A central theme in mental health services research is the characterization of patterns of service utilization and the identification of their determinants. For example, there is considerable interest in the effects of changes in the health care delivery system on utilization of inpatient, outpatient, emergency room, and home mental health care services. Although considerable statistical worlc in this area has been conducted (see Gibbons 2001 for an overview), little work, ifany, has been done to incorporate both the longitudinal and multivariate nature of health services research data. While some investigators have proposed approaches to the analysis of multivariate patterns of service use in cross-sectional data, and others have proposed longitudinal approaches for the analysis of a single service use repeatedly measured over time, very little if any work has been done on the analysis of longitudinall; measured multivariate service utilization data. Simple piecemeal univariate analyses ignore the correlated and often compensatory nature of service utilization data (eg. health care system changes that lead to decreases in emergency room use may lead to increase in outpatient treatment use). In this study, we will develop a general mixed-effects multivariate probit regression model for the simultaneous analysis of repeatedly measured multivariate binary data. Correlations between multiple binary measures at a single point in time are modeled as a factor analytic process, and correlation among the repeated measurements over time are modeled as : random-effects process. The net result is that we can now model the effects of design variables (e.g, changes in the health care delivery system) and case mix variables (e,g., age, sex, and race) on multivariate utilization patterns. Generalizations of the mode will include, extension to ordinal response data (e.g., no use, mild use, moderate use, high use, or O visits, I, visit, 2 visits, 3 or more visits), mixtures of discrete and continuous responses (e.g., the joint analysis of service utilization and cost), and extension to a multivariate logistic regression model. An integral part of the project will be to both explore and develop alternative approaches to likelihood evaluation (fixed-point and adaptive quadrature, Laplace approximation, and Monte Carlo integration), parameter estimation (Newton Raphson, Fisher scoring, and the EM algorithm), and hypothesis testing. A large-scale simulation study will b conducted to study the statistical properties of the general model and various alternative formulations. Finally, the model will be applied in the analysis of data collected by Dr. Margarita Alegria at the University of Puerto Rico on the effects of health care reform on longitudinal mental health services utilization. In addition to development of the statistical theory and estimation procedure, we propose to develop a WINDOWS based freeware computer program, MIXMVP, to be distributed from the MIXREG/MIXOR web site www.uic.edu/labs/biostat. No general multivariate probit regression software is currently available. ? ?
