Missing and spurious interaction in additive, multiplicative and odds ratio models

Additive, multiplicative, and odd ratio neutral models for interactions are for long advocated and controversial in epidemiology. We show here that these commonly advocated models are biased, leading to spurious interactions, and missing true interactions. INTRODUCTION The concept of interaction stands for long controversial in epidemiology circles [1]–[7]. Main stream of these approaches arrive to additive effects as a meaningful model for testing “biologic interaction” [8][9][5], and deny, except in few special cases [10], a similar role for multiplicative effects. The issue is problematic because case-only designs for gene-environment and gene-gene interactions rely on the validity of multiplicative models [11][12], and have been regarded as more efficient alternatives to the typical random sampling of cases and controls [13]. We bring two hypothetical examples a priori detached from any explicit mathematical equation, but amenable to be unambiguously classified as interaction and non-interaction, respectively. We here evaluate the models for interaction dominant in epidemiology circles, by pursuing at least consistency with these two instances of our notion of interaction. INTERACTION NOTION Colloquially, by interaction we mean that the concurrent exposition to a set of factors produces an effect that is surprising when compared to what one would expect from the effects of the intervening factors, if they acted independently. For example, spark and oxygen (factors) are each practically innocuous, with only the spark releasing a small and transient amount of heat (the effect). In the presence of gasoline, inner factors “unavailable” to the analysis can be regarded as the particular chemical configuration holding the potential energy that is released only in the join exposition to spark and oxygen that lead to the surprising effect (fire) compared to their separated individual effects. Internally, the chemical bonds storing the stabilizing energy in gasoline break out by oxidation with O2 (combustion), and the chemical (organic compound) changes into CO2, H2O, generating heat, light, sound, as the effect of an exothermic reaction (Figure 1).