A marginal structural model for partial compliance in smarts

The cyclical and heterogeneous nature of many substance use disorders highlights the need to adapt the type and/or the dose of treatment to accommodate the specific and changing needs of individuals. The Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE) is a sequential multiple assignment randomized trial (SMART) that provided longitudinal data for constructing dynamic treatment regimes (DTRs) to improve patients' engagement in therapy. However, the high rate of noncompliance and lack of analytic tools to account for noncompliance has impeded researchers from using the data to achieve the main goal of the trial; namely, construction of individually tailored DTRs. We address this by defining our target parameter as the mean outcome under different DTRs for potential compliance strata and propose a marginal structural model with principal stratification to estimate this quantity. We model the principal strata using a Bayesian semiparametric approach. An important feature of our work is that we consider partial rather than binary compliance strata, which is more relevant in longitudinal studies. We assess the performance of our method through simulation. We illustrate its application on ENGAGE and demonstrate the optimal DTRs depend on compliance strata compared with ignoring compliance information as in intention-to-treat analyses.