A Bayesian Classification Trees Approach to Treatment Effect Variation with Noncompliance

Estimating varying treatment effects in randomized trials with noncompliance is inherently challenging since variation comes from two separate sources: variation in the impact itself and variation in the compliance rate. In this setting, existing frequentist and flexible machine learning methods are highly sensitive to the weak instruments problem, in which the compliance rate is (locally) close to zero. Bayesian approaches, on the other hand, can naturally account for noncompliance via imputation. We propose a Bayesian machine learning approach that combines the best features of both approaches. Our main methodological contribution is to present a Bayesian Causal Forest model for binary response variables in scenarios with noncompliance by repeatedly imputing individuals' compliance types, allowing us to flexibly estimate varying treatment effects among compliers. Simulation studies demonstrate the usefulness of our approach when compliance and treatment effects are heterogeneous. We apply the method to detect and analyze heterogeneity in the treatment effects in the Illinois Workplace Wellness Study, which not only features heterogeneous and one-sided compliance but also several binary outcomes of interest. We demonstrate the methodology on three outcomes one year after intervention. We confirm a null effect on the presence of a chronic condition, discover meaningful heterogeneity in a "bad health" outcome that cancels out to null in classical partial effect estimates, and find substantial heterogeneity in individuals' perception of management prioritization of health and safety.