . + 6. HT. = X 9 *H Q * + 6. Where E(e e ): S2e, 5*2, 52* 2 5 * 31 5*32 5 2 * 3 5 * 41 5*42 5 *43 52 * 4 5 * 51 5*52 5 * 53 5*54 5 2 * 5 5 * 61 5*62 5 * 63 5*64 5 * 65 5 2 * 6 5 * 71 5*72 5 * 73 5*74 5 *75 5*76 5 2 * 7 5* 81 5*82 5 * 83 5*84 5 * 85 5*86 5*87 5 * 91 5*92 5 * 93 5*94 5 *95 5*96 5*97 L Note: S2es 5 2 e98 82 E 9 9 ( 5*ij — 5*ji )» e is homescedastic & nonautocorrelated across observations Equation 4 is the initial measurement model for the relationship between the latent health variable, its indicators and measurement error, e (epsilon). The measurement error, £ (epsilon), a measurement errors vector of the 8 scales plus the health 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transition of the RAND SF-36, is assumed to have zero expectation and is homescedestic and nonautocorrelated across observations, e (epsilon) is also unrelated to the disturbance term, £c(zeta). SEMSI for a Single Scale of the RAND SF-36 SF36ir ? = C K q i t T + X * fiq it + Y q k HC# + H q k HQa + (5) i * i i*2 2*i i*i4 i4*i t* i x*i i n i *i i n SF36o = X *HQ» + e (6) 9 * 1 9 * 1 1*1 9 * 1 Where. Ic = 1,2.3........9. SF36t2: PF:, RP,, BP2 , V I\, GH:, SF2 , REj, or MH2 SF36o = (PFo, RPo, BP* VTo, GH* SF* RE* MHo, HT0 )’ E (’H Q o ) = 0. E(£ * 'H Qo) = 0 . E(e * H Q o ) = 0. E (C q k ) =0. E 5 < » k ) = S 2 fak. E(6i C q t) = 0.6, is the i-th column of e. E (e ) = 0. e is home scedas tic & nonautocorreiated across observations. SEMSI for a single scales of the RAND SF-36 used to model the health outcomes measured by a single indicator (such as physical functioning or...). Therefore, eight versions of the SEMSI Models are used to estimate each scale of the RAND SF-36. In terms of model specification, SEMSI for a single scales of the RAND SF-36 is the same as the SEMSI for health care costs, with the exception that its dependent variable is a scale of the RAND SF-36. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SEM for Latent Health Outcomes with Observed Multiple Indicators SEM with a Latent Health Variable for Latent Health Outcomes Measured with Multiple Scales of RAND SF-36 (SEMMI) *H Q 2 = C X q T + X’ pq + Y q HC. + K q*H Q t + ^ (7) 1 *1 1 * 2 2 * 1 1 * 1 4 1 4 * 1 1 * 1 1 * 1 1 * 1 1 * 1 1 * 1 SF36t = X *HQt + e (8 ) 1 8 * 1 18*11*1 1 8 * 1 Where, ’H Q t = (’H Q o , ’H Qx)', SF36, = (P F o , R P o , B P o . V T o . G H o , SF* RE* M H o . H T q , PF2 , R P 2 , B P 2 , V T 2 , G H 2 , SF2 , RE2 , M H 2 , H T ^*, X = (i, X 2 , Xj,.... X$,1, Xi X 3, .... X ^)’, E ("HQo) — 0, E(£ q *HQo) — 0 , E(e *HQo) = 0. E (C q ) =0. E (? q £ ,) = 82 ; . E(Ci ^ q) = 0. e i is the i-th column of e. E (e ) = 0, e is homescedastic & nonautocorrelated across observations. SEMMI is used to model health outcomes. In contrast to SEMSI for a single scale of the RAND SF-36, its dependent variable (the health outcomes) is represented by a latent health variable with the multiple measures of the RAND SF-36. i.e., there are two latent health constructs in the SEMMI, the latent health status at the baseline modeled as independent variables ( HQo) and the latent health outcomes model as the dependent variable (*HQ2). Intuitively, they should be measurement invariance over time (X), i.e., the measurement model should be modeled with the equality constraints of corresponding factor loading over time. (Pentz & Chou 1994). Also, the covariance between residuals of the same measured variables at different time points (such as the residuals of physical function at the baseline and the end of survey, Et and £ 10) should also be specified and evaluated to help account for 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. associations caused by unmeasured variables (Bollen 1989; Maruyama 1998; Anderson & Williams 1992; Hays 1994). In the measurement models (Equations 4 ,6 and 8), e is a vector of random error term with zero mean and constant variance. The unbiased estimations for either true health outcomes or health costs can be estimated by Equations 3, S and 7. The error terms C , and e are assumed to be independent of each other and of the latent health status (’HQO. In terms of econometrics, the measurement models above are multiple indicator models. Since the models have more than three indicators, there are more equations than unknown parameters. All measurement models are overestimated (Greene 1992, Judge 1979). Therefore, these structural equation models are overidentified. (Bollen 1989, Hsiao 1984). Unbiased and efficient parameter estimation of the SEM models may be obtained by the maximum likelihood (ML) method (Judge 1979, Greene 1992). SEM for Both Health Care Costs and Latent Health Outcomes (SEMHCHOMI) Generally, when endogeneity between health care costs and health outcomes exists, the SEM models above will not be consistent and are subject to “simultaneous equation problem”. The challenge of health measurement makes such simultaneous 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equation solutions nearly impossible for a classical linear regression model with a single dependent variable. Since multiple indicators are used to measure a latent variable (e.g., perceived health status), SEM provides a unique approach for the simultaneous assessment of the relationships among multiple dependent variables in a single model. Therefore, SEM can adjust for the potential "simultaneous equation problem" and test more complex hypotheses (Bollen 1989; Maruyama 1998). SEM for both Health Care Costs and Latent Health Outcomes Measured with Multiple Scales of RAND SF-36 h c2 = oteT+ X’ pc + YcHC8+nc*HQ, + Cc (9) 1*1 1 * 2 2 * 1 1 * 1 4 1 4 * 1 1 * 1 1 * 1 1 * 1 1 * 1 1 * 1 •HQ2 s O q T + X’ + Yq HCo+<HQo + Cq (10) 1*1 1 * 2 2 * 1 1 * 1 4 1 4 * 1 1 * 1 1 * 1 1 * 1 1 * 1 1 * 1 SF36, = X *HQt + e (11) 1 8 • I 1 8 • 1 1 • 1 1 8 • 1 Where, 'HQ, = ('HQo. •H Q 2 ) \ HC2 : LTC1 2 , LVC1 2 , or LRXCI2 , SF36, = (PF„ RP„ BPt, VT,. GH,, SF,. RE,, MH,, HTt, PF,, RP2 , BP,, VT2 , GH2, SF2 , RE* MH2, HTj)’, X sfi.X^ X 2 X9, l, X,, X 3, .... X 9)’, E (* H Q o ) = 0. E(£c H Q o ) = 0 , E(?,*HQb) = 0 . E (e * H Q a ) = 0, E (C c) =0. E (£ c £ c )= , E(6i ^ J = 0, E, is the i-th column of E. E(^q) =0, E (5 , Cq) =82ft. E(£c ?q)=0. E(e, ^ q) = 0, E, is the i-th column of E. E (E) = 0, e is homescedastic & nonautocorrelated across observations. As in SEMMI, the measurement invariance over time and the covariance between residuals of the same measured variables at different time points (such as the 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. residuals of physical function at the baseline and the end of survey, Et and Eio) should also be specified and evaluated in SEMHCHOMI. For practical reasons, health care costs were derived from health utilization during one year. The patients’ perceived health status or health-related quality of life was measured by the RAND SF-36 at the baseline and at the end of each year. Therefore, the simultaneous system can be modeled as a recursive system. Then the simultaneous structural equation model is identified. Both equations in the structural model (Equations 9 and 10, which are recursive of each other) may be just identified by both order and rank conditions. Provided there are more than three indicators for each latent variable, identification of the measurement models should not be a problem. Therefore, the model as a whole should be identified (Gujarati 1988). 3.5 Model Evaluation and Estimation The structural equation models for health outcomes and health care costs were evaluated and estimated by the maximum likelihood estimator because of its capacity to accommodate large models and its robustness for deviations from multivariate normality (Harlow 198S, Huba & Harlow 1987). However, order and rank conditions cannot guarantee the identification and estimation of SEM. (Bentler & Weeks, 1980: 295). Currently, most statistical software (such as EQS and SAS/CALIS) can numerically examine and report identification problems using a procedure that is 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fundamentally connected to both the maximization of the fit function and the calculation of standard errors (SAS v6.12 manual 1998, Bentler 1996, Arbuckl 1997, Joreskog & Sorboml989). SAS/CALIS procedure was used to evaluate and estimate the structural equation models. Model selection and evaluation is quite vast in its scope. It is a challenging topic and far from being perfect. A variety of criteria and fit indices for model selection and evaluation have been proposed for different objectives based on various assumptions and approaches. It is not surprising that no model can fulfill the entire criteria. It does not guarantee that the proposed fit indices will point out a useful model (Maddala 1992). The desirable characteristics of a statistical model include: interpretability, goodness of fit and parsimony. Interpretability is very important but difficult to investigate. It can be subjectively judged only by the relevant theories. However, there are a lot of statistics available for the goodness of fit of a model (Browne and Cudeck 1993). It is very easy and much dangerous to increase the number of parameters to improve the goodness of fit statistic at the costs of sacrificing the interpretability. Therefore, balancing the three criteria: interpretability, goodness of fit, and parsimony is very important as well as a challenge. An ideal and useful model should be established on acceptable theories, and supported by an available data in terms of the major criteria for both goodness of fit and parsimony, which are currently accepted by the most scholars. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In fact, even goodness of fit of SEM is problematic due to the complexity of SEM. Chi-square test, a test of the null hypothesis that the theoretical model fits the data, is the most common test for overall model fit. However, previous studies have shown that SEM is sensitive to sample size: (I) Sample size should be more than 100 observations and 5 to 20 times of the number of parameters being estimated; (2) if sample size is very large, Chi-square testing can result in the rejection of a model that appears to fit the data quite well. For this reason, it has been recommended that the model Chi-square statistic be used as a goodness of fit index, with smaller chi- square values (relative to the degrees of freedom) indicative of a better model fit (James et al 1982, Joreskog & Sorbom, 1989, Mulaik et al 1989). To evaluate SEM and CLRM directly, a cross-validation approach, a single sample cross-validation index for covariance structure, was used (Browne and Cudeck 1989). