E-value Formulae for the Odds Ratio

Abstract

The E-value is the minimum strength of association that a potential confounder needs to have with either the exposure or the outcome, if it were to alone explain an observed association between the two.
Originally defined in terms of the risk ratio (relative risk), this short note explores the E-value formulae where one or several of the three relationships is measured using the odds ratio instead.
A rigorous but elegant alternative is presented to the square root approximation that has been proposed earlier as a convenient but wrong way to combine odds ratios and E-values.