Primary Submission Category: Sensitivity Analysis
Automatically Calibrated Sensitivity Models for Causal Inference with Unmeasured Confounding
Authors: Alexander McClean, Zach Branson, Edward Kennedy,
Presenting Author: Alexander McClean*
Accounting for unmeasured confounding is crucial when estimating causal effects with observational data. For this purpose, we propose several data-driven methods based on novel automatically calibrated sensitivity (ACS) models, which bound the error due to unmeasured confounding by an analogous notion of error due to measured confounding, multiplied by a sensitivity parameter. We illustrate how to construct ACS models via several examples and demonstrate their advantages over standard sensitivity and post hoc calibration analyses. We focus on estimating a one-number summary of Average Treatment Effect sensitivity — an intuitive alternative to more frequently considered estimands in the literature — with ACS models defined at the level of (1) the causal effect, (2) the counterfactual outcome regressions, and (3) the odds ratio of the probability of receiving treatment. Under all models, we observe that either a margin condition or smooth approximation is required for efficient estimation and develop methods for estimation and inference with both. Moreover, we establish that our estimators are doubly robust, and attain parametric efficiency and asymptotic normality under nonparametric conditions on the relevant nuisance function estimators. Finally, we illustrate our methods with two data analyses, examining the effect of exposure to violence on attitudes towards peace and mothers’ smoking on infant birth weight.