Treatment Effect Decomposition and Bootstrap Hypothesis Testing in Observational Studies

Causal inference with observational data has drawn attention across various fields. These observational studies typically use matching methods which find matched pairs with similar covariate values. However, matching methods may not directly achieve covariate balance, a measure of matching effectiveness. As an alternative, the Balance Optimization Subset Selection (BOSS) framework, which seeks optimal covariate balance directly, has been proposed. This paper extends BOSS by estimating and decomposing a treatment effect as a combination of heterogeneous treatment effects from a partitioned set. Our method differs from the traditional propensity score subclassification method in that we find a subset in each subclass using BOSS instead of using the stratum determined by the propensity score. Then, by conducting a bootstrap hypothesis test on each component, we check the statistical significance of these treatment effects. These methods are applied to a dataset from the National Supported Work Demonstration (NSW) program which was conducted in the 1970s. By examining the statistical significance, we show that the program was not significantly effective to a specific subgroup composed of those who were already employed. This differs from the combined estimate—the NSW program was effective when considering all the individuals. Lastly, we provide results that are obtained when these steps are repeated with sub-samples.