Primary Submission Category: Sensitivity Analysis
Sensitivity of weighted least squares estimators to omitted variables
Authors: Leonard Wainstein, Chad Hazlett,
Presenting Author: Leonard Wainstein*
This paper introduces tools for assessing the sensitivity, to unobserved confounding, of a common estimator of the causal effect of a treatment on an outcome that employs weights: the weighted linear regression of the outcome on the treatment and observed covariates. We demonstrate through the omitted variable bias framework that the bias of this estimator is a function of two intuitive sensitivity parameters: (i) the proportion of weighted variance in the treatment that unobserved confounding explains given the covariates and (ii) the proportion of weighted variance in the outcome that unobserved confounding explains given the covariates and the treatment, i.e., two weighted partial R2 values. Following previous work, we define sensitivity statistics that lend themselves well to routine reporting, and derive formal bounds on the strength of the unobserved confounding with (a multiple of) the strength of select dimensions of the covariates, which help the user determine if unobserved confounding that would alter one’s conclusions is plausible. We also develop tools for adjusted inference. The key contribution of these tools is that they apply with any non-negative weights (e.g., inverse-propensity score, matching, or covariate balancing weights). The proposed tools also refrain from distributional assumptions on the data or unobserved confounding, and can address bias from misspecification in the observed data.