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4. Results As discussed in Chapter 3 Methodology, data for 2,218 patients from the “Area-wide Design” survey of the KP/USC Study were used to evaluate and estimate the SEMs in order to simplify the research question to focus on the questions under study. In the present study, to make a comparison with the classical linear regression models in the previous KP/USC Study, it is necessary to use a standard approach to evaluate and estimate both the classical linear models and the proposed SEMs. The classical linear regression model can be viewed as a specific case of structural equation model and estimated using either the ordinary least square (OLS) or the maximum likelihood estimation (MLE) approaches. To assess the impact of measurement error, the classical linear regression models for health care costs or a single observed indicator of health outcomes were evaluated and estimated by Erst using the maximum likelihood estimator of the S AS/C AL1S procedure. In this study, the MLE estimations of the linear regression models were the same as the OLS results. Then the analytic samples were analyzed by using the CALIS procedure of the SAS System following a two-step procedure recommended by Anderson and Gerbing (1988). hi the first step, confirmatory factor analysis was used to develop a 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurement model that demonstrated an acceptable fit to the data, hi step two, the full theoretical model, including measurement and structural models, was estimated, tested and revised until a theoretically meaningful and statistically acceptable model was found. In this chapter we will show how these two steps were completed. First of all, descriptive statistics were presented. The correlations among the multiple scales of the RAND SF-36 were focused. Then measurement models and theoretical structural equation models were estimated and evaluated. Finally the effects of intervention policies and the health status at the baseline on the health care costs and health outcomes at the end of the survey, and their variations due to the different statistical models, were estimated and presented. 4.1 Descriptive Statistics The standard deviations and inter-correlations among the 8 scales and the health transition score of the RAND SF-36 are presented in Table 1. More detail information about the major variables in this study can be found in previous publications from the KP/USC study (McCombs et al 1995, 1998, Johnson & McCombs et al 1998, Cody & McCombs 1998). All correlations among the scales of the RAND SF-36 are positive at both the baseline and the end of survey, except for health transition. The correlation coefficients among the 8 scales of the RAND SF-36 ranged from 0.22 to 0.63, and were 75% of the correlation coefficients that were larger than 0.40. The correlation coefficients between the physical functioning, role 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. limitation due to physical health, body pain, general health perceptions, energy/fatigue, and social functioning are all above 0.40 (0.409-0.629) at both the baseline and the end of survey. The emotional well-being or mental health was found to be moderately to strongly associated with role limitation due to emotional problems, energy and social functioning (r > 0.40) and marginally associated with general health perception at both the baseline and the end of survey. The correlations between the corresponding scales over time were all larger than or equal to 0.40 (0.40 - 0.71) except for health transition scores. Health transitions at both the baseline and the end of survey were weakly negatively associated with 8 RAND SF- 36 scales (-0.12 - -0.35), i.e., if the health transition is decrease then the scores of 8 RAND SF-36 scales will decrease in the next period. These results suggest that the RAND SF-36 scales are moderately to highly inter-correlated cross-sectionally and longitudinally, and their variations could be accounted for by a underlined latent health construct. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T a b le 1 . Correlation Coefficients o f t h e Scores o f R A N D S F -3 6 Scales HT S 2 aa at s G b 0 9 i a v s VT *8 3 B u U O a C D O i at B b a. H B B 2 u at E b 0 9 8 1 VT es B tt & 0 9 0. at f i b O b _ X = ? ’ " 9 9 9 = o O 9 4 - _ « a s * *= 6 so 9 ^ 2 - 3 I S 5 5 eioeio9 00000009 t 2 . . a a a s a s s* b b b b b 9 $ s _ s k k 8 * s r r a b b b b b b 9 3 2 a n n f* aw* 9 5 = S J S = ! = ! 8 S 8 ^99999999 H : a a s ? 5 s s ? s? bbbbboob 9 $ « S a s s s ; s a s a f 0 0 0 0 0 0 0 0 9 S s _ s s a a s a s s s s s s s « b b 9 bbbbobbbb 5 — • 5 5 5 3 9I »| P> N W A > * S 2 0 0 0 9 0 0 0 0 0 0 0 0 9 S 2 _ s i s s ; a ; a a s j a a s = as O O O o 9 O0 0 O0 OOO9 5 2 . a s s s s a ; a a ; s s a a : a? 0 0 0 0 0 9 0 0 0 0 0 0 0 0 9 82 . K 9 a 8 a a « S ^ i a i K a a a S 83 0 0 0 0 0 0 9 ^000000009 82 w •» A ^ a < e O ^ m £ { 0 0 0 9 82 1 i f i I f ' u 1 . II 1 L i i a 5-1 a 3 ill tSSlESSi! e Z 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I k f t k i i T r a iM M 4.2 Measurement Model As described above, the measurement model was developed and evaluated first. In the structural equation models with latent variables, a measurement model describes the nature of the relationship between a latent variable(s) and a number of observed indicators that represent the latent variable(s). A null model reflecting the hypotheses of no covariation among the variables was estimated first to serve as a baseline for modeling the measurement model. The initial measurement model consisted of nine equations that nine measures of RAND SF-36 were predicted by one latent health variable, corresponding to a patient’s general perceived health status or health-related quality of life, i.e., the latent health variable was initially measured by 9 observed indicators, the health transition score and 8 scales of the RAND SF-36. The initial measurement model, Model M l, was evaluated by using the baseline data first (Table 2). The Chi-square value for the initial measurement model was statistically significant, X2 (D F = i6 , n= 2.218) = 264.402 and p < 0.01, and should reject hypotheses that the model provides an ideal fit to the data. Technically, when the proper assumptions are met, this chi-square statistic may be used to test the null hypothesis that the model fits the data. A smaller Chi-square value is indicative of a better model fit (Bentler 1980, 1990). In practice, however, the statistic is very sensitive to sample size and 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. multivariate normality assumption, and it will very often result in the rejection of a well-fitting model. For this reason, it has been recommended that the model Chi- square statistic be used as a goodness of fit index. The Bender’s Comparative Fit Index (CFI), Bender & Bonett’s Non-normed Index (NNFI), and Normed Index (NFI) are the most common measures of practical tit for structural equation modeling (Bender 1980,1990, Bender & Bonett 1980). Model M l fitted the data well in terms of practical tit criteria, with the Bender’s CFI equal to 0.9704, NNFI equal to 0.9335 and NFI equal to 0.9687. As a rule of thumb, empirically acceptable CFI, NNFI and NFI values are above 0.90. However, upon further analysis, the standardized factor loading of health transition at the baseline was a littie low (- 0.295) and R2 was only 0.087. The result suggested that health transition might be a weak indicator for the latent health variable. Table 2. Goodness-of-Fit Indexes for Measurement Models Models Sample Size Indicator Chi-Square DF CFI NNFI NFI Model Ml: Initial Measurement Model With 9 Scales Null M odel 2218 9 8440.350 2218 9 264.402 36 1 6 0.9704 0.9335 0.9687 Model M2: Final Measurement Model with 8 Scales Null M odel 2218 8 8230.631 Baseline 2218 8 230.359 28 9 0.9730 0.9160 0.9720 E n d of Survey 2218 8 7919.606 2218 8 295.227 28 9 0.9637 0.8872 0.9627 Note DP: Degree o f Freedom C FI: Bender* Comparative Fit Index NNFI: Bender & Bonett* (1980) Noo-normed Index 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A revised measurement model dropping health transition. Model M2, was re- estimated. Goodness-of-fit indices for the re-specified measurement model (Model M2) are presented in Table 2. The Chi-square value for the model was statistically significant, X2 (df=9, n= 2,218) = 230.359 and p < 0.01. However, the goodness-of-fit of the measurement model was empirically acceptable (Bender’s CFI = 0.973, NNFI =0.992, and NFI=0.972). Standardized factor loadings for the indicator variables are presented in Table 3. The SAS system's CAL1S procedure provides approximate standard errors for these coefficients and large-sample t-tests of the null hypothesis that the coefficients are equal to zero in the population. The t scores obtained for the coefficients in Table 3 range from 22.778 to 45.061, indicating that all factor loadings were highly significant (p < .001). This finding provides evidence supporting the convergent validity of these indicators, since the fact that all factor loadings for the indictors measuring the same construct are statistically significant means that all indicators are effectively measuring the same construct. (Anderson & Gerbing 1988). Table 3 also provides the reliabilities of these indicators and the square of the factor loadings, along with the composite reliability for the latent health construct. Composite reliability is an index of internal consistency comparable to coefficient alpha for the scale (Cronbach, 1951; Fomell & Larcker, 1981). The higher the alpha, 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the stronger the correlations between the various items that constitute the scale, if other factors are equal. The latent health variable demonstrated acceptable levels of reliability, with coefficients of 0.871, in excess of the acceptable level, 0.70. The final column of Table 3 provides the variance extracted estimate for each scale. This is a measure of the amount of variance captured by a construct, relative to the variance due to random measurement error. The latent health variable demonstrated variance extracted estimates equal to 0.446, close to 0.S0, the level recommended by Fomell and Larcker (1981). While the test is quite conservative, very often variance- extracted estimates will be below 0.S, even when reliabilities are acceptable (Fomell & Larcker, 1981). The revised measurement model, Model M2, was also evaluated by using the data from the end of the survey. The final model fit the data from the end of the survey well, with X2 (DF=9, n= 2,218) = 295.227 (p < .01), Bender’s CFI equal to 0.964, NNFI equal to 0.887 and NFI equal to 0.963 (Table 2). