The case-only design is an extreme form of a less-is-more strategy, because no controls are sampled at all [7]. In place of controls we make a strong assumption. If one can safely assume that factors A and B occur independently of each other in the source population (an assumption that may often hold with an environmental factor and a genetic variant), then one can test a multiplicatively-defined interaction using only cases. Reiterating the argument given by Piegorsch et al (6], this can be seen as follows. Consider the multiplicative interaction parameter: ψ=Pr[D|A,B]Pr[D|A¯,B¯]Pr[D|A¯,B]Pr[D|A,B¯]
