In many medical studies, data are collected simultaneously on multiple biomarkers from each individual. Levels of these biomarkers are measured periodically over certain time duration, giving rise to longitudinal trajectories. The subjects under study may also be subject to dropout due to several competing causes, the likelihood of which may be affected by the levels of these biomarkers. In this dissertation, we investigate flexible Bayesian modeling of such data, taking into account any available covariate information as well as possible censoring of the drop-out times. We propose joint models for multiple biomarkers with multiple causes of dropout. Our proposed models allow the trajectories to have multiple joinpoints, the locations of which are estimated from the data. We explore two ways of modeling longitudinal data incorporating the dropout information. Dirichlet process priors are used to make the models robust to misspecication. The Dirichlet process also leads to a natural clustering of subjects with similar trajectories, which can be of importance in efficiently estimating the joinpoints. Efficient Markov chain Monte Carlo algorithms are developed for fitting the proposed models. The performance of all the methods is investigated through simulation studies. One of the proposed models is seen to give rise to improved estimates of individual trajectories. Data from ACTG 398 study is used to illustrate the applicability of that model
