On Interactions Between Observed and Unobserved Covariates in Matched Observational Studies

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 report of sensitivity of causal conclusions to hidden bias. We give sharper odds ratio bounds to fix this deficiency. We apply our new method to study the effect of anger/hostility tendency on the risk of having heart problems.