Sufficient-component causes are discussed within the potential outcome framework so as to formalize notions of sufficient causes, synergism and sufficient cause interactions. Doing so allows for the derivation of counterfactual conditions and statistical tests for detecting the presence of sufficient cause interactions. Under the assumption of monotonic effects, more powerful statistical tests for sufficient cause interactions can be derived. The statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models.
VanderWeele, Tyler J. and Robins, James M., "A Theory of Sufficient Cause Interactions" (September 2006). COBRA Preprint Series. Working Paper 13.