  The cyclical and heterogeneous nature of many substance use disorders
highlights the need to adapt the type 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 multi-stage randomized trial
that aimed to provide longitudinal data for constructing treatment strategies
to improve patients' engagement in therapy. However, the high rate of
noncompliance and lack of analytic tools to account for noncompliance have
impeded researchers from using the data to achieve the main goal of the trial.
We overcome this issue by defining our target parameter as the mean outcome
under different treatment strategies for given potential compliance strata and
propose a Bayesian semiparametric model to estimate this quantity. While it
adds substantial complexities to the analysis, one important feature of our
work is that we consider partial rather than binary compliance classes which is
more relevant in longitudinal studies. We assess the performance of our method
through comprehensive simulation studies. We illustrate its application on the
ENGAGE study and demonstrate that the optimal treatment strategy depends on
compliance strata.
