Testing for gene-gene interaction with AMMI models

Studies have shown that many common diseases are influenced by multiple genes and their interactions. There is currently a strong interest in testing for association between combinations of these genes and disease, in particular because genes that affect the risk of disease only in the presence of another genetic variant may not be detected in marginal analysis. In this paper we propose the use of additive main effect and multiplicative interaction (AMMI) models to detect and to quantify gene-gene interaction effects for a quantitative trait. The objective of the present research is to demonstrate the practical advantages of these models to describe complex interaction between two unlinked loci. Although gene-gene interactions have often been defined as a deviance from additive genetic effects, the residual term has generally not been appropriately treated. The AMMI models allow for the analysis of a two way factorial data structure and combine the analysis of variance of the two main genotype effects with a principal component analysis of the residual multiplicative interaction. The AMMI models for gene-gene interaction presented here allow for the testing of non additivity between the two loci, and also describe how their interaction structure fits the existing non-additivity. Moreover, these models can be used to identify the specific two genotypes combinations that contribute to the significant gene-gene interaction. We describe the use of the biplot to display the structure of the interaction and evaluate the performance of the AMMI and the special cases of the AMMI previously described by Tukey and Mandel with simulated data sets. Our simulated study showed that the AMMI model is as powerful as general linear models when the interaction is not modeled in the presence of marginal effects. However, in the presence of pure epitasis, i.e. in the absence of marginal effects, the AMMI method was not found to be superior to other tested regression methods.