A mixture model for longitudinal data with application to assessment of noncompliance

In clinical trials of a self-administered drug, repeated measures of a labo ratory marker, which is affected by study medication and collected in all t reatment arms, can provide valuable information on population and individua l summaries of compliance. In this paper. we introduce a general finite mix ture of nonlinear hierarchical models that allows estimates of component me mbership probabilities and random effect distributions for longitudinal dat a arising from multiple subpopulations, such as from noncomplying and compl ying subgroups in clinical trials. We outline a sampling strategy for fitti ng these models, which consists of a sequence of Gibbs. Metropolis-Hastings , and reversible jump steps, where the latter is required for switching bet ween component models of different dimensions. Our model is applied to iden tify noncomplying subjects in the placebo arm of a clinical trial assessing the effectiveness of zidovudine (AZT) in the treatment of patients with HI V, where noncompliance was defined as initiation of AZT during the trial wi thout the investigators' knowledge. We fit a hierarchical nonlinear change point model for increases in the marker MCV (mean corpuscular volume of ery throcytes) for subjects who noncomply and a constant mean random effects mo del for those who comply. As part of our Fully Bayesian analysis, we assess the sensitivity of conclusions to prior and modeling assumptions and demon strate how external information and covariates call be incorporated to dist inguish subgroups.