In experimental aging studies and other longitudinal studies, it has become increasingly common to observe an event time of interest, called survival time, along with longitudinal covariates measured at several time points. A growing interest in the scientific community is to model both processes simultaneously to explore their relationship and to borrow strength from each component in the model building process. Such joint modeling approaches have become feasible due to the rapidly improving computing environment. Quite a few innovative approaches have been proposed in the last decade, but they typically involve strong model restrictions. This proposal aims at developing less restrictive alternative models and targets the associated computational and theoretical challenges. We will develop: 1. Nonparametric mixed-effects approach for longitudinal covariates that provide model flexibility; 2. More general survival models and approaches, and model checking tools for the survival component; 3. The method of sieves to alleviate the computational burden and to provide computational stability; 4. User-friendly software including applications of aims 1-3 to aging studies; 5. Additional tools to incorporate non-ignorable censoring and various measurement error structures. This research is motivated by several aging studies that address the relationship between patterns of reproduction and longevity. It draws tools from a related area called Functional Data Analysis, viewing the observed longitudinal data as scattered realizations of a smooth underlying process, possibly observed with measurement errors. The new approaches will not only shed light on the relationship between life-span and longitudinal markers such as reproductive histories, but will also be broadly applicable to clinical and epidemiological studies. They involve emerging statistical tools that will provide advanced methodology and flexible approaches to model complex biological systems, and will also facilitate model checking.
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