Genetic association tests in the presence of epistasis or gene-environment interaction

A genetic variant is very likely to manifest its effect on disease through its main effect as well as through its interaction with other genetic variants or environmental factors. Power to detect genetic variants can be greatly improved by modeling their main effects and their interaction effects through a common set of parameters or "generalized association parameters" (Chatterjee et al. [2006] Am. J. Hum. Genet. 79:1002-1016) because of the reduced number of degrees of freedom. Following this idea, I propose two models that extend the work by Chatterjee and colleagues. Particularly, I consider not only the case of relatively weak interaction effect compared to the main effect but also the case of relatively weak main effect. This latter case is perhaps more relevant to genetic association studies. The proposed methods are invariant to the choice of the allele for scoring genotypes or the choice of the reference genotype score. For each model, the asymptotic distribution of the likelihood ratio statistic is derived. Simulation studies suggest that the proposed methods are more powerful than existing ones under certain circumstances.