Bayesian Joint Modeling of Longitudinal and Time-to-Event Data with Application to Alzheimer's Disease

In many longitudinal epidemiological and clinical studies, it is routine to collect multiple repeated measures, as well as one or multiple time-to-event outcomes. The follow-ups are usually long enough to measure some aspects of the disease. It would be interesting and appropriate to link the longitudinal marker trajectories in a joint model approach in association with the time-to-event outcomes for valid inferences. The joint modeling method has attracted increasing attention in the statistical field recently and many extensions have been explored. In this dissertation, several research topics related to joint modeling of the longitudinal and time-to-event data were investigated. The first part of the work was to construct the Bayesian joint models based on two different linking structures: latent class framework and shared random effects framework. Both single and bivariate longitudinal outcomes were considered. The second part of this work was to propose a joint model with a random changepoint for the non-linear longitudinal marker trajectories. We investigated 5 different formulations to characterize the transition zone for the changepoint data. We further extended the model for a bivariate longitudinal data with correlated changepoints and took into account the competing risks and interval censor in the survival model, which is methodologically challenging. We adopted Bayesian approach for statistical inference and the proposed methodologies were evaluated based on simulation studies. The motivational application for this study is based on the Memory and Aging Project of Rush University Medical Center. Alzheimer’s disease, like many other chronic diseases, is a neurodegenerative disease involving a long-term process of cognitive decline and motor dysfunction which often begin before the disease diagnosis. The statistical methodological development in this dissertation aims for a better understanding of the natural history of pre-dementia cognitive aging, motor function change and time to Alzheimer’s disease by joint modelling these outcomes together for more insightful and valid statistical inferences.