Sharpening the Rosenbaum Sensitivity Bounds to Address Concerns About Interactions Between Observed and Unobserved Covariates

TL;DR

This paper improves Rosenbaum sensitivity bounds for observational studies by addressing interactions between observed and unobserved covariates, providing more accurate assessments of hidden biases affecting causal inferences.

Contribution

It introduces sharper odds ratio bounds to correct the exaggeration of sensitivity analysis caused by covariate interactions in Rosenbaum bounds.

Findings

New bounds reduce bias exaggeration in sensitivity analysis.

Application demonstrates improved accuracy in causal effect estimation.

Method enhances robustness of observational study conclusions.

Abstract

In observational studies, it is typically unrealistic to assume that treatments are randomly assigned, even conditional on adjusting for all observed covariates. Therefore, a sensitivity analysis is often needed to examine how hidden biases due to unobserved covariates would affect inferences on treatment effects. In matched observational studies where each treated unit is matched to one or multiple untreated controls for observed covariates, the Rosenbaum bounds sensitivity analysis is one of the most popular sensitivity analysis models. In this paper, we show that in the presence of interactions between observed and unobserved covariates, directly applying the Rosenbaum bounds will almost inevitably exaggerate the report of sensitivity of causal conclusions to hidden bias. We give sharper odds ratio bounds to fix this deficiency. We illustrate our new method through studying the effect of anger/hostility tendency on the risk of having heart problems.