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 3. Validity & Reliability of the Latent Health with Eight SF-36 Scales Latent Health Construe! w /1 Eight SF-36 Scales Latent Health Physical Functioning Role Limitation due to Physical Health Body Pain General Health Perceptions Energy/Fatigue Social Functioning Role Limitation due to Emotional Problems Emotional Well-being Convergent validity* g |d Loading t-value Loading 6.492 27.780 0.611 8.564 35.835 0.717 7.366 34.156 0.688 7.267 34.341 0.683 7.452 37.892 0.740 9.613 45.061 0.835 5.441 22.778 0.510 5.942 28.412 0.607 Indicator Variance Eatracted Estimate*** R e lia b ility * * Error Variance R-squarc 0.871** 0.483*** 0.374 0.626 0.514 0.487 0.473 0.527 0.467 0.533 0.548 0.452 0.698 0.302 0.261 0.739 0.368 0.632 Note I m H c b I o c lUHtbUMy Convergent validity* Laical construct rctUbWly** E rror V arian ce V i r t s B C * F il r a r t c d l U t i a u l c * * * P e r c e n t a g e o f v a r i a t i o n I n t h e i n d i c a t o r l h a l U c a p t a i n e d b y ( h e l a t e n t c o n s t r u c t O u t i i ii s u p p o s e d l o m e a s u r e ( L o n g , 1 9 1 3 ) T h e m e a s u r e m e n t w i l l c o r r e l a t e w i l h o i l i e r m e t h o d s t h a t m e a s u r e t h e s a m e c o n c e p t ( M c D o w e l l 1 9 9 9 ) . it a l l ( a c l o r l o a d i n g s f o r t h e i n d i e t a r s n c a s u r i o g t h e s a n e c o n s t r u c t a r c s t a t i s t i c a l l y s i g n i f i c a n t m e a n s l h a l a l l i n d i c a l o n a r e e f f e c t i v e l y m e a s u r i n g D i e s a m e c o n s t r u c t ( A n d e r s o n a n d G c i b i n g 1 9 8 8 ) . A n a n a l o g o f c o e f f i c i e n t a l p h a r e l i a b i l i t y e s t i m a t i o n f o r t h e K a l e ( C r o o b a c h , 1 9 5 1 ) , a n d a n I n d e a o f i n t e r n a l c o n s i s t e n c y r e l i a b i l i t y . T h e h i g h e r a l p h a , t h e s t r o n g e r c o r r e l a t i o n s b e t w e e n t h e v a r i o u s i t e m s t h a t c o n s t i t u t e t h e K a l e , if o t h e r f e c t u r e q u a l . T h e m i n i m a l l y a c c e p t a b l e l e v e l f o r r e l i a b i l i t y f o r i n s t r u m e n t u s e d i n r e s e a r c h : 06 o r 0 . 7 ( 0 . 7 i s p r e f e r a b l e ) T h e p r o p o r t i o n o f v a r i a t i o n i n t h e i n d i c a t o r l h a l i s n o t c a p t a i n e d b y t h e l a t e n t c o n s t r u c t l h a l i s s u p p o s e d l o m e a s u r e . T h e a m o u n t o f v a r i a n c e l h a l i s c a p t u r e d b y a n u n d e r l y i n g f a c t o r i n r e l a t i o n t o t h e a m o u n t o f v a r i a n c e d u e t o m e a s u r e m e n t e r r o r . D e s i r a b l e a c c e p t a b l e l e v e l : 0 . 5 ( H o r n c t i d t L a r c k e r 1 9 8 1 ) Combined these findings generally support the reliability and validity of the latent health constructs and their indicators. The measurement model of a latent health variable measured with 8 scales of the RAND SF-36 (Model M2), was therefore retained as the study’ s final measurement model. Table 3 also provides the important properties of the measurement model. All regression coefficients of the latent health to the RAND SF-36 scales (lambda) are highly significant and have reasonable signs. That is, the latent health was positively related to the 8 scales of the RAND SF-36. The R3 of the measurement model for each scale of the RAND SF-36 ranged from 0.37 to 0.70, except for role limitation due to emotional problems (R2 =0.26). In other words, the measurement model can explain about 40% or more of the RAND SF-36 scale variances with the exception of role limitation due to emotional problems. 4.3 Structural Models The proposed SEMs are identical to those classical linear regression models in terms of model specifications, with the exception that all observed indicators for an individual’ s general perceived health status, the scales of the RAND SF-36, are modeled as a latent health variable. The S AS/CALIS procedure was used to evaluate and estimate these SEMs. In the following sections, the analysis results will be introduced in three groups on the basis of the number of the dependent variable: (1) 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the SEMs with a latent health for a single observed dependent variable (SEMSI) (health care costs or health outcomes with single indicator, such as physical function), (2) the SEM with a latent health for a latent health outcomes variable with multiple indicators (SEMMI), and (3) the SEMs with a latent health for both health care costs and a latent health outcomes variable (SEMHCHOMI). SEMs for an Observed Single Dependent Variable (SEMSI) The group of SEMs is modified by replacing all independent variables for a patient’s perceived health status (the scales of the RAND SF-36) in the classic linear regression models in the previous analyses with a latent health variable that was represented by a group of multiple observed scales of the RAND SF-36. Though the dependent variables were different, the model specification of the SEMSI for health care costs is the same as that of the SEMSI for a single observed health outcomes variable, such as the physical function scale of the RAND SF-36. Therefore, there should be a total of 11 sets of SEMSI, i.e., the SEM for the Total Health Care Costs, Physician Office Visit Costs, Prescription Drug Costs, Physical Functioning, Role Limitation due to Physical Health, Body Pain, General Health Perceptions, Energy/Fatigue, Social Functioning, Role Limitation due to Emotional Problems, and Mental Health. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Model fit indices for the SEMSI models appear in Table 4. Overall goodness of fit indices for the models were practically acceptable, with values on the Bender’s CFI and NFI in excess of 0.90, except the NNFI (0.69-0.77). Table S showed that the regression loadings in the measurement models were statistically significant and with reasonable signs, i.e., the latent health status was positively related to all 8 scales of the RAND SF-36 at the baseline. The SEMSI estimations of the latent health variable in both the measurement model and the structural model were all statistically significant and have reasonable signs (Table S, 6, 8), i.e., the latent health is positively related to health outcomes and negatively related to health care costs. These findings generally provide support for the validity of the proposed SEMSI models. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 4. Goodness-of-Fit Indexes for Structural Equation Models Models Latent Variable Chi-Square DF CFI NNFI NFI SEMSI Null PF_T2 Q O L _ T O Q O L J T O 2154.61 1953 394 0.941 0.706 0.932 RP_T2 Q O L _ T O 1817.13 394 0.951 0.755 0.941 BP_T2 Q O L _ T O 1910.51 394 0.947 0.739 0.938 GH_T2 Q O L _ T O 2193.24 394 0.939 0.696 0.930 VT_T2 Q O L _ T O 2070.51 394 0.942 0.714 0.933 SF_T2 Q O L J T O 1785.04 394 0.951 0.757 0.941 REJT2 Q O L J T O 1899.13 394 0.947 0.737 0.937 MH_T2 Q O L J T O 2180.48 394 0.938 0.693 0.929 PCS_T2 Q O L J T O 2065.85 394 0.943 0.719 0.934 MCS_T2 Q O L _ T O 2091.57 394 0.9418 0.706 0.932 LTC12 Q O L J T O 1764.31 394 0.953 0.767 0.943 LVC12 Q O L J T O 1763.44 394 0.952 0.760 0.942 LRXC12 Q O L J T O 1773.24 394 0.953 0.767 0.943 SEMMI Null QOL_T2 Q O L J T O Q O L JT 2 43044.79 3464.07 2415 836 0.935 0.813 0.920 SEMHCHOMI N u U QOL_T2 Q O L _ T O + LTC12 QOL.T2 44397.659 3494.84 2485 851 0.937 0.816 0.921 QOL_T2 +LVC12 r r 3481.19 851 0.936 0.813 0.920 QOL_T2 +LRXC12 Q O L J T O Q O L JT 2 3491.41 851 0.937 0.817 0.922 Note: CFI: Bender* Comparative Fit Index NM : Bender & Bonett* (1980) Non-nonned Index NFI: Bender & Boneat (1980) NFI QOLJTO: Individual* health-related quality o f life at the haw line QOLJT2: Individual* health-related quality o f life at the end o f survey LTC12: Log Total Health Coats during the last two year LVC12: Log MD Office Visit Coats during the last two year LRXC12: Log Drug Costs during the last taro year PF_T2: Physical Function Scares at the End o f Survey RPJT2: Physical Role Scares at the End o f Survey BPJT2: Body Pain Scores at the Fnri o f Survey GH_T2: General Health Scares at the End o f Survey VTJT2: Vitality Scores at the End o f Survey SF_T2: Social Function Scores at the End o f Survey KEJT2: Emodon Role Scares at the End o f Survey MH_T2: Menial Health Scares at the End o f Survey PCSJT2: Standardised Physical Component Scale at the End o f Survey MCS_T2: Standardised Mental Component Scale at the End o f Survey SEMSI: SEM with a latent health for a jingle Indicator dependent variable SEMMI: SEM with a latent health far a latent health outcomes measured with multiple indicators SEMHCHOMI: SEM with a latent health for both health costs and a latent health outcomes 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 5. Estimations of the Measurement Portions of Structural Equation Models Dependent SEMSI Variable Latent Variable PF_T2 QOL_Ti RP_T2 Q OL_T8 BP_T2 QOL_T8 GH_T2 Q O L J T O VT_T2 Q O L JT O SF_T2 Q O L J T O RE_T2 Q O L JT O MH.T2 Q O L J T O PCS_T2 Q O L JT O MCS.T2 Q O L J T O Measurement Model PF 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 R P 1 .0 3 1 1.190 1.213 1.155 1.210 1.203 1.228 1.289 1.109 1.2826 33.882 30.770 30.312 30.684 29.943 29.912 29.668 28.016 32.648 28.2534 BP 0.831 1 .0 1 1 1.066 1.004 1.046 1.027 1.044 1.122 0.934 1.1032 30.908 27.925 28.025 27.817 26.894 27.012 26.668 25.206 30.147 25.1846 Gil 0.836 0.987 1.024 1.066 