2D score based estimation of heterogeneous treatment effects

In the study of causal inference, statisticians show growing interest in estimating and analyzing heterogeneity in causal effects in observational studies. However, there usually exists a trade-off between accuracy and interpretability for developing a desirable estimator for treatment effects, especially in the case when there are a large number of features in estimation. To make efforts to address the issue, we propose a score-based framework for estimating the Conditional Average Treatment Effect (CATE) function in this paper. The framework integrates two components: (i) leverage the joint use of propensity and prognostic scores in a matching algorithm to obtain a proxy of the heterogeneous treatment effects for each observation, (ii) utilize non-parametric regression trees to construct an estimator for the CATE function conditioning on the two scores. The method naturally stratifies treatment effects into subgroups over a 2d grid whose axis are the propensity and prognostic scores. We conduct benchmark experiments on multiple simulated data and demonstrate clear advantages of the proposed estimator over state of the art methods. We also evaluate empirical performance in real-life settings, using two observational data from a clinical trial and a complex social survey, and interpret policy implications following the numerical results.