Detecting latent gene-environment interaction when analyzing binary traits

In genome-wide association studies (GWAS), it is desirable to test for interactions (GxE) between single-nucleotide polymorphisms (SNPs,Gs) and environmental variables (Es). However, directly accounting for interaction is often infeasible, because E is latent. For quantitative traits (Y) that are approximately normally distributed, it has been shown that indirect testing on GxE can be done by testing for heteroskedasticity of Y between genotypes. However, when traits are binary, the existing methodology based on testing the heteroskedasticity of the trait across genotypes cannot be generalized. In this paper, we propose an approach to indirectly test GxE for binary traits based on the non-additive effect G, and subsequently propose a joint test that accounts for the main and interaction effects of each SNP during GWAS. We illustrate the statistical features including type-I-error control and power of the proposed method through extensive numerical studies. Applying our method to the UK Biobank dataset, we showcase the practical utility of the proposed method, revealing SNPs and genes with strong potential for latent interaction effects.