A non-parametric Bayesian approach for adjusting partial compliance in sequential decision making

TL;DR

This paper introduces a non-parametric Bayesian method to accurately estimate the effects of dynamic treatment regimes accounting for patient compliance, addressing biases and generalizability issues in high non-compliance settings.

Contribution

It proposes a novel Bayesian framework combining Gaussian copula and Dirichlet process models to adjust for partial compliance in sequential decision making.

Findings

Method performs well in non-linear, non-Gaussian simulations.

Robustness demonstrated in high non-compliance scenarios.

Addresses bias and reproducibility issues in treatment effect estimation.

Abstract

Existing methods in estimating the mean outcome under a given dynamic treatment regime rely on intention-to-treat analyses which estimate the effect of following a certain dynamic treatment regime 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 potential differential compliance behavior. These are particularly problematic in settings with high level of non-compliance such as substance use disorder treatments. 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 sequence which is not of interest. We fill this important gap by defining the target parameter as the mean outcome under a dynamic treatment regime given potential compliance strata. We propose a flexible non-parametric Bayesian approach, which consists of a Gaussian copula model for the potential compliances, and a Dirichlet process mixture model for the potential outcomes. Our simulations highlight the need for and usefulness of this approach in practice and illustrate the robustness of our estimator in non-linear and non-Gaussian settings.