Sensitivity Analysis in Observational Research: Introducing the E-Value

Abstract

Sensitivity analysis can be useful in assessing how robust associations are to potential unmeasured or uncontrolled confounding. In this paper we introduce a new measure that we call the “E-value,” a measure related to the evidence for causality in observational studies, when they are potentially subject to confounding. The E-value is defined as the minimum strength of association on the risk ratio scale that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific treatment-outcome association, conditional on the measured covariates. A large E-value implies considerable unmeasured confounding would be needed to explain away an effect estimate. A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. We propose that in all observational studies intended to produce evidence for causality, the E-value be reported, or some other sensitivity analysis be used. We suggest calculating the E-value for both the observed association estimate (after adjustments for measured confounders) and for the limit of the confidence interval closest to the null. If this were to become standard practice, the ability of the scientific community to assess evidence from observational studies would be improved considerably, and ultimately, science would be strengthened.