Stochastic mechanistic interaction

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We define mechanistic interaction between the effects of two variables on an outcome in terms of departure of these effects from a generalized noisy-OR model in a stratum of the population. We develop a fully probabilistic framework for the observational identification of this type of interaction via excess risk or superadditivity, one novel feature of which is its applicability when the interacting variables have been generated by arbitrarily dichotomizing continuous exposures. The method allows for stochastic mediators of the interacting effects. The required assumptions are provided in the form of conditional independencies between the problem variables, which may relate to a causal-graph representation of the problem. We also develop a theory of mechanistic interaction between effects associated with specific paths of the causal graph.

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