Powerful Tukey’s One Degree-of-Freedom Test for Detecting Gene–Gene and Gene–Environment Interactions

Genome-wide association studies (GWASs) have identified thousands of single nucleotide polymorphisms (SNPs) robustly associated with hundreds of complex human diseases including cancers. However, the large number of GWAS-identified genetic loci only explains a small proportion of the disease heritability. This “missing heritability” problem has been partly attributed to the yet-to-be-identified gene–gene (G × G) and gene–environment (G × E) interactions. In spite of the important roles of G × G and G × E interactions in understanding disease mechanisms and filling in the missing heritability, straightforward GWAS scanning for such interactions has very limited statistical power, leading to few successes. Here we propose a two-step statistical approach to test G × G/G × E interactions: the first step is to perform principal component analysis (PCA) on the multiple SNPs within a gene region, and the second step is to perform Tukey’s one degree-of-freedom (1-df) test on the leading PCs. We derive a score test that is computationally fast and numerically stable for the proposed Tukey’s 1-df interaction test. Using extensive simulations we show that the proposed approach, which combines the two parsimonious models, namely, the PCA and Tukey’s 1-df form of interaction, outperforms other state-of-the-art methods. We also demonstrate the utility and efficiency gains of the proposed method with applications to testing G × G interactions for Crohn’s disease using the Wellcome Trust Case Control Consortium (WTCCC) GWAS data and testing G × E interaction using data from a case–control study of pancreatic cancer.