  Many studies have focused on investigating deviations from additive
interaction of two dichotomous risk factors on a binary outcome. There is,
however, a gap in the literature with respect to interactions on the additive
scale of >2 risk factors. In this paper, we present an approach for examining
deviations from additive interaction among three on more binary exposures. The
relative excess risk due to interaction (RERI) is used as measure of additive
interaction. First, we concentrate on three risk factors - we propose to
decompose the total RERI to: the RERI owned to the joint presence of all 3 risk
factors and the RERI of any two risk factors, given that the third is absent.
We then extend this approach, to >3 binary risk factors. For illustration, we
use a sample from data from the Greek EPIC cohort and we investigate the
association with overall mortality of Mediterranean diet, body mass index
(BMI), and, smoking. Our formulae enable better interpretability of any
evidence for deviations from additivity owned to more than two risk factors and
provide simple ways of communicating such results from a public health
perspective by attributing any excess relative risk to specific combinations of
these factors.
