Despite the accumulation of quantitative trait loci (QTL) data in many complex human diseases, most of current approaches that have attempted to relate genotype to phenotype have achieved limited success, and genetic factors of many common diseases are yet remained to be elucidated. One of the reasons that makes this problem complex is the existence of single nucleotide polymorphism (SNP) interaction, or epistasis. Due to excessive amount of computation for searching the combinatorial space, existing approaches cannot fully incorporate high-order SNP interactions into their models, but limit themselves to detecting only lower-order SNP interactions. We present an empirical approach based on ridge regression with polynomial kernels and model selection technique for determining the true degree of epistasis among SNPs. Computer experiments in simulated data show the ability of the proposed method to correctly predict the number of interacting SNPs provided that the number of samples is large enough relative to the number of SNPs. For cases in which the number of the available samples is limited, we propose to perform sliding window approach to ensure sufficiently large sample/SNP ratio in each window. In computational experiments using heterogeneous stock mice data, our approach has successfully detected subregions that harbor known causal SNPs. Our analysis further suggests the existence of additional candidate causal SNPs interacting to each other in the neighborhood of the known causal gene. Software is available from https://github.com/HirotoSaigo/KDSNP .
Keywords: Epistasis; GWAS; gene–gene interaction; kernel ridge regression; polynomial kernel.