Testing for Mechanistic Interactions in Long-Term Follow-Up Studies

In follow-up studies, interactions are often assessed by including a cross-product term in a (multiplicative) Cox model. However, epidemiologists/clinicians often misinterpret a significant multiplicative interaction as a genuine mechanistic interaction. Though indices specific to mechanistic interactions have been proposed, including the 'relative excess risk due to interaction' (RERI) and the 'peril ratio index of synergy based on multiplicativity' (PRISM), these indices assume no loss to follow up and no competing death in a study. In this paper, the authors propose a novel 'mechanistic interaction test' (MIT) for censored data. Monte-Carlo simulation shows that when the hazard curves are proportional to, non-proportional to, or even crossing over one another, the proposed MIT can maintain reasonably accurate type I error rates for censored data. It has far greater powers than the modified RERI and PRISM tests (modified for censored data scenarios). To test mechanistic interactions in censored data, we recommend using MIT in light of its desirable statistical properties.