Interaction between discrete causes

Abstract

The interaction contrast of disease rates (ICDR), a measure of deviation from an additive model of no interaction, is shown always to be zero or slightly negative when the assumptions of no interaction in the sufficient-component discrete causes model hold. Since all physical sources of interaction which one might postulate between discrete causes imply a deviation from this model, the ICDR is a good parameter to screen for causal interaction. Specific models which deviate from the assumptions of no interaction in the sufficient-component discrete causes model should be sought when the ICDR differs from zero. An example of parameterizing interaction in one such model is presented. The additive model is inconsistent with the multiplicative when two causes are studied; negative or no interaction in the multiplicative model might represent positive interaction in the additive model. Use of the multiplicative model to screen for causal interactions could thus lead to inappropriate decisions regarding the need to seek causal explanations for interaction. Since positive interaction in the multiplicative model implies positive interaction in the additive, there will be no such inappropriate decisions when positive interaction is observed in the multiplicative model.