Joint modeling compliance and outcome for causal analysis in longitudinal studies.

This article discusses joint modeling of compliance and outcome for longitudinal studies when noncompliance is present. We focus on two-arm randomized longitudinal studies in which subjects are randomized at baseline, treatment is applied repeatedly over time, and compliance behaviors and clinical outcomes are measured and recorded repeatedly over time. In the proposed Markov compliance and outcome model, we use the potential outcome framework to define pre-randomization principal strata from the joint distribution of compliance under treatment and control arms, and estimate the effect of treatment within each principal strata. Besides the causal effect of the treatment, our proposed model can estimate the impact of the causal effect of the treatment at a given time on future compliance. Bayesian methods are used to estimate the parameters. The results are illustrated using a study assessing the effect of cognitive behavior therapy on depression. A simulation study is used to assess the repeated sampling properties of the proposed model.