Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding
This provides a highly credible sensitivity analysis method for causal inference in fields like epidemiology or social sciences, though it is incremental as it builds on existing bounded confounding assumptions.
The paper tackles the problem of bounding average treatment effects in the presence of unmeasured confounding with bounded influence, deriving sharp partial identification bounds using distributionally robust optimization and proposing estimators with double sharpness and double validity properties, achieving semiparametric efficiency under consistency and maintaining validity under misspecification.
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.