Abstract: In observational studies, it is typically unrealistic to assume that treatments are assigned randomly, even conditional on adjusting for all observed covariates. Therefore, a sensitivity analysis is often needed to examine how hidden biases due to unobserved covariates 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. We show that in the presence of interactions between observed and unobserved covariates, directly applying the Rosenbaum bounds almost inevitably exaggerates 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 by studying the effect of a anger/hostility tendency on the risk of experiencing heart problems.

Key words and phrases: Causal inference, gene-environment interaction, interaction terms, matching, observational studies, sensitivity analysis.