Assessing Causal Mechanistic Interactions: A Peril Ratio Index of Synergy Based on Multiplicativity

The assessments of interactions in epidemiology have traditionally been based on risk-ratio, odds-ratio or rate-ratio multiplicativity. However, many epidemiologists fail to recognize that this is mainly for statistical conveniences and often will misinterpret a statistically significant interaction as a genuine mechanistic interaction. The author adopts an alternative metric system for risk, the ‘peril’. A peril is an exponentiated cumulative rate, or simply, the inverse of a survival (risk complement) or one plus an odds. The author proposes a new index based on multiplicativity of peril ratios, the ‘peril ratio index of synergy based on multiplicativity’ (PRISM). Under the assumption of no redundancy, PRISM can be used to assess synergisms in sufficient cause sense, i.e., causal co-actions or causal mechanistic interactions. It has a less stringent threshold to detect a synergy as compared to a previous index of ‘relative excess risk due to interaction’. Using the new PRISM criterion, many situations in which there is not evidence of interaction judged by the traditional indices are in fact corresponding to bona fide positive or negative synergisms.