Complex dependent data involving cluster sampling, longitudinal designs and hierarchical sampling schemes arise frequently in epidemiologic studies of aging and chronic diseases. Such data allow investigators to estimate important effects of covariates on response in an efficient manner. For example, longitudinal data are essential to assess changes in health status over time and determinants of those changes; cluster designs arise naturally in studies involving groups such as families or as the only feasible way to gather large probability samples. Generalized linear mixed models and marginal methods such as generalized estimating equation approaches provide effective analyses of complex dependent data but give rise to additional estimation/inferential/interpretational problems that this proposal will address. Generalized linear mixed models typically involve intractable integrals and popular methods for avoiding this integration yield highly biased estimates of covariate effects and variance components. The generalized estimating equations approach offers several alternative methods for confidence interval construction and variance estimation but few studies have examined or compared the performance of these methods and no guidelines exist to help data analysts choose appropriate and efficient methods or to understand why different methods yield different results. Case-control family designs should allow investigators to more efficiently estimate the associations of interest in the case-control sample, to estimate associations controlled for family characteristics and propensities and to measure familial aggregation (within-family dependence) of the response. However, there has been little investigation of statistical methods for such data. This research will develop and evaluate statistical methods to analyze complex dependent data by developing and evaluating methods for fitting generalized linear mixed models; developing guidelines for the choice of appropriate and efficient confidence interval construction and variance estimation for marginal models; and developing and evaluating methods to analyze case-control family data. This research extends our previous work and addresses many of the issues raised by the 1996 Nantucket conference on the state of the art of methods for longitudinal data analysis and 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 comparisons of alternative approaches will identify which are the best for specific applications as well as potentially identify new methods. The results of this research will provide clear guidelines as to the advantages and disadvantages of alternative approaches so that biomedical investigators can effectively construct and use longitudinal and cluster study designs, perform improved inference and avoid inappropriate analyses or incorrect interpretations.
