Doubly robust matching estimators for high dimensional confounding adjustment

TL;DR

This paper introduces a doubly robust matching estimator that combines propensity and prognostic scores for high-dimensional confounding adjustment, enabling valid treatment effect estimation when covariates are numerous.

Contribution

It proposes a novel matching method on both scores that remains consistent if either score model is correctly specified, addressing high-dimensional confounding.

Findings

Estimator is doubly robust and consistent under certain conditions.

Simulation studies show effective confounding control.

Application to insurance data illustrates practical utility.

Abstract

Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible. In cases where a sparsity condition holds, variable selection or penalization can reduce the dimension of the covariate space in a manner that allows for valid estimation of treatment effects. In this article, we propose matching on both the estimated propensity score and the estimated prognostic scores when the number of covariates is large relative to the number of observations. We derive asymptotic results for the matching estimator and show that it is doubly robust, in the sense that only one of the two score models need be correct to obtain a consistent estimator. We show via simulation its effectiveness in controlling for confounding and highlight its potential to address nonlinear confounding. Finally, we apply the proposed procedure to analyze the effect of gender on prescription opioid use using insurance claims data.