The analysis of GxE is motivated by interest in either “characterization” of the joint effects of genetic and environmental risk factors or “discovery” of novel risk factors or interaction effects. In either context, it is important to define several categories of interactions, including: qualitative interaction, where the effect of one exposure is reversed by the other; pure interaction, where the effect of one exposure is present only in the presence of the other; and quantitative interaction, where the effect of one exposure, on some specified scale, is of a different magnitude in the presence of the other [De Gonzalez and Cox 2007]. Whereas qualitative interactions are not removable by any transformation [Satagopan and Elston 2013], the presence of quantitative interaction depends on whether the effects are being measured in an underlying additive scale, for example using risk-differences; multiplicative scale, using risk-ratios; or some other scale [Walter and Holford 1978].
