A Bayesian Semiparametric Approach to Treatment Effect Variation with Noncompliance

Jared Fisher (BYU) joins us to discuss 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 ML-based 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, and require pre-specifying subgroups of interest. 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 semiparametric approach that combines the best features of both approaches. Our main contribution is to embed Bayesian Additive Regression Trees (BART) in a broader Bayesian noncompliance framework in which we repeatedly impute individuals’ compliance types. This allows us to flexibly estimate varying treatment effects among compliers while mitigating the weak instruments problem. We then apply our method to the Oregon health insurance experiment and show that analyses that only focus on a single source of variation can miss important heterogeneity.