Matching-Based Nonparametric Estimation of Group Average Treatment Effects

TL;DR

This paper introduces two nonparametric matching-based methods for estimating group average treatment effects, addressing instability and bias issues in existing approaches, with theoretical guarantees and practical implementation.

Contribution

It proposes novel matching and bias-corrected matching estimators for GATEs, improving robustness and reducing bias compared to traditional methods.

Findings

The bias-corrected matching estimator is consistent and asymptotically normal.

The methods outperform existing approaches in simulations and real data.

An open-source R package, MatchGATE, is provided for implementation.

Abstract

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 non-negligible bias when the dimension of full covariates is high. To mitigate this, the bias-corrected matching estimator incorporates additional outcome regression 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.