Detecting latent interaction effects when analyzing binary traits

In genome-wide association studies (GWAS), it is often desirable to test for interactions, such as gene-environment (G x E) or gene-gene (G x G) interactions, between single-nucleotide polymorphisms (SNPs, G's) and environmental variables (E's). However, directly accounting for interaction is often infeasible, because the interacting variable is latent or the computational burden is too large. 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 interaction effects for binary traits and subsequently propose a joint test that accounts for the main and interaction effects of each SNP during GWAS. The final method is straightforward to implement in practice-it simply involves adding a non-additive (i.e., dominance) term to standard GWAS additive models for binary traits and testing its significance. 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.