1.062 1.023 1.033 1.114 0.945 1.1024 31.996 29.554 29.342 30.588 29.341 28.975 28.740 27.883 31.229 27.8334 V T 0.784 0.870 0.998 0.994 1.061 1.002 1.022 1.127 0.678 1.1159 31.216 28.515 28.084 28.899 28.616 27.877 27.587 26.377 30.260 26.4715 SF 1.060 1.265 1.290 1.247 1.322 1.324 1.337 1.429 1.145 1.4301 32.590 30.003 29.567 29.751 29.277 29.584 29.275 28.006 31.331 28.1307 R E 0.545 0.709 0.728 0.705 0.760 0.748 0.779 0.850 0.614 0.8547 20.037 20.427 20.278 20.355 20.576 20.479 20.754 20.204 20.175 20.4618 Mil 0.548 0.723 0.760 0.729 0.805 0.766 0.792 0.942 0.619 0.9042 21.942 22.409 22.550 22.520 23.024 22.612 22.719 23.385 21.943 22.9436 Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 5. Estimations of the Measurement Portions of Structural Equation Models (C ontinued) vcpenoem SEMSI SEMMI SEMHCHOMI Variable L T C 1 2 LV C I2 L R X C I2 OOLT2 OOLT2ALTC12 OOLT2 a L V C I2 O O L lT2 A L R X C I2 Laical V a r ia b le OOLT8 O O L T8 OOLT8 OOLT8 O O L T2 OOLT8 O O L T2 OOL.T8 Q O L _T 2 QOUT8 O O L T2 Measurement Model PF 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 R P 1 .2 0 1 1.202 1.202 1.192 1.192 1.202 1.202 1.197 1.197 1.199 1.199 20.813 29.753 29.779 38.229 38.229 37.898 37.896 38.055 38.055 37.961 37.961 BP 1.022 1.025 1.024 1.006 1.008 1.018 1.018 1.013 1.013 1.015 1.015 27.002 28.951 26.974 34.409 34.409 34.125 34.125 34.253 34.253 34.181 34.181 Gil 1.009 1.010 1 .0 1 1 1.015 1.016 1.026 1.026 1.020 1.020 1.023 1.023 28.852 28.805 28.842 36.049 36.049 35.789 35.789 35.881 35.881 35.854 35.854 V T 0.987 0.989 0.989 0.994 0.994 1.005 1.005 0.990 0.998 1.002 1.002 27.692 27.644 27.677 35.747 35.747 35.442 35.442 35.596 35.596 36.532 36.532 SP 1.303 1.307 1.304 1.164 1.184 1.175 1.175 1 .171 1.171 1.173 1.173 29.468 29.427 29.437 37.057 37.057 38.706 36.706 36.921 36.921 36.809 36.809 R E 0.724 0.726 0.725 0.783 0.783 0.791 0.791 0.788 0.788 0.789 0.780 20.050 20.045 20.042 28.542 28.542 28.361 28.361 28.465 28.465 28.412 28.412 Mil 0.749 0.752 0.752 0.765 0.765 0.773 0.773 0.770 0.770 0.772 0.772 22.274 22.265 22.283 29.718 29.716 29.513 29.513 29.827 29.627 29.588 29.588 Note: • Parameter Estimation LRXCI2; Log Drug Coats duriag the last two year •• T tuiislks PP_T2: Physical Biectiaa Scores at the Bad of Survey CFI: Bcnlkrb Comparative Bi ladea RP_T2; Physical Role Scores at Ibc Ead of Survey NNFI: Beallcr A Boactlb (1980) Noa-eotmed ladea BP_T2: Body Paia Scores at the Bad of Survey NFI; Bcatkr A Boaetlt (1980) NFI GH.T2: Gcacral Health Scores at ihe Ead of Survey QOL_78: ladividiialfc healdi-relatcd qaalily of life al the base bee VT_T2: Vilabty Scares at the Ead of Survey QOL.T2: ladi videalb health-related qaalily of life al ihe cad of survey SF_T2: Social ftactiaa Scores al the Ead of Sarvey LTCI2: Log Total Health Costs dariag die last (wo year RE_T2: Emotion Role Scores at the Ead of Survey I.VCI2: Log MD Office Visil Costs duriag the last Iwo year MII_T2: Mcatal Health Scores at the Ead of Survey SEM for Latent Health Outcomes with Observed Multiple Indicators (SEMMI) The proposed model tested in this group is identical to SEMSI above, except that a latent health variable at the end of survey was used to replace all single observed dependent health outcomes variables, the multiple scales of the RAND SF-36. Therefore, the SEMMI can simultaneously estimate all health outcomes measured with the RAND SF-36 scales in a single model. In the SEMMI there were two measurement models for the latent health constructs at two different time points, the latent health status at the baseline and the latent health outcomes at the end of survey. The two measurement models for the two different latent health constructs should have measurement invariance over time (Byme, Shavesion, & Muthen 1989; Pentz & Chou 1994). The covariance between residuals of the same measured variables at different time points should also be specified and evaluated to help account for associations caused by unmeasured variables (Bollen 1989; Maruyama 1998; Anderson & Williams 1992; Hays 1994). Fit indices for SEMMI appear in Table 4. Overall goodness of fit indices for the SEMMI was empirically acceptable, with values on the Bender’s CFI and NFI in excess of 0.90. Table 5 shows that the coefficients in the measurement model were statistically significant and with reasonable signs. The SEMMI estimations of the latent health variable in both the measurement model and the structural model are all 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. statistically significant and have reasonable signs. Therefore, the SEMMI practically fits the data well and is a valid simultaneous model for the multiple scales of health outcomes. SEM for both Health Care Costs and Latent Health Outcomes (SEMHCHOMI) The SEM with a latent health for both health care costs and a latent health outcomes variable measured with the multiple scales of the RAND SF-36 (SMHCHOMI) can simultaneously estimate health care costs and all health outcomes measured by the multiple scales of the RAND SF-36 in a single model. Fit indices for the SEMHCHOMI model appear in Table 4. Overall goodness of fit indices for the models were statistically acceptable, with values on the Bender’s CFI and NFI in excess of 0.90. Table S shows that the coefficients in the measurement model were statistically significant and with reasonable signs. The SEMHCHOMI estimations of the latent health variable in both the measurement model and the structural model are all statistically significant and have reasonable signs. Therefore, the SEMHCHOMI empirically fits the data well and is a valid simultaneous model for both health outcomes and health care costs. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4 Effects of the Interventions and the Health Status The coefficients of the latent health constructs in both structural and measurement portions of the SEMs are presented in Table S and Table 6. The regression coefficients of the latent health status in the SEMSIs for the health outcomes ranged from 0.636 to 0.856 (all p<0.01), and those in the model for health care costs ranged from -0.012 to -0.009 (all p<0.05). The coefficient of the latent health status in the SEMMI for the latent health outcome was 0.673 (p<0.01). The coefficients of the latent health status in the SEMHCHOMI for the latent health variable ranged from 0.673 to 0.674 (p<0.01), and those in the model for the health care costs from -0.019 to - 0.010 (p<0.05). In the measurement models, the latent health status was significantly and positively related to all scales of the RAND SF-36. In sum, the coefficients of the latent health variable to the variety of health care costs and health outcomes in the SEMs are all highly statistically significant (p<0.01) and have reasonable signs. That is, the latent health is negatively related to health care costs and positively related to the health outcomes and the 8 scales of the RAND SF-36 at both time points. The coefficients of the intervention variables in the structural portions of the SEMs are presented in Table 6. Only the regression coefficient of the KP model to the prescription drug costs at the last year was found to be significant and negative (£= - 0.119 and p<0.02). The coefficient of the State Model to the prescription drug costs 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. at the last year was found to be negative but not significantly different from zero (0 = -0.016 and p>0.10). It suggests that the members in the group of KP Model spent significantly less money on prescription drugs than those in the Control Model. The Kaiser enrollees in the group of the State Model might spend less money on prescription drug than those in the Control Model. Though the associations were non-significant, the State model was negatively associated with all three types of health costs during the last two-year period. As shown in Table 6 , the coefficient of the State Model to the mental health at the end of the survey was positive and marginally significant (P = 0.9S2 and p<0.05). The regression coefficients of the intervention (the KP or State models) to the other single observed health outcome variables were found to be non-significant (p > 0.0S). Though the associations were non-significant, the KP model was positively associated with the body pain, general health, role limitation due to emotional problems and mental health at the end of survey; the State model was positively associated with the body pain, vitality/energy, social function, role limitation due to emotional problems and mental health at the end of survey. Both intervention policies, KP and State Models, were positively associated with the latent health outcomes at the end of survey. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Table 6. Estimations of the Treatment & Health Status of Structural Equation Models Latent SMSI Variable D ep d ld eU t V ariab le Q O L J T O PFJF2 Q O L J T O RPJF2 Q O L J T O BPJT2 Q O L J T O GII.T2 Q O L J T O VTT2 Q O L J T O SFJT2 Q O L JT O REJF2 Q O L J T O MIIJT2 Q O L J T O FCSJT2 Q O L J T O MCS.T2 Sample Site 2218 2218 2218 2218 2218 2218 2218 2218 2218 2218 C M -square 2154.61 1817.13 1910.51 2193.24 2070.51 1785.04 1899.13 2180.48 2065.85 2091.57 DP 394 394 394 394 394 394 394 394 394 394 CFI 0.941 0.951 0.947 0.939 0.942 0.951 0.947 0.938 0.943 0.941 Structural Model Effect of Treatments Kaiser Model* -0.711 -0.774 0.024 0.495 •0.442 •0.310 0.462 0.701 -0.702 0.622 M 0.451 0.554 0.497 0.448 0.456 0.560 0.556 0.472 0.459 0.506 *** -1.578 -1.398 0.049 1.105 -0.971 •0.554 0.831 1.487 •1.530 1.229 Stale M odel •0.192 -0.251 0.133 •0.266 0.173 0.473 0.965 0.952 •0.590 1.134 0.446 0.548 0.492 0.444 0.451 0.554 0.550 0.467 0.454 0.501 -0.431 •0.458 0.270 -0.598 0.384 0.854 1.753 2.041 -1.299 2.266 larraf M mM Verlebk Q O L J T O 0.707 0.700 0.706 0.856 0.844 0.694 0.636 0.763 0.719 0.712 0.031 0.042 0.040 0.039 0.040 0.044 0.043 0.043 0.034 0.044 23.129 16.591 17.740 22.255 21.064 15.909 14.676 17.953 21.239 16.287 Reproduced with permission o f th e copyright owner. Further reproduction prohibited without permission. Table 6. Estimations of the Treatment & Health Status of Structural Equation Models (continued) Latent SEMSI SEMMI SEMHCHOMI Variable QOLJTO QOLJTO QOLJTO QOLJTO QOLJH QOLJTO Q O LJR