A non-parametric Bayesian approach for adjusting partial compliance in sequential decision making.
Indrabati Bhattacharya, Brent A Johnson, William J Artman, Andrew Wilson, Kevin G Lynch, James R McKay, Ashkan Ertefaie
Author Information
Indrabati Bhattacharya: Department of Statistics, Florida State University, Tallahassee, Florida, USA. ORCID
Brent A Johnson: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, USA.
William J Artman: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, USA. ORCID
Andrew Wilson: Courant Institute of Mathematical Sciences, New York University, New York, New York, USA.
Kevin G Lynch: Center for Clinical Epidemiology and Biostatistics and Department of Psychiatry, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
James R McKay: Department of Psychiatry, University of Pennsylvania, Philadelphia, Pennsylvania, USA.
Ashkan Ertefaie: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, USA. ORCID
Existing methods for estimating the mean outcome under a given sequential treatment rule often rely on intention-to-treat analyses, which estimate the effect of following a certain treatment rule regardless of compliance behavior of patients. There are two major concerns with intention-to-treat analyses: (1) the estimated effects are often biased toward the null effect; (2) the results are not generalizable and reproducible due to the potentially differential compliance behavior. These are particularly problematic in settings with a high level of non-compliance, such as substance use disorder studies. Our work is motivated by the Adaptive Treatment for Alcohol and Cocaine Dependence study (ENGAGE), which is a multi-stage trial that aimed to construct optimal treatment strategies to engage patients in therapy. Due to the relatively low level of compliance in this trial, intention-to-treat analyses essentially estimate the effect of being randomized to a certain treatment, instead of the actual effect of the treatment. We obviate this challenge by defining the target parameter as the mean outcome under a dynamic treatment regime conditional on a potential compliance stratum. We propose a flexible non-parametric Bayesian approach based on principal stratification, which consists of a Gaussian copula model for the joint distribution of the potential compliances, and a Dirichlet process mixture model for the treatment sequence specific outcomes. We conduct extensive simulation studies which highlight the utility of our approach in the context of multi-stage randomized trials. We show robustness of our estimator to non-linear and non-Gaussian settings as well.
