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

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  • Jacob Dorn
  • Kevin Guo
  • Nathan Kallus

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.

Suggested Citation

  • Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2112.11449
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    References listed on IDEAS

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    Cited by:

    1. Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org.
    2. Nathan Kallus, 2022. "Treatment Effect Risk: Bounds and Inference," Papers 2201.05893, arXiv.org, revised Jul 2022.
    3. Nathan Kallus & Miruna Oprescu, 2022. "Robust and Agnostic Learning of Conditional Distributional Treatment Effects," Papers 2205.11486, arXiv.org, revised Feb 2023.
    4. Nathan Kallus, 2022. "What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment," Papers 2205.10327, arXiv.org, revised Nov 2022.

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