Technical Considerations in the Use of the E-Value

The E-value is defined as the minimum strength of association on the risk ratio scale that an unmeasured confounder would have to have with both the exposure and the outcome, conditional on the measured covariates, to explain away the observed exposure-outcome association. We have elsewhere proposed that the reporting of E-values for estimates and for the limit of the confidence interval closest to the null become routine whenever causal effects are of interest. A number of questions have arisen about the use of E-value including questions concerning the interpretation of the relevant confounding association parameters, the nature of the transformation from the risk ratio scale to the E-value scale, inference for and using E-values, and the relation to Rosenbaum's notion of design sensitivity. Here we bring these various questions together and provide responses that we hope will assist in the interpretation of E-values and will further encourage their use.