QOLJTO QOLJTO QOLJTO QOL_T2 D ependent V ar. LTCI2 LVCI2 LRXCI2 QOL_T2 LTCI2 QOL_T2 LVCI2 QOLJTO LKXCI2 QOL_T2 Sample Size Chi-square D F C F I 2218 1764.31 394 0.953 2218 1763.44 394 0.952 2218 1773.24 394 0.953 2218 3464.07 836 0.935 2218 3494.84 851 0.937 2218 3481.19 851 0.936 2218 3491.41 851 0.937 Structural Model Effeet of Treatm ent* Kaiser Model* 0.002 0.019 ■ 0 .1 1 9 •0.097 0.002 •0.094 0.017 •0.072 -0.119 •0.106 a * 0.045 0.075 0.047 0.297 0.045 0.294 0.075 0.295 0.047 0.296 ••* 0.052 0.256 -2.561 ■ 0 .3 2 6 0.042 •0.318 0.226 -0.242 •2.561 •0.360 Slate M odel •0.019 •0.013 •0.016 0.051 •0.019 0.127 •0.015 0.078 •0.016 0.053 0.045 0.074 0.046 0.293 0.045 0.291 0.074 0.292 0.046 0.292 •0.4264 •0.180 •0354 0.173 •0.419 0.437 •0.198 0.267 •0.334 0.181 Latent Health Variable Q O L J T O -0.012 •0.010 •0.009 0.673 -0.012 0.674 -0.011 0.673 •0.010 0.674 0.003 0.005 0.003 0.021 0.003 0.021 0.005 0.021 0.003 0.021 -3.685 -2.002 •2.674 32.594 •3.946 32.425 •2.216 32.529 •3.049 32.494 Nate; • Para meter Estimslina PFJF2: Physical Atactica Scores at the Bad of Survey •• T statistics RPJTO: Physical Role Scares at the Ead of Survey CFI; Bcallcf* Comparstive Hi lades BPJTO: Body M a Scores at die Bad of Survey NNFI; Bcntlcr a lioactl* (1900) Non-normcd ladea GIIJTO: Ocacral Health Scares at the Bad of Survey NFI: Bcatler k Bcnett* (1990) NH VTJTO: Vitality Scares at the Ead of Survey QOLJTO: Individual* health-related quality of life al the base line SF_T2: Social Hiactiaa Scares at the Ead of Survey QOLJTO: ladivirtual* health-related quality of life at die end of survey RKJTO: Emotion Role Scares at the Ead of Survey LTCI2; Log Total Health Cons during the last two year MILTO: Mental Health Scores at dre Ead of Survey LVCI2; Log MD Office Visit Costs duriag the last two year FC8.T2: Tnitndhril H rystcsl Cnrapoarl M ir at dn B ad of Surrey L9XCI2: Log Drug Costs during the last two year MC8_T2: Snamnttnl H rn l C o w p o a c M S csfc a UieEadcf S am cy 4.5 Model Comparison In the following, the model variations of the effects of the interventions, the health status at the baseline in both structural and measurement models will be presented. The difference between the coefficients estimated by the classical linear regression model (CLRM) and the SEMs for the single observed health outcomes or health care costs (SEMSI) will be reviewed first. Then the difference among the three SEMs (SEMSI, SEMMI, and SEMHCHOMI) will be examined. In the terms of model evaluation, it is a great challenge to assess the SEM over CLRM directly due to lack of good statistical indices. Browne & Cudeck (1983, 1989) proposed a set of goodness-of-fit indices based on cross-validation of covariance matrix (Browne & Cudeck 1983, 1989). Te expected Cross-validation Index (ECVI), a single sample cross-validation based on covariance matrix was used to compare the model fit of the proposed SEM over CLRM models. A statistical software package, AMOS, has a procedure for these cross-validation indexes. However it is not appropriate for complex models and large dataset (Arbuckle 1997). The following strategy was used in the pilot analysis: a. To view CLRM as a special case of SEM, a saturated observed variable model, and to estimate the CLRMs by using the MLE procedure of AMOS. 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. b. To simplify the proposed SEMSI models by dropping the independent variables in their structural portions. c. To calculate and compare the cross-validation index of both the simplified SEMSI and the CLRM in the simplified models by using AMOS. That means that we will test how poor the cross-validation index will be compared to the saturated model (CLRM), if a SEM is modified to have a better interpretability. Table 7. Expected Cross-Validation Index (ECVI) of CLRMs & SEMs Modal DapVar DF X A 2 C F I E C V I Lo90 HI90 CLRM SF-36I_T2 153 10113.21 0 5.372 5.212 5.534 SF-36LT2 0 0 1 0.171 0.171 0.171 SEM PF_T2 86 1191.107 0.906 0.631 0.582 0.683 RP_T2 86 718.416 0.941 0.418 0.381 0.458 BP_T2 86 782.931 0.936 0.447 0.408 0.489 GH_T2 86 1038.543 0.917 0.562 0.517 0.611 VT_T2 86 812.98 0.926 0.506 0.464 0.551 SF_T2 86 619.724 0.949 0.373 0.339 0.411 RE_T2 86 752.901 0.937 0.433 0.396 0.475 M H _T2 86 1051.751 0.912 0.568 0.523 0.617 Note: LVC12: Log MD Office Visit Costs during the last two year LRXC12: Log Drug Costs during the last two year PF_T2: Physical Function Scores at the End of Survey RP_T2: Physical Role Scores at the find of Survey BP_T2: Body Pain Scores at the End of Survey GH_T2: General Health Scores at the End of Survey VT_T2: Vitality Scores at the End of Survey SF_T2: Social Function Scores at the End of Survey RE_T2: Emotion Role Scores at the End of Survey MH_T2: Mental Health Scores at the End of Survey 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The results of cross-validation analyses are showed in Table 7. hi terms of the expected Cross-validation Index (ECVI) calculated by using the simplified models, the proposed SEMSI models were not too bad compare to CLRM in terms of the expected overall discrepancy overall possible calibration sample. The ECVI of the SEMSI could be improved by either increasing parameter or decreasing the degree of freedom of the model, until to find a perfect fit, a saturated model (CLRM). The key is to balance the interpretability and fitness of a model. However, the results should be interpreted with caution due to the limitation mentioned above. Comparisons of the estimations between the classic linear regression model (CLRM or OLS) and the SEMSIs are given in Table 8 . In the corresponding linear regression models (OLS), the following patterns were found: (1) Only some regression coefficients of the single observed indicators of health status, the scales of the RAND SF-36, were marginally significant (such as the coefficients of the physical function, role limitation due to physical health, body pain, general health and vitality/energy in the linear model for the physical function at the end of survey). (2 ) Some of the OLS estimations of the single observed indicators had unreasonable signs, i.e., the signs of the regression coefficients were difficult to interpret. For example, the social function status at the baseline was positively associated with the prescription drug costs (0 = 0.006 and t = 2.401). It is hardly acceptable that better patient health status at the baseline would result in a higher health care costs, if other factors are fixed. (3) The health outcomes at the end of survey were strongly 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. associated with the corresponding variable for health status at the baseline. For example, the physical function at the baseline was positively and highly significantly associated with the physical function at the end of survey (P = 0.546 and t = 23.971). (4) All regression coefficients of the single observed indicators of health status estimated by classical linear regression model were less than those estimated by SEMSIs, the SEMs for a single observed health outcomes variable. While the regression coefficients of health status at the baseline estimated by the SEMSIs were all statistically significant and had reasonable signs in both the measurement and structural portions of SEMSIs. The results suggested that the OLS estimations of the perceived health status are attenuated. The regression coefficients of the interventions, pharmacist consultation models, estimated by the classical linear regression models were close to those SEM estimations (Table 8 ). Only the OLS estimation of the KP model to the prescription drug costs at the last two-year was found to be negative and significant (P = -0.129 and t = -2.730). However, the OLS estimation of the State Model to the mental health scale at the end of survey was not statistically significant (P = 0.714 and t = 1.652). It seems that the estimation of an alternative treatment was hardly contaminated by the measurement errors of health status. Empirically, an OLS estimation of an alternative treatment in such a quasi-experimental study is unbiased and valid. 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 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Jiff llli m j J l r ! I i i l i l SSI sSsiggp ^ k 't'k 's' ” ! **1 i! | 1,111 1 I ? s ^SSHes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SEM, a more general and sophisticated modeling method, can adjust the biased estimations and invalid inference resulting from measurement errors of the independent variable(s) in a CLRM. It is very difficult to directly assess the two kinds of models in terms of model fit, due to shortage of good fit indices. Cross- validation of covariance matrix is a good option. In the present pilot analysis, the SEM at least does not perform worse than CLRM in term of model fitness based on the cross-validation of covariance matrix at the costs of the degree of freedom. SEM is superior to CLRM in estimation and inference, at least equal to CLRM in model fit and prediction. Comparisons among the regression estimations of the three SEMs (SEMSI, SEMMI, and SEMHCHOMI) are presented in Table 5, 6 , and 8 . The difference between the regression coefficients estimated by SEMSI and SEMMI demonstrated that SEMMI can provide some new information for health outcomes research. The regression coefficients of the latent health status and the interventions estimated by SEMHCHOMI ate the same as the corresponding estimations of SEMSI and SEMMI, i.e., the SEMHCHOMI estimations of the interventions to health care costs were the same as those estimated by SEMSI Models (Table 6 ). The SEMHCHOMI estimations of the latent health status to both the latent health outcomes in the structural portions and the observed health indicators in the measurement portions were close to those estimated by SEMMI. For example, both SEM estimations of the 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. latent health status to the log total health costs were around - 0 . 