Variance estimation for the average treatment effects on the treated and on the controls

TL;DR

This paper develops methods to accurately estimate the variance of doubly robust ATT and ATC estimators, incorporating multiple sources of uncertainty, and evaluates their finite sample performance through simulations and real data application.

Contribution

It introduces variance estimation techniques for doubly robust ATT and ATC estimators, including asymptotic and wild bootstrap methods, addressing multiple uncertainty sources.

Findings

Wild bootstrap methods outperform standard bootstrap in finite samples.

Variance estimators are consistent and reliable across different treatment heterogeneity scenarios.

Application demonstrates practical utility in observational medical data.

Abstract

Common causal estimands include the average treatment effect (ATE), the average treatment effect of the treated (ATT), and the average treatment effect on the controls (ATC). Using augmented inverse probability weighting methods, parametric models are judiciously leveraged to yield doubly robust estimators, i.e., estimators that are consistent when at least one the parametric models is correctly specified. Three sources of uncertainty are associated when we evaluate these estimators and their variances, i.e., when we estimate the treatment and outcome regression models as well as the desired treatment effect. In this paper, we propose methods to calculate the variance of the normalized, doubly robust ATT and ATC estimators and investigate their finite sample properties. We consider both the asymptotic sandwich variance estimation, the standard bootstrap as well as two wild bootstrap methods. For the asymptotic approximations, we incorporate the aforementioned uncertainties via estimating equations. Moreover, unlike the standard bootstrap procedures, the proposed wild bootstrap methods use perturbations of the influence functions of the estimators through independently distributed random variables. We conduct an extensive simulation study where we vary the heterogeneity of the treatment effect as well as the proportion of participants assigned to the active treatment group. We illustrate the methods using an observational study of critical ill patients on the use of right heart catherization.