Can DAGs Clarify Effect Modification?

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Abstract
The system proposed by VanderWeele and Robins for categorization of effect modifiers that are causal nodes in a directed acyclic graph (DAG) was not intended to empower DAGs to fully represent complex interactions among causes. However, once one has algebraically identified effect modifiers, the DAG implies a role for them. The limitations of epidemiologic definitions of “effect modification” are discussed, along with the implications of scale dependency for assessing interactions, where the scale can be either absolute risk, relative risk, or odds. My view is that probabilistic independence leads to the log-complement as a natural scale for interaction, but even that scale does not necessarily admit unambiguous inference. Any 2 direct causes of D are effect modifiers for each other on at least 2 scales, which can make a reasonable person question the utility of the concept. Still, etiologic models for joint effects are important, because most diseases arise through pathways involving multiple factors. I suggest an enhancement in construction of DAGs in epidemiology that includes arrow-on-arrow representations for effect modification. Examples are given, some of which depend on scale and some of which do not. An example illustrates possible biologic implications for such an effect modification DAG.