Sensitivity analysis via the proportion of unmeasured confounding

TL;DR

This paper introduces a novel sensitivity analysis method for observational studies, quantifying the impact of unmeasured confounding through the proportion of confounded units, with derived bounds and estimators for the average treatment effect.

Contribution

It proposes a new approach using the proportion of unmeasured confounding as a sensitivity parameter, providing sharp bounds and flexible estimators for ATE in observational studies.

Findings

Derived sharp bounds on ATE based on the proportion of unmeasured confounding.

Developed nonparametric estimators for flexible covariate adjustment.

Applied the method to real data on right heart catheterization, demonstrating robustness.

Abstract

In observational studies, identification of ATEs is generally achieved by assuming that the correct set of confounders has been measured and properly included in the relevant models. Because this assumption is both strong and untestable, a sensitivity analysis should be performed. Common approaches include modeling the bias directly or varying the propensity scores to probe the effects of a potential unmeasured confounder. In this paper, we take a novel approach whereby the sensitivity parameter is the "proportion of unmeasured confounding:" the proportion of units for whom the treatment is not as good as randomized even after conditioning on the observed covariates. We consider different assumptions on the probability of a unit being unconfounded. In each case, we derive sharp bounds on the average treatment effect as a function of the sensitivity parameter and propose nonparametric estimators that allow flexible covariate adjustment. We also introduce a one-number summary of a study's robustness to the number of confounded units. Finally, we explore finite-sample properties via simulation, and apply the methods to an observational database used to assess the effects of right heart catheterization.