0 1 1 (t values were around -3.0) in both SEMSI and SEMHCHOMI for the total health care costs. The SEM estimations of the latent health status to the latent health outcomes in the structural portions were around 0.674 (t values were around 32.0) in both SEMMI and SEMHCHOMI (Table 6 ). The SEM estimations of the latent health status to the physical function in the measurement proportions were around 1.013 (t values were around 34.0) in both SEMMI and SEMHCHOMI (Table S). As we discussed in Chapter 3 (Methodology), SEMHCHOMI may be recursive, because the health outcomes were measured at the end of survey, while the health care costs were measured by accumulating all health expenditures during the last two-year period. Therefore, health outcomes and health care costs were not truly simultaneously associated. It is not a surprise that the SEMHCHOMI estimations were the same as those estimated by SEMSI for health care costs and SEMMI for the latent health outcomes. In summary, the latent health construct with multiple scales of the RAND SF-36 and the SEMs with the latent health status for health care costs and health outcomes are empirically supported by the data of the KP/USC study. The OLS estimations of the multiple scales of the RAND SF-36 are attenuated by their measurement errors. However, there is no strong evidence to show that the OLS estimations of treatment effect are contaminated by the measurement errors of the multiple scales of the RAND SF-36. If the health outcomes were measured at the end of survey, while the 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. health care costs were measured by accumulating all health expenditures during a period, the estimations of simultaneous modeling for health outcomes and health care costs were the same as those estimated separately by the SEMs for health care costs or the SEM for the latent health outcomes. Table 9. Correlation Coefficients Between SEM Health Status Index (SEMHSI) and Other General Health Status Measures Health Status Measures at Baseline SEMHSI Index at Baseline HUI at Year 2 Correlations P-vahie Correlations P-vaiue Estimated HUI 0.52 0.0001 Analogue Health Status Scale 0.36 0.0001 0.44 0.0001 Sf-36 General Health T-Score 0.47 0.0001 0.49 0.0001 Sf-36 Health Transition Item -0.15 0.0001 -0.24 0.0001 Chronic Disease Score -0.14 0.0001 -0.14 0.0001 # of Physician Office Visits -0.17 0.0001 -0.18 0.0001 # o f Hospital Admissions -0.11 0.0001 -0.11 0.0001 New Prescription in Last 2 Years -0.21 0.0001 -0.26 0.0001 Note: Estimated HUI was estimated from SF-36 using the Dr. Nichol’s algorithm following the steps: 1. Regress HUI2 on the scales of SF-36 and demographics using the Year 2 data. HUCunut, = f (PF. RP, BP. GH. VT. SF. RE, MH. AGE SEX) (R -s q u a re : 0 . 4 7 1 5 ) 2. HUI at the baseline was estimated by the linear model from the Step 1. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 10. Mean Scores in SEM Health Status Index (SEMHSI) and Others General Health Status Measures Between the Cardiovascular and Anxiety Drug Users Health Status Cardiovascular Drue User Anxiety Drue User Measures at Baseline Yes No P-value Yes No P-value N 1473 745 1834 384 SEM HSI 78.99 76.54 0.0001 78.79 75.21 0.0001 Estim ated HUI 0.7958 0.7588 0.0001 0.7931 0.7366 0.0001 Analogue Health 66.95 63.61 0.0001 66.52 62.50 0.0001 Status Scale Sf-36 General Health 48.89 45.34 0.0001 48.33 44.68 0.0001 T-Score Table 11. Mean Scores in SEM Health Status Index (SEMHSI) Between Drug Users and Non-Users Drugs Users Non-user P-value Cardiac D isease 78.99 76.54 0.0001 Anxiety & Tension 78.79 75.21 0.0001 Psychotic Illness 78.26 69.94 0.0001 Respiratory Illness & Asthma 78.55 77.20 0.0001 Depression 78.71 73.72 0.0001 Diabetes 78.44 75.68 0.0001 Hypertension 78.91 77.09 0.0001 Pain 78.86 75.33 0.0001 Pain & Inflammation 79.21 76.79 0.0001 Rheumatic Conditions 78.66 74.79 0.0001 Thyroid Replacement 78.43 75.61 0.0001 Acid Peptic D isease 78.70 74.39 0.0001 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5. Discussion In this chapter, some important theoretical and practical issues regarding the measurement error of patient-reported health status and structural equation modeling will be discussed, Further analyses will be suggested. Though it is well known that measurement error will lead to biased estimation and invalid inference, there were few documents available to examine the consequence of the multiple scales of a HRQOL instrument that are subject to measurement errors. In the present study, a set of structural equation models with a latent health construct represented by the eight scales of the RAND SF-36 was proposed and evaluated by using the completed data with 2,218 patients from the area-wide design survey of the KP/USC study. The latent health construct with the eight scales of the RAND SF-36 and the SEMs with the latent health construct for health care costs and health outcomes are empirically supported by the data from the KP/USC study. The SEM estimations of the latent health variable in both the measurement model and the structural model are all statistically significant and have reasonable signs. That is, the latent health variable is negatively associated to health care costs and positively associated to health outcomes and the 8 scales of the RAND SF-36 at the baseline and at the end of survey. The OLS estimations of the multiple scales of the RAND SF-36 are attenuated by their measurement error. However, there is no strong evidence to show that the OLS estimations of treatment effect are 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contaminated by the measurement error of the multiple scales of the RAND SF-36. The estimations of the KP treatment effect in either costs or health outcomes by using an SEM approach were close to the earlier OLS estimates reported in the McCombs’s papers. The earlier OLS estimations of KP treatment effect were verified to be unbiased by using the SEM approach (McCombs, 1998). In addition, if the health outcomes were measured at the end of survey, while the health care costs were measured by accumulating all health expenditures during a period, the estimations of simultaneous modeling for health outcomes and health care costs were the same as those estimated separately by the SEMs for health care costs or by the SEM for the latent health outcomes. In the present study, we found that the RAND SF-36 scales were highly significant associated with health outcomes and health care costs, and that the OLS estimations of self-reported health status variables are attenuated by their measurement error. It is the first evidence to document the impact of measurement errors associated with the multiple scales of a HRQOL instrument. Whether the patient-reported health- related quality of life (e.g., the RAND SF-36) is a significant health risk adjuster is an important question for health economists. Most empirical studies have reported a negative answer. Only Hombrook’s study using the classical linear regression model and data from Kaiser Permanente demonstrated that the scales of the RAND SF-36 are significant risk-adjusters for adults. However, the signs of OLS estimations of the RAND SF-36 scales in his models were a problem (Hombrook 1995). The results of 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this study offer another explanation for this question. In 1999, Dwyer and Mitchell reported the same kind of results by using the data of Health and Retirement Study (HRS). They found that health problems influence retirement plans more strongly than do economic variables after controlling the potential measurement errors and endogeneity of self-rated health problems (Dwyer and Mitchell 1999). Attenuations due to measurement error in health status measures should be a concern in the study of health economics. The structural equation model is a good option for adjusting the potential bias. Contamination or resonation of measurement error is a very important issue for any health outcomes and health economic studies. Though it is difficult to reason out a clear conclusion for a multiple variables case, according to the previous study based on the simplified two-independent-variable linear regression model, if an explanatory variable (X2) is subject to measurement error, the measurement error impact on its regression coefficient (fe) and other coefficients (such as 0 0 is associated with three factors: ( 1 ) the strength of the true explanatory variable effect (P2), (2 ) the strength of the measurement error (5a2 ), and (3) the true correlation between the explanatory variable (X2)and a treatment variable(s) (Xi). Carroll and Morgan’s study showed that a randomized study design could eliminate the potential bias of measurement error in an ordinary linear square model and yield valid regression estimation and inference for the treatment effect (Morgan 1987, Carroll 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1989). To assess the effects of alternative treatment on health outcomes, treatment variables should be independent of the measurement of the health status at the baseline. After examining the biases in estimating wage equations that may arise from measurement errors in various health proxies, Savoca (1995) advised that if the effect of non-health variables on wages is of primary interest, a researcher could significantly reduce the bias in coefficient estimates by controlling for measurement error in health status measures (Savoca 1995). In the present study, both the strength of the true effects of the patient reported health status (represented by multiple scales of the RAND SF-36) and the strength of their measurement errors were strong enough to be a problem. However, the health status variables were apparently uncorrelated (or at least partially) with the treatments (pharmacist consultation models) in this case where the treatment was assigned by the area-wide study design. Therefore, the linear regression models could produce unbiased estimation and valid inference for the treatment effects. SEM may be more useful in retrospective analyses in which the treatment is not ’ assigned’ but selected by the patient and physician, thus, creating a correlation between health status and treatment effects. It is appropriate for a researcher to examine the correlations between the health status at the baseline and the treatment variable Erst and to use structural equation modeling to adjust the measurement error in health status measures. Although there is considerable debate about the direction of causation between 6 