E-values for effect heterogeneity and approximations for causal interaction

Background Estimates of effect heterogeneity (i.e. the extent to which the causal effect of one exposure varies across strata of a second exposure) can be biased if the exposure–outcome relationship is subject to uncontrolled confounding whose severity differs across strata of the second exposure. Methods We propose methods, analogous to the E-value for total effects, that help to assess the sensitivity of effect heterogeneity estimates to possible uncontrolled confounding. These E-value analogues characterize the severity of uncontrolled confounding strengths that would be required, hypothetically, to ‘explain away’ an estimate of multiplicative or additive effect heterogeneity in the sense that appropriately controlling for those confounder(s) would have shifted the effect heterogeneity estimate to the null, or alternatively would have shifted its confidence interval to include the null. One can also consider shifting the estimate or confidence interval to an arbitrary non-null value. All of these E-values can be obtained using the R package EValue. Results We illustrate applying the proposed E-value analogues to studies on: (i) effect heterogeneity by sex of the effect of educational attainment on dementia incidence and (ii) effect heterogeneity by age on the effect of obesity on all-cause mortality. Conclusion Reporting these proposed E-values could help characterize the robustness of effect heterogeneity estimates to potential uncontrolled confounding.