Main-Effects Model Is a Special Kind of Additive Model in the Presence of Linkage Disequilibrium

Statistical epistasis refers to a departure from additivity on some scale related to a trait. The implication of it may vary due to the choice of scale. In this paper, we focus on statistical epistasis between two loci for a binary trait and mainly investigate two common scales, the penetrance and the variance of the penetrance. For each scale, the model that keeps additivity is first studied and then the statistical epistatic effect is tested as a deviation from the model. The additive model describes additivity on the penetrance scale and the main-effects model assumes additivity on the variance of the penetrance. These two models have been proved to be equivalent when the loci are in linkage equilibrium (LE). Our goal is to show that they are not equivalent in the presence of linkage disequilibrium (LD) and to reveal that the degrees of deviations from these two models may not be the same.