A FAST ALGORITHM FOR DETECTING GENE–GENE INTERACTIONS IN GENOME-WIDE ASSOCIATION STUDIES

With the recent advent of high-throughput genotyping techniques, ge-netic data for genome-wide association studies (GWAS) have become in-creasingly available, which entails the development of efficient and effective statistical approaches. Although many such approaches have been developed and used to identify single-nucleotide polymorphisms (SNPs) that are asso-ciated with complex traits or diseases, few are able to detect gene–gene inter-actions among different SNPs. Genetic interactions, also known as epistasis, have been recognized to play a pivotal role in contributing to the genetic vari-ation of phenotypic traits. However, because of an extremely large number of SNP–SNP combinations in GWAS, the model dimensionality can quickly become so overwhelming that no prevailing variable selection methods are capable of handling this problem. In this paper, we present a statistical frame-work for characterizing main genetic effects and epistatic interactions in a GWAS study. Specifically, we first propose a two-stage sure independence screening (TS-SIS) procedure and generate a pool of candidate SNPs and in-teractions, which serve as predictors to explain and predict the phenotypes of a complex trait. We also propose a rates adjusted thresholding estimation (RATE) approach to determine the size of the reduced model selected by an independence screening. Regularization regression methods, such as LASSO or SCAD, are then applied to further identify important genetic effects. Sim-ulation studies show that the TS-SIS procedure is computationally efficient and has an outstanding finite sample performance in selecting potential SNPs as well as gene–gene interactions. We apply the proposed framework to an-alyze an ultrahigh-dimensional GWAS data set from the Framingham Heart Study, and select 23 active SNPs and 24 active epistatic interactions for the body mass index variation. It shows the capability of our procedure to resolve the complexity of genetic control