A Dirichlet Process Mixture Model for Non-Ignorable Dropout

. Longitudinal cohorts are a valuable resource for studying HIV disease progression; however, dropout is common in these studies. Subjects often fail to re-turn for visits due to disease progression, loss to follow-up, or death. When dropout depends on unobserved outcomes, data are missing not at random, and results from standard longitudinal data analyses can be biased. Several methods have been proposed to adjust for non-ignorable dropout; however, many of these approaches rely on parametric assumptions about the distribution of dropout times and the functional form of the relationship between the outcome and dropout time. More flexible approaches may be needed when the distribution of dropout times does not follow a known distribution or violates proportional hazards assumptions, or when the relationship between the outcome and dropout times does not have a simple polynomial form. We propose a Bayesian semi-parametric Dirichlet process mixture model to flexibly model the relationship between dropout time and the outcome and show that more accurate inference can be obtained by non-parametrically modeling the distribution of subject-specific effects as well as the distribution of dropout times. Results from simulation studies as well as an application to a longitudinal HIV cohort study database illustrate the strengths of our Bayesian semi-parametric approach.