  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.
