Contrasting theories of interaction in epidemiology and toxicology

Epidemiologists and toxicologists face similar problems when assessing interactions between exposures, yet they approach the question very differently. The epidemiologic definition of "interaction" leads to the additivity of risk differences (RDA) as the fundamental criterion for causal inference about biological interactions. Toxicologists define "interaction" as departure from a model based on mode of action: concentration addition (CA; for similarly acting compounds) or independent action (IA; for compounds that act differently).

We compared and contrasted theoretical frameworks for interaction in the two fields.

The same simple thought experiment has been used in both both epidemiology and toxicology to develop the definition of "noninteraction," with nearly opposite interpretations. In epidemiology, the "sham combination" leads to a requirement that noninteractive dose-response curves be linear, whereas in toxicology, it results in the model of CA. We applied epidemiologic tools to mathematical models of concentration-additive combinations to evaluate their utility.

RDA is equivalent to CA only for linear dose-response curves. Simple models demonstrate that concentration-additive combinations can result in strong synergy or antagonism in the epidemiologic framework at even the lowest exposure levels. For combinations acting through nonsimilar pathways, RDA approximates IA at low effect levels.

Epidemiologists have argued for a single logically consistent definition of interaction, but the toxicologic perspective would consider this approach less biologically informative than a comparison with CA or IA. We suggest methods for analysis of concentration-additive epidemiologic data. The two fields can learn a great deal about interaction from each other.