Joint modeling of longitudinal data and informative dropout time in the presence of multiple changepoints

In longitudinal studies of patients with the human immunodeficiency virus (HIV), objectives of interest often include modeling of individual-level trajectories of HIV ribonucleic acid (RNA) as a function of time. Such models can be used to predict the effects of different treatment regimens or to classify subjects into subgroups with similar trajectories. Empirical evidence, however, suggests that individual trajectories often possess multiple points of rapid change, which may vary from subject to subject. Additionally, some individuals may end up dropping out of the study and the tendency to drop out may be related to the level of the biomarker. Modeling of individual viral RNA profiles is challenging in the presence of these changes, and currently available methods do not address all the issues such as multiple changes, informative dropout, clustering, etc. in a single model. In this article, we propose a new joint model, where a multiple-changepoint model is proposed for the longitudinal viral RNA response and a proportional hazards model for the time of dropout process. Dirichlet process (DP) priors are used to model the distribution of the individual random effects and error distribution. In addition to robustifying the model against possible misspecifications, the DP leads to a natural clustering of subjects with similar trajectories which can be of importance in itself. Sharing of information among subjects with similar trajectories also results in improved parameter estimation. A fully Bayesian approach for model fitting and prediction is implemented using MCMC procedures on the ACTG 398 clinical trial data. The proposed model is seen to give rise to improved estimates of individual trajectories when compared with a parametric approach.