Double Robust Variance Estimation with Parametric Working Models

TL;DR

This paper demonstrates that empirical sandwich and bootstrap variance estimators are doubly robust in causal inference, providing valid variance estimates when only one of the parametric models is correctly specified, unlike traditional influence function methods.

Contribution

It introduces and empirically evaluates doubly robust variance estimators (empirical sandwich and bootstrap) that remain valid when only one model is correctly specified, improving variance estimation in causal studies.

Findings

Empirical sandwich and bootstrap estimators are doubly robust.

Influence function based variance estimator requires both models to be correct.

Simulation studies confirm the robustness of the proposed estimators.

Abstract

Doubly robust estimators have gained popularity in the field of causal inference due to their ability to provide consistent point estimates when either an outcome or exposure model is correctly specified. However, for nonrandomized exposures the influence function based variance estimator frequently used with doubly robust estimators of the average causal effect is only consistent when both working models (i.e., outcome and exposure models) are correctly specified. Here, the empirical sandwich variance estimator and the nonparametric bootstrap are demonstrated to be doubly robust variance estimators. That is, they are expected to provide valid estimates of the variance leading to nominal confidence interval coverage when only one working model is correctly specified. Simulation studies illustrate the properties of the influence function based, empirical sandwich, and nonparametric bootstrap variance estimators in the setting where parametric working models are assumed. Estimators are applied to data from the Improving Pregnancy Outcomes with Progesterone (IPOP) study to estimate the effect of maternal anemia on birth weight among women with HIV.