The E-Value in Regression

The E-value is most simply described as the smallest strength of association that 1 or more unmeasured confounds must have with both risk factor and outcome to nullify a significant relationship between the risk factor and the outcome in a fully adjusted regression. Thus, the E-value is a measure of how robust a finding may be against unmeasured confounding. This article provides the reader with a primer on the E-value, and with a cheat sheet that simplifies concepts. The full definition of the E-value is stated, and each element in the definition is explained. The E-value is most commonly applied to statistics such as the relative risk, odds ratio, and hazard ratio but can be applied to other statistics, as well. The E-value is usually calculated for 2 estimates: the statistic that measures risk and the limit of the 95% confidence interval (CI) of the statistic that is closest to the null. The former E-value tells us how strong unmeasured confounding should be to bring the value of the statistic to null. The latter E-value tells us how strong unmeasured confounding should be to bring the null value into the 95% CI, thereby making a statistically significant finding nonsignificant. This article also explains the calculation and the interpretation of the E-value. A detailed discussion is provided on what unmeasured confounding means with reference to the E-value. The specificity of the E-value to the context of the study, and the variables adjusted for, is emphasized. Interpretation of the E-value should be based on the plausibility of existence of the unmeasured confounds and the prevalence of these confounds in the population. E-values, surprisingly, are not commonly reported. They should be reported by researchers, requested by reviewers and editors, and calculated by readers to understand how robust statistically significant findings are against unmeasured confounding.