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. health care costs and health outcomes and why the association arises, practically modeling the effect of alternative treatment on health care costs and health outcomes should be based on the data available. If a patient’s health status were measured at different time points during a survey, while his health care costs were measured by accumulating all health expenditures during a given period, then the variables of health outcomes and health care costs were sequential in time series and not truly simultaneously associated. Therefore health outcomes and health care costs can be modeled recursively and estimated separately. It is reasonable that the coefficients estimated by the SEMs with a latent health status for both health outcomes and health care costs were the same as those estimated by the SEMs with a latent health status for health care costs and the SEMs with a latent health status for the latent health outcomes separately. In general, structural equation modeling is an ideal statistical method for health outcomes research. By taking full advantage of strong association among the variables to identify latent variable(s), we can use SEM to separate the measurement error of the variable(s) from the disturbance term in classical linear regression model (Bollen 1989). Therefore, SEM approach can be used to eliminate the estimation bias stemming from both random and systematic errors among measured variables, and to control multiple collinearity among independent variables. The ‘true’ relationships among latent constructs rather than indicator variables can be examined (Judd et. al., 7 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1986, Lu, M.S., 1998). Since multiple indicators are permitted to measure a latent construct (e.g., health status), SEM provides a unique workbench for simultaneous assessment of the relationships among multiple dependent variables in a single model to examine the causality between different variables (Bentler, 1990), both direct and indirect effects among the latent constructs, to evaluate alternative models for given data using comprehensive indices of the overall fit and to test complex hypotheses (Hays & DiMatteo 1987). In this specific case, the nature and measurement health status and health outcomes present a great challenge. Health is a latent variable that can be only measured by variety of proxies. There are strong associations among these proxies and endogeity between health outcomes and health care costs. SEM is particularly well suited to model health status and health outcomes. In the presented study, by taking full advantage of the associations among the multiple measures of a patient’s health status to identify possible latent variable(s) for the patient’s health status, we can use SEM to eliminate the estimation bias stemming from measurement errors among patient reported health measures, and simultaneously assess multiple dependent variables in a single model. Another advantage of SEM over classical linear regression analysis is that SEM can yield an objective health status indices (HSI), or Multiple Indicator Multiple Cause 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Model index (MIMICI) to measure health status and health outcomes. The health status index (SEM/HSI) is fully characterized by objective data-based causes (health determining factors) and health indicators without any concerns from arbitrarily predetermined weights (Wynand 1991). It can integrate different kinds of health information, such as diagnosis, drug usage, and health care utilization, into an comprehensive health index, hi the presented study, an expected latent health status index (SEM/HSI) could be derived from the SEMs. The SEM/HSI was significantly positively associated with Analogue Health Scale (p=0.36, P<=0.0001), SF-36 General Health Scores (p=0 .4 7 , P<=0.0001), and the Health Utility Index (HUI) estimated from SF-36 by using the algorithm developed by Nichol et al. (Nichol, 2000) (p=0.52, P<=0.0001); but significantly negatively associated with the numbers of physician office visits (p=-0.17, P<=0.0001), and hospital admissions (p=-0.11, P<=0.0001) at the baseline, and the number of new prescriptions in the last two year (p=-0.21, P<=0.0001). It is consistent with the HUI at the end of survey, Year 2 (Table 9). The mean scores of SEM HIS was significantly lower in patients using the drugs against cardiac disease (PNoDtug=78.99, PDnig=76.54, P<=0.0001), anxiety & tension (PNoDmg=78.79, PDrug=75.21, P<=0.0001), psychotic illness (PNoDnig=78.26, PDrug=69.94, P<=0.0001), respiratory illness & asthma (PNoDmg=78.5S, PDmg=77.20, P<=0.0001), depression (HNoDnig=78.71, PDrug=73.72, P<=0.0001), diabetes (PNoDrug=78.44, PDmg=75.68, P<=0.0001), hypertension (PN oDm g =78.91, PDrug=77.09, , P<=0.0001), pain (PNoDrug=78.86, pD tu g =75.33, P<=0.0001), inflammation 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0*NoDrog=79.21, Ht>nig=76.79, P<=0.0001), rheumatic conditions (^N oD nigs 78.66, |^D«ug=74.79, P<=0.0001), thyroid replacement (HNoDmg=78.43, jiDnig=75.61, P<=0.0001), and acid peptic disease (HNoDnig=78.70, PDrug=74.39, P<=0.0001), than those without using these drugs. It captures decreased quality of life as measured with the Global Analogue Health Scale, SF-36 General Health Scores, and the estimated HUI in the patients with several diseases or conditions (Table 10-11). The SEM/HSI discriminates well between these drug users and non-users and appears to be a valid index for patient general health status. It is quite common in health-related research that general health status or HRQOL is measured by self-reported instruments with multiple scales. The measurement of the multiple scales of the self-reported HRQOL instrument is subject to measurement error. If two or more variables are measured with errors, the potential inconsistency of the classical linear regression model becomes more complex. Theoretical reasoning is difficult if not impossible. So far this study is the only empirical study available to document the validity of the classical linear regression model where there are multiple variables subject to measurement error. However, the final models and conclusions presented in the paper were based on only one dataset and must therefore be regarded as tentative until the results are replicated in other samples. The estimations and conclusions should be interpreted with caution. The SEM models were also limited to require the dependent variables to be continuous, and 7 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. joint normality distribution assumption if estimated by a MLE procedure. In addition, in the present study, a one-latent health construct model, a latent health construct measured by the multiple scales of the RAND SF-36, was proposed and evaluated. Clinical practice and previous studies showed that there might be two or a couple of factors (such as physical and mental health) underlying the patient perceived health concept represented by the RAND SF-36. The physical and mental health constructs are empirically correlated (Friedman & Booth-Kewley 1987) and distinguished (Hall, Epstein, & McNeil 1989; Hay & Stewart 1990; Ware, Davies- Avery & Brook 1980). Hays (1994) reported a second-order, cross-lagged panel measurement model of the RAND SF-36 with latent physical and mental health. The analyses of physical and mental health constructs revealed substantial stability effects across time (Hays 1994). The present study could be complemented by introducing a second-order measurement model into the SEM for health outcomes and health care costs. Additional suggestions to improve the SEM include using difference variables from baseline as the dependent variable and analyzing sub-groups categorized by risk classification or disease classification of the patients. Unlike classical linear regression model, the SEM estimations of the difference from baseline as the dependent variable (Difference Model) must be specified differently from the 7 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equations modeling the scores at the end of survey as dependent variable (Score Model). In CLRM, the estimations of Difference Model (eg., PF2-PF0) are same as those of Score Model (eg., PF2) except the estimation of the baseline score of the dependent variable (PFo). The difference of two estimations is -1, i.e., the estimation of the baseline score in the difference model is equal to the estimation in the score model (Pi) minus one. While in SEM, the measures of patient reported health were separated from linear regression model and replaced by a latent variable and measurement models. The SEM estimations of the difference variable from baseline as the dependent variable should be interpreted as the changes of the difference from baseline per unit change of an independent variable. However, the utility of SEM in controlling the bias from measurement errors has been adequately demonstrated in the analyses of the Score Models. However, due to the uneven distribution of risk or disease classification of patient and the strong association between the risk or disease classification and the independent variables related to diagnosis, drug use and health care utilization, the sub-group analyses by risk or disease classification of patients may dramatically change the model specifications. However, the health risk and disease confounding effect was control by the relevant independent variables in the presented study. The level of effort needed to conduct the sub-group results analysis is beyond the scope of the dissertation given that. 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bibliography Arbuckle, JL., 1997, AMOS Users’ Guide V 3.6 (SamllWater Corp. and SPSS Inc). Anderson, JC. and Gerbing, DW., 1988, Structural equation modeling in practice: A review and recommended two, step approach. Psychological Bulletin 103,411-423 Anderson, RT. Aaronson, NK. and Wolkin, D., 1993, Critical review of the international assessments of health-related quality of life, Quality Life Research 2, 369-395. Anderson, SE. and Williams, LI, 1992, Assumptions about unmeasured variables with studies of reciprocal relationships: The case of employee attitudes. Journal of Applied Psychology 77,638-650 Bentler, PM., 1980, Multivariate analysis with latent variables: causal modeling, A. Rev. Psychol. 