Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles

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 flexible machine learning methods are sensitive to the weak instruments problem and can yield unstable estimates of heterogeneity when run repeatedly with different initialization or random seeds. 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, we can flexibly estimate heterogeneous treatment effects among compliers. Simulation studies demonstrate the usefulness of our approach when compliance and treatment effects are heterogeneous. We use this 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 focus on three outcomes one year after intervention. We confirm a null effect on the presence of a chronic condition, discover meaningful heterogeneity in the impact of the intervention on metabolic parameters though the average effect is null in classical partial effect estimates, and find heterogeneity in the intervention's effect on individuals' perception of management prioritization of health and safety.