Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding

TL;DR

This paper develops a robust method for bounding the average treatment effect in causal inference when unmeasured confounders have limited influence, ensuring valid and efficient sensitivity analysis even under model misspecification.

Contribution

It introduces doubly-sharp and doubly-valid estimators for ATE bounds under bounded confounding influence, combining distributionally robust optimization with novel robustness properties.

Findings

Establishes sharp bounds on ATE with bounded confounders.

Proposes estimators that are both double sharp and double valid.

Provides valid confidence intervals even with nuisance parameter misspecification.

Abstract

We consider the problem of constructing bounds on the average treatment effect (ATE) when unmeasured confounders exist but have bounded influence. Specifically, we assume that omitted confounders could not change the odds of treatment for any unit by more than a fixed factor. We derive the sharp partial identification bounds implied by this assumption by leveraging distributionally robust optimization, and we propose estimators of these bounds with several novel robustness properties. The first is double sharpness: our estimators consistently estimate the sharp ATE bounds when one of two nuisance parameters is misspecified and achieve semiparametric efficiency when all nuisance parameters are suitably consistent. The second is double validity: even when most nuisance parameters are misspecified, our estimators still provide valid but possibly conservative bounds for the ATE and our Wald confidence intervals remain valid even when our estimators are not asymptotically normal. As a result, our estimators provide a highly credible method for sensitivity analysis of causal inferences.