A Markov compliance behavior and outcome model for causal analysis in longitudinal studies

We propose a Markov compliance behavior and outcome model for analyzing longitudinal randomized studies when non-compliance cannot be ignored. We consider longitudinal studies where subjects are randomized to the treatment or control group only at baseline, but subjects' compliance behaviors may vary over time. The proposed model solves the problem in the potential outcome framework, and provides causal estimates on the treatment effect via principal stratification. Previous research (Lin, Ten Have, and Elliott, JASA 2007) considered the effect of subjects' joint compliance behavior on the joint distribution of the longitudinal outcomes, but not the effect of outcomes at time t-1 on the compliance behaviors at time t, which is often of great interest to investigators. The proposed Markov compliance behavior and outcome model provides estimates both on the effect of the compliance behavior on the following outcome, and on the effect of the outcome on the following compliance behavior. The model requires assumptions to be made about the unobservable correlation among a subject's potential outcomes. We conduct a sensitivity analysis by varying the correlation. We applied the proposed model on a longitudinal study and estimate the parameters and causal effect using Markov chain Monte Carlo (MCMC) methodology.