Longitudinal studies continue to grow in importance in medical research. Though statistical methods for the analysis of longitudinal data were severely limited ten years ago, a sustained program of research by the investigators submitting this proposal and other methodologists has led to the creation of important new methods for the analysis of longitudinal data, including the family of random effects models for analysis of continuous variables obtained in unbalanced or incomplete designs, and the methods based on generalized estimating equations. Despite these important advances, many gaps exist in the methodology presently available for longitudinal data analysis. This proposal describes research which will provide new methods to fill several of the important gaps. The proposed research will extend methodology in three directions. First, the investigators will develop statistical methods to solve several important problems which are not adequately addressed by current methodology. They will 1) develop methods for the analysis of longitudinal data when respondents. belong to a clustered sample, 2) extend the split-plot ANOVA commonly used in the analysis of repeated measurements to allow a broader class of correlation structures based on random effects models, 3) develop maximum likelihood methods for the analysis of discrete longitudinal data, and 4) develop methods for the combined analysis of waiting times (to death or medical events) and repeated observations of continuous measures of health status. Second, they will develop methods for analysis of correlated data when the correlation arises from spatial dependency, and for investigating measurement error in spatially correlated data when the covariates axe also spatially correlated. Third, they will develop graphical and numerical methods which examine the adequacy of the assumptions underlying the random effects models used in the analysis of longitudinal data.
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