Complex dependent data involving cluster sampling, longitudinal designs and other forms of correlated data arise frequently in studies of health. For example, longitudinal data are essential to assess changes in health status over time and determinants of those changes. Cluster designs arise naturally in sample surveys, in group randomized trials, in health care profiling of institutions or physicians and in studies of familial aggregation of disease. Models incorporating random effects such as generalized linear mixed models and non-linear mixed effects models provide effective analyses of such complex dependent data but typically require the specification of the distribution of the random effects. The consequence of misspecifying aspects of the distribution of the random effects is of considerable debate in the literature. Some research has shown that such misspecification can produce biased estimates of parameters of interest and potentially misleading inference while other research has demonstrated that there is little impact. Through theory, simulation and application to real datasets, this application will investigate, in a systematic and unified way, which aspects of the specification of a random effects distribution are innocuous as opposed to important, how to diagnosis specification errors, and develop possible remedies to those errors. The proposed work will investigate the effects of misspecifying random effects distributions in nonlinear mixed models by 1) conducting a comprehensive assessment of the bias and efficient loss due to misspecification of random effects distributions; 2) developing and evaluating the performance of diagnostic methods to detect misspecification of random effects distribution; 3) investigating the performance of methods that may minimize the effects of misspecification of random effects distribution in nonlinear mixed models. This research extends our previous work and addresses many of the issues raised by the 1999 NSF-CBMS Regional Conference on generalized linear mixed models. We will produce illustrative, comparative analyses of data from several longitudinal and clustered studies of chronic disease. The results of this research will explain seemingly contradictory findings in the literature, provide a thorough assessment to the consequences of misspecifying random effects distributions and provide new methods to detect such misspecification. The results will provide biomedical investigators with effective methods to analyze data gathered using longitudinal and cluster study designs and guidelines for avoiding inappropriate analyses. The proposed research will comprehensively assess the consequences of misspecifying features of methods commonly used to analyze data in longitudinal studies of health. The research will develop new statistical methods to help investigators avoid misleading and inappropriate analyses and will provide them with effective methods to study important issues in studies of health. ? ? ?
