Matching-Based Nonparametric Estimation of Group Average Treatment Effects

Heterogeneous treatment effects, which vary according to individual covariates, are crucial in fields such as personalized medicine and tailored treatment strategies. In many applications, rather than considering the heterogeneity induced by all covariates, practitioners focus on a few key covariates to develop tailored treatment decisions. Based on this, we aim to estimate the group average treatment effects (GATEs), which represent heterogeneous treatment effects across subpopulations defined by certain key covariates. Previous strategies for estimating GATEs, such as weighting-based and regression-based methods, suffer from instability or extrapolation bias, especially when several propensity scores are close to zero or one. To address these limitations, we propose two novel nonparametric estimation methods: a matching-based method and a bias-corrected matching method for estimating GATEs. The matching-based method imputes potential outcomes using a matching technique, followed by a nonparametric regression. This method avoids the instability caused by extreme propensity scores but may introduce nonnegligible bias when the dimension of full covariates is high. To mitigate this, the bias-corrected matching estimator incorporates additional outcome regression (OR) models, enhancing robustness and reducing bias. We show the consistency, double robustness, and asymptotic normality of the bias-corrected matching estimator. We empirically demonstrate the advantages of the proposed methods with extensive simulation studies and a real-world application. An open-source R package, MatchGATE, is available to implement the proposed methods.