31,419-456. 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Shavelson, RJ. and Muthen, B., 1989, Testing for partial measurement invariance, Psychological Bulletin, 105,456-466 Canadian-Erythropoietin-Study-Group, 1990, Association between recombinant human erythropoietin and quality of life and exercise capacity of patients receiving haemodialysis, BMJ 300, 573-578. Caroll, RJ., 1989, Covariance analysis in generalized linear measurement error models, Statistics in Medicine 8,1075-1093. Cleary, PD. Epstein, AM. Oster, G. Morrissey, GS. Stason, WB. Debussey, S. Plachetka, J. and Zimmerman, M., 1991, Health-related quality of life among patients undergoing percutaneous transluminal coronary angioplasty, Medical Care 2910,939-50. Cody, M, McCombs, JS. And Parker, JP., 1998, The Kaiser Permanent/USC patient consultation study: change in quality of life outcomes, American Journal of Health, System Pharmacy, Vol. 5524,: 2615-20,1998 Croog, SH. Levine, S. Testa, MA. Brown, B. Bulpitt, CJ. Jenkins, CD. Klerman, GL. and Williams, GH., 1986, The effects of antihypertensive therapy on the quality of life, N Engl. J. Med. 314,1657-1664. Cronbach, U , 1951, Coefficient alpha and the internal structure of tests, Psychometrika, 16, 297-334. Cudeck, R. and Browne, MW., 1983, Cross-validation of covariance structures. Multivariate Behavioral Research, 18,147-167 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dwyer, DS, and Mitchell, OS., 1999, Health problems as determinants of retirement: Are self-rated measures endogenous? Journal of Health Economics 18, 173-193. Fomell, C. and Larcker, DF, 1981, Evaluating structural equation models with unobservable variables and measurement error, Journal of Marketing Research 18, 39-50 Fitzpatrick, R. Fletcher, A. Gore, S. Jones, D. 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Sherboume CD. and Mazel RM., 1992,, The RAND 36-Item Health Survey 1.0., Health Economics, 2,217-227 Hays RD. Marshall, GN. Yu, E. Wang, I. and Sherboume, CD., 1994, Four-year cross-lagged associations between physical and mental health in the Medical Outcomes Study. J Consult Clin Psych 62, 441-449 Health Assessment Lab, 1999, http://qmetric.com/products/publications/ sf36bibliographv.php3. accessed on Oct. 13,2000 Hombrook, MC. and Goodman, MJ., 1995, Assessing relative health plan risk with the RAND-36 Health Survey. Inquiry 32, 56-74. Hsiao, C., 1984, Identification. Handbook of Econometrics. G.-Z. a. Intriligator, MO., Amsterdam (North, Holland. I)- Huba, GJ. and Harlow, L., 1987, Robust structure equation models: implications for developmental psychology. Child Development 58,147-166. Kerwin, ML. Howard_GS. Maxwell, SE. and Borowski, JG., 1987, Implications of covariance structure analysis (LISREL) versus regression models for counseling research. 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Groshen, SL. and Nye, MT., 1998, The Kaiser Permanente/ USC patient consultation study: The use and cost of health care services, American Journal Of Health, System Pharmacy 55 (23), 2485-99. McDowell, I, Newell C., 1996, Measuring Health: A Guide to Rating Scales and Questionnaires. New York, NY, (Oxford University Press). McHomey, CA. Ware, JE Jr. Rogers, W. Raczek, AE. and Lu, JFR., 1992, The validity and relative precision of MOS short- and long-form health status scales and Dartmouth COOP char. Medical Care 30(MS), MS253-MS265. McHomey, CA. Ware, JE Jr. and Raczek, AE. 1993, The MOS 36-item short, form health survey (SF-36), H: psychometric and clinical tests of validity in measuring physical and mental health condition. Medical Care 31,247-263. McHomey, CA. Ware, JE Jr. Lu, JFR. and Sherboume, CD., 1994, The MOS short, form health survey (SF-36) III: tests of data quality, scaling assumptions, and reliability across diverse patient group. Medical Care 32,40-66, 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Morgan, T.M. and Elashoff, R.M., 1987, Effect of covariate measurement error in randomized clinical trials. Statistics in Medicine 6,31-41. Mulaik, SA. James, LR. van Alstine, J. Bennett, N. Lind, S. and Stllwell, DD., 1989, An evaluation of goodness-of-fit indices for structural equation models, Psychological Bulletin, 10S, 430445. New England Health Institute, 1992, http://qmetric.com/products/publications/ sf36bibliographv.php3. accessed on Oct.13,2000 Nichol, MB, Sengupta, N and Globe, DR, Evaluating Quality-Adjusted Life Years: Estimation of the Health Utility Index (HUI2) from the SF-36, Medical Decision Making, 21(2), 105-112 Pentz, MA. and Chou, CP., 1994, Measurement Invariance in longitudinal clinical research assuming change from development and intervention, Journal of Consulting and Clinical Psychology 62(3), 450-462 Plummer, M., 1993, Measurement error in dietary assessment: an investigation using covariance structure models. Part I. Statistics in Medicine 12(10), 925-35. Rothenberg, RB., 1990, Chronic Diseases in the 1900s. SAS Institute Inc., SAS Version 6.12 Manual, SAS Institute Inc., 1998. Savoca, E., 1995, Controlling for mental health in earnings equations: what do we gain and what do we lose? Health Economics, 4(5), 399410. Siegrist, J. and Junge, A., 1989, Conceptual and methodological problems in research on the quality of life in clinical medicine. Social Sci Med 29,463-468. Stewart, A., 1988, Psychometric Considerations in Functional Status Instruments, The workshop on functional status measurement in primary care, the Classification Committee of WONCA (the World Organization of National Colleges, Academies and Academic Associations of General Practitioners/Family Physicians), Calgary, Alberta, Canada, October, 1988. Ware, JE. Davies-Avery, A. and Brook, RH., 1980, Conceptualization and measurement of health for adults in the Health Insurance Study: Vol6 , Analysis of relationships among health status measures Publication No. R, 1987/6-HEW, Santa Monica, CA, (The RAND Corporation). 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ware, JE. and Sherboume, CD., 1992, 'The MOS 36-item short, form health survey SF-36,, I: conceptual framework and item selection.” Medical Care 30,473-483. Ware, JE, Stewart, A. Tarlov, AR., 1992, Measuring Functioning and Well Being, The Medical Outcomes Study Approach. Durham and London, (Duke University Press). Ware, JE. Snow, KK. Kosinski, M. and Gandek, B., 1993, SF-36 Health Survey: Manual and Interpretation Guide, Boston, MA, (The Health Institute, New England Medical Center). World Health Organization, 1958, The first ten years of the World Health Organization, (Geneva: World Health Organization). Wu, DM., 1973, Alternative tests of independence between stochastic regressors and disturbances, Econometrica, 41,733-50 Wynand, P. and Evenlien, MH., 1991, The MIMIC health status index What it is and what it does, Econometrics of Health Care. Paelinck, JHP, (Kluwer Academic Publishers) Yanez m , ND. Kronmal, RA. and Shemanski, LR., 1998, “The effects of measurement error in response variables and tests of association of explanatory variables in change models.” Statistics in Medicine 17, 2597-2606. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendices Appendix I. The Consequence of Measurement Error In general terms, suppose that the regression involves two sets of independent variables, Xi and X2. X| is a matrix of observation variables without measurement errors, X2* is a matrix of unobservable true variables, X2* is observed as X2 with measurement errors, and ‘y’ is a vector of dependent variables in which we are interested, such as health outcomes variables. y = Xi P i + X2 * + v (Nxl) (Nxk) (kxl) (Nxg) (gxl) (Nxl) X2 = X2*+ U (Nxg) (Nxg) (Nxg) Assumption: E(U)=0, E(v)=0, E(uv )=0, u is the I-th column of U where, Pi is a vector of parameters for Xi, P2 is a vector of parameter for X2*. V is a vector of error term for the regression model. U is the matrix of measurement errors of X2* Ignoring the measurement error, we have a regression model, y =X, P,+ X2 Pj+ e (Nxl) (Nxk) (kxl) (Nxg) (gxl) (Nxl) = X B + e Nx(k+g)][(k+g)xl)] (Nxl) 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where, e = v - u p 2 , X = (Xi.X2 ), B = (Pi* p2’)’ If ordinary least squares method (OLS) is used, the OLS estimator of B, b b = (X X) lX y = B + (X' X) lX e is biased because ‘e’ and ‘X’ are not independent, since ‘X ’ contains X2. (i.e. E(X2’U )o O ), For large samples with sample size N, b-B= (X’ X/N)’lX e/N We assume that the following limits exist: Plim(X X/N) = plim Plim(Xe/N) = plim[X’(v - Up2)/N] = plim X 1 X 1IN Xi’X z/N ' Var(Xi) Cov(Xi'Xz) Xz'Xi/N Xz'Xz/N Cov(Xz’X 1 Var(Xz) X \(v-U 0 z)/N X'z(y-Upz)fN = plim 0 -Var(fJ)0z Therefore, the inconsistency may be expressed as PIim(b - B) = plim b \-0 \ bz — 0 z plim(bt - P s) = VQCO-'CovOCtXz) [VarCXO-CovCX, X2 )V ar(X 2) 'lCov(X 2.X l)]',Var(U) fa piim(b2 - P2) = * [V ar(X 1 )-Cov(X l X2 )Var(X2 ) 1 Cov(X2 .X 1 ) ] 'IVar(U) p 2 When X2 is a single variable X 2. then 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Var(U) = §u2 and [Var(Xl)-Cov(Xl.x2 )Var(x2)',Cov(x2,Xl)] = S ^ d -R x m 2 ) RX ix 2 is the multiple correlation coefficient between Xi and x2. plim(b! - PO ={Cov(XlX2 y V(Xi)}{5u2 M 5x22(1-Rxix22)]} plimOh - p 2 ) = - 8u2 P2 /[ S ^ ^ l - R x ^ 2 )] The coefficient estimates of both subsets are inconsistent. Because §u2 and [ 5x2 (l- Rxix22 )] are positive scalars, the sample bias of the parameter estimate of p2 is biased downward to zero. However, the direction of asymptotic bias of Pi is difficult to predict, since it depends on both the bias in p2 and Cov(XiX2)/ V(Xi), which is the probability limit of the least squares estimator of the parameters in the ‘auxiliary* regression of x2 on Xi. E(x2|X1i Xi^Xn Xlk)=vX , In sum, if a variable is subject to measurement error, then it will not only affect its own parameter estimate (attenuation), but it will also affect the parameter estimates of other variables that are measured without error (resonation). 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Controlling for biases from measurement errors in health outcomes research: A structural equation modeling approach
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