The proposed research will develop methods for the statistical analysis of serial observations obtained in longitudinal studies. Such studies are fundamental to research on growth, developments. aging, and chronic disease. A variety if diverse methods for longitudinal data are in use or under development. Most methods in widespread use are inappropriate and/or inadequate because of their failure to correctly model serial corrrelation, and their inability to correctly handlle missing data and subject attrition. The biases induced by the use of inadequate statistical methods are not widely appreciated. The proposed research will focus specifically on modelling serial correlation and on the developmemt of methods which can handle unbalanced designs, missing observations and subject attrition. A major focus of our work continues to be the use of random effects models. They offer a unified approach to the analysis of serial responses, including growth curves and repeated measures data. The general methodology for linear models with measured response was developed during our preceding grant period, using empirical Bayes estimation anf the EM algorithm; proposed work focuses on model validity and robust estimation methods. The proposed research will develop new approaches to random effects models with categorical response, and will, in addition, consider extensions of the general approach to deal with nonlinear models for measured response. We also propose Bayesian modifications to the estimation methods to stabilize estimated variance and covariance components, and speed converging of the EM algorithm. The current proposal extends the scope of previous research by including the development of analytical methods based in autoregressive and renewal models. Work will proceed in parallel for meadured and categorical responses. The proposed research will develop a series of case studies, which compare a variety of analytical methods, especially time series and random effects models, using data collected in ongoing longitudinal studies. Finally, we propose to develop explicit models for subject attrition in longitudinal studies. Models which allow the probability of selection to depend upon latent variables or unobserved variables will be developed, and contrasted with the """"""""usual"""""""" models, which assume that selection can be explained entirely as a result of observed history.
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