Primary Submission Category: Sensitivity Analysis
Unifying $L_2$ sensitivity analyses for regression and weighting estimators
Authors: Yaxuan Huang, Melody Huang, Samuel Pimentel,
Presenting Author: Yaxuan Huang*
Sensitivity analyses addressing possible unobserved confounding are a vital piece of evidence when causal inferences are drawn from observational studies. Recent methodological work has introduced many new approaches for sensitivity analysis; however, each method is typically tied to a particular estimation strategy, making it difficult to compare sensitivity approaches across studies. Leveraging recent work on connections between regression estimators and weighting estimators (Chattopadhyay & Zubizarreta 2023), we establish a new unified framework for sensitivity analysis for both regression and weighting, under which standard approaches for both types of estimators appear as alternative parameterizations of an $L_2$ constraint on the errors from unobserved confounding. We show how our framework can lead to intuitive characterizations of $L_2$ sensitivity analysis for doubly robust and weighted regression estimators of causal effects, and allows bounds to be made sharp without estimating additional nuisance parameters. We discuss conceptual parallels of our framework relative to recently-introduced doubly valid, doubly sharp $L_infty$ sensitivity analyses. By moving away from worst-case characterizations of unobserved confounding error, the proposed $L_2$ approach results in improvements in both stability and interpretability. Supported by the National Science Foundation under Grant No. 2142146.