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

Abstract

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.

Nonparametric Bayesian Q-learning for optimization of dynamic treatment regimes in the presence of partial compliance

“…Q-learning determines an optimal DTR in reverse sequential order, that is, the optimal decision rule at each stage is estimated by optimizing a predicted counterfactual outcome under optimal treatment in the subsequent stages. To our knowledge, our proposal is the first approach in the DTR literature that adjusts for partial compliance and is in sharp contrast with Artman et al 25 and Bhattacharya et al, 26 as it does not require specifying a finite set of decision rules (e.g. the design embedded DTRs in a multi-stage clinical trial).…”

“…Kim et al 24 adapted a similar approach to accommodate post-treatment variables in the context of mediation analyses. Recently, a Bayesian marginal structural model, 25 and a Bayesian principal stratification-based approach 26 have been proposed to estimate the mean outcome under a given treatment regime.…”