Directed Acyclic Graphs, Effect Measure Modification, and Generalizability

Abstract

Directed acyclic graphs (DAGs) have had a major impact on the field of epidemiology by providing straightforward graphical rules for determining when estimates are expected to lack causally interpretable internal validity. Much less attention has been paid, however, to what DAGs can tell researchers about effect measure modification and external validity. In this work, we describe 2 rules based on DAGs related to effect measure modification. Rule 1 states that if a variable, $P$, is conditionally independent of an outcome, $Y$, within levels of a treatment, $X$, then $P$is not an effect measure modifier for the effect of$X$on$Y$on any scale. Rule 2 states that if$P$is not conditionally independent of$Y$within levels of$X$, and there are open causal paths from $X$to$Y$within levels of$P$, then $P$is an effect measure modifier for the effect of$X$on$Y$on at least 1 scale (given no exact cancelation of associations). We then show how Rule 1 can be used to identify sufficient adjustment sets to generalize nested trials studying the effect of$X$on$Y$ to the total source population or to those who did not participate in the trial.