Sufficient Cause Interactions and Statistical Interactions

When the outcome and all exposures of interest are binary it is sometimes possible to draw conclusions from empirical data about mechanistic interactions in the sufficient cause sense. Empirical conditions are given for sufficient cause interactions and these conditions are compared with and contrasted to interaction coefficients in linear, log-linear and logistic regression models. Conditions that suffice to allow for the interpretation of statistical interactions as sufficient cause interactions are derived. Discussion is presented concerning the implications of the inclusion of confounding variables in the model.