How Choice of Effect Measure Influences Minimally Sufficient Adjustment Sets for External Validity

Epidemiologic researchers generalizing or transporting effect estimates from a study to a target population must account for effect-measure modifiers (EMMs) on the scale of interest. However, little attention is paid to how the EMMs required may vary depending on the mathematical nuances of each effect measure. We defined 2 types of EMMs: a marginal EMM, where the effect on the scale of interest differs across levels of a variable, and a conditional EMM, where the effect differs conditional on other variables associated with the outcome. These types define 3 classes of variables: class 1 (conditional EMM), class 2 (marginal but not conditional EMM), and class 3 (neither marginal nor conditional EMM). Class 1 variables are necessary to achieve a valid estimate of the RD in a target population, while an RR requires class 1 and class 2 and an OR requires classes 1, 2, and 3 (i.e., all variables associated with the outcome). This does not mean that fewer variables are required for an externally valid RD (because variables may not modify effects on all scales), but it does suggest that researchers should consider the scale of the effect measure when identifying an EMM necessary for an externally valid treatment effect estimate.