Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal Matching

TL;DR

This paper introduces a unified framework for estimating various causal effects called GATE and proposes Kernel Optimal Matching (KOM) as a method to optimally estimate these effects with theoretical guarantees and practical applications.

Contribution

The paper unifies multiple causal estimands into GATE and develops KOM to optimally estimate GATE with theoretical analysis and empirical validation.

Findings

KOM provides uniform control over mean squared error.

KOM outperforms traditional methods in simulation studies.

Application to real case studies demonstrates practical utility.

Abstract

In causal inference, a variety of causal effect estimands have been studied, including the sample, uncensored, target, conditional, optimal subpopulation, and optimal weighted average treatment effects. Ad-hoc methods have been developed for each estimand based on inverse probability weighting (IPW) and on outcome regression modeling, but these may be sensitive to model misspecification, practical violations of positivity, or both. The contribution of this paper is twofold. First, we formulate the generalized average treatment effect (GATE) to unify these causal estimands as well as their IPW estimates. Second, we develop a method based on Kernel Optimal Matching (KOM) to optimally estimate GATE and to find the GATE most easily estimable by KOM, which we term the Kernel Optimal Weighted Average Treatment Effect. KOM provides uniform control on the conditional mean squared error of a weighted estimator over a class of models while simultaneously controlling for precision. We study its theoretical properties and evaluate its comparative performance in a simulation study. We illustrate the use of KOM for GATE estimation in two case studies: comparing spine surgical interventions and studying the effect of peer support on people living with HIV.