Detection of SNP epistasis effects of quantitative traits using an extended Kempthorne model

Epistasis effects (gene interactions) have been increasingly recognized as important genetic factors underlying complex traits. The existence of a large number of single nucleotide polymorphisms (SNPs) provides opportunities and challenges to screen DNA variations affecting complex traits using a candidate gene analysis. In this article, four types of epistasis effects of two candidate gene SNPs with Hardy-Weinberg disequilibrium (HWD) and linkage disequilibrium (LD) are considered: additive x additive, additive x dominance, dominance x additive, and dominance x dominance. The Kempthorne genetic model was chosen for its appealing genetic interpretations of the epistasis effects. The method in this study consists of extension of Kempthorne's definitions of 35 individual genetic effects to allow HWD and LD, genetic contrasts of the 35 extended individual genetic effects to define the 4 epistasis effects, and a linear model method for testing epistasis effects. Formulas to predict statistical power (as a function of contrast heritability, sample size, and type I error) and sample size (as a function of contrast heritability, type I error, and type II error) for detecting each epistasis effect were derived, and the theoretical predictions agreed well with simulation studies. The accuracy in estimating each epistasis effect and rates of false positives in the absence of all or three epistasis effects were evaluated using simulations. The method for epistasis testing can be a useful tool to understand the exact mode of epistasis, to assemble genome-wide SNPs into an epistasis network, and to assemble all SNP effects affecting a phenotype using pairwise epistasis tests.