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Stochastic Mechanistic Interaction

We propose a fully probabilistic formulation of the notion of mechanistic interaction (interaction in some fundamental mechanistic sense) between the effects of putative (possibly continuous) causal factors A and B on a binary outcome variable Y indicating 'survival' vs 'failure'. We define mechanistic interaction in terms of departure from a generalized 'noisy OR' model, under which the multiplicative causal effect of A (resp., B) on the probability of failure cannot be enhanced by manipulating B (resp., A). We present conditions under which mechanistic interaction in the above sense can be assessed via simple tests on excess risk or superadditivity, in a possibly retrospective regime of observation. These conditions are defined in terms of generalized conditional independence relationships (generalised because they may involve non-stochastic 'regime indicators') that can often be checked on a graphical representation of the problem. Inference about mechanistic interaction between direct, or path-specific, causal effects can be accommodated in the proposed framework. The method is illustrated with the aid of a study in experimental psychology.