Related papers: H\"older Bounds for Sensitivity Analysis in Causal Reasoning

H\"older Bounds for Sensitivity Analysis in Causal Reasoning

URL: http://arxiv.org/abs/2107.04661v1
Date: Fri, 9 Jul 2021 20:26:36 GMT
Title: H\"older Bounds for Sensitivity Analysis in Causal Reasoning
Authors: Serge Assaad, Shuxi Zeng, Henry Pfister, Fan Li, Lawrence Carin
Abstract summary: We derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding. These bounds are tight either when U is independent of T or when U is independent of Y given T.
Score: 66.00472443147781
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We examine interval estimation of the effect of a treatment T on an outcome Y given the existence of an unobserved confounder U. Using H\"older's inequality, we derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding (i.e., the strength of the connection U->T, and the strength of U->Y). These bounds are tight either when U is independent of T or when U is independent of Y given T (when there is no unobserved confounding). We focus on a special case of this bound depending on the total variation distance between the distributions p(U) and p(U|T=t), as well as the maximum (over all possible values of U) deviation of the conditional expected outcome E[Y|U=u,T=t] from the average expected outcome E[Y|T=t]. We discuss possible calibration strategies for this bound to get interval estimates for treatment effects, and experimentally validate the bound using synthetic and semi-synthetic datasets.

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