Primary Submission Category: Bayesian Causal Inference
A Bayesian Classification Trees Approach to Treatment Effect Variation with Noncompliance
Authors: Jared Fisher, David Puelz, Sameer Deshpande,
Presenting Author: Jared Fisher*
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 machine learning methods are quite flexible but are highly sensitive to the so-called weak instruments problem, in which the compliance rate is (locally) close to zero. Parametric Bayesian approaches, which account for noncompliance via imputation, are more robust in this case, but are much more sensitive to model specification. In this paper, 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. In this Bayesian noncompliance framework, we repeatedly impute individuals’ compliance types, allowing us to flexibly estimate varying treatment effects among compliers. Binary outcomes add a layer of complexity as estimation involves the probability of occurrence, not the binary outcome, and these probabilities are not observed. We apply the method to detect and analyze heterogeneity in a study of workplace wellness, where there are a plethora of binary outcomes of interest.