Genome‐Wide Analysis of Gene‐Gene and Gene‐Environment Interactions Using Closed‐Form Wald Tests

Abstract

Despite the successful discovery of hundreds of variants for complex human traits using genome-wide association studies, the degree to which genes and environmental risk factors jointly affect disease risk is largely unknown. One obstacle toward this goal is that the computational effort required for testing gene-gene and gene-environment interactions is enormous. As a result, numerous computationally efficient tests were recently proposed. However, the validity of these methods often relies on unrealistic assumptions such as additive main effects, main effects at only one variable, no linkage disequilibrium between the two SNPs in a pair or gene-environment independence. Here we derive closed-form and consistent estimates for interaction parameters and propose to use Wald tests for testing interactions. The Wald tests are asymptotically equivalent to the likelihood ratio tests, largely considered to be the gold standard tests but generally too computationally demanding for genome-wide interaction analysis. Simulation studies show that the proposed Wald tests have very similar performances with the likelihood ratio tests but are much more computationally efficient. Applying the proposed tests to a genome-wide study of multiple sclerosis, we identify interactions within the major histocompatibility complex region. In this application, we find that (1) focusing on pairs where both single nucleotide polymorphisms