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 highly sensitive to the weak instruments problem, in which the compliance rate is (locally) close to zero. 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 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 impact of the intervention on metabolic parameters though the average effect is null in classical partial effect estimates, and find substantial heterogeneity in individuals' perception of management prioritization of health and safety.

It is important to estimate the local average treatment effect (LATE) when compliance with a treatment assignment is incomplete. The previously proposed methods for LATE estimation required all relevant variables to be jointly observed in a single dataset; however, it is sometimes difficult or even impossible to collect such data in many real-world problems for technical or privacy reasons. We consider a novel problem setting in which LATE, as a function of covariates, is nonparametrically identified from the combination of separately observed datasets. For estimation, we show that the direct least squares method, which was originally developed for estimating the average treatment effect under complete compliance, is applicable to our setting. However, model selection and hyperparameter tuning for the direct least squares estimator can be unstable in practice since it is defined as a solution to the minimax problem. We then propose a weighted least squares estimator that enables simpler model selection by avoiding the minimax objective formulation. Unlike the inverse probability weighted (IPW) estimator, the proposed estimator directly uses the pre-estimated weight without inversion, avoiding the problems caused by the IPW methods. We demonstrate the effectiveness of our method through experiments using synthetic and real-world datasets.