Choosing statistical models to assess biological interaction as a departure from additivity of effects

Vanderweele and Knol define biological interaction as an instance wherein "two exposures physically interact to bring about the outcome." A hallmark of biological interaction is that the total effect, produced when factors act together, differs from the sum of effects when the factors operate independently. Epidemiologists construct statistical models to assess biological interaction. The form of the statistical model determines whether it is suited to detecting departures from additivity of effects or for detecting departures from multiplicativity of effects. A consensus exists that biological interaction should be assessed as a departure from additivity of effects. This paper compares three statistical models' assessment of a data example that appears in several epidemiology textbooks to illustrate biological interaction in a binomial outcome. A linear binomial model quantifies departure from additivity in the data example in terms of differences in probabilities. It generates directly interpretable estimates and 95% confidence intervals for parameters including the interaction contrast (IC). Log binomial and logistic regression models detect no departure from multiplicativity in the data example. However, their estimates contribute to calculation of a "Relative Excess Risk Due to Interaction" (RERI), a measure of departure from additivity on a relative risk scale. The linear binomial model directly produces interpretable assessments of departures from additivity of effects and deserves wider use in research and in the teaching of epidemiology. Strategies exist to address the model's limitations.