Deep determinism and the assessment of mechanistic interaction

Given two variables that causally influence a binary response, we formalize the idea that their effects operate through a common mechanism, in which case we say that the two variables interact mechanistically. We introduce a mechanistic interaction relationship of "interference" that is asymmetric in the two causal factors. Conditions and assumptions under which such mechanistic interaction can be tested under a given regime of data collection, be it interventional or observational, are expressed in terms of conditional independence relationships between the problem variables, which can be manipulated with the aid of causal diagrams. The proposed method is able, under appropriate conditions, to test for interaction between direct effects, and to deal with the situation where one of the two factors is a dichotomized version of a continuous variable. The method is illustrated with the aid of a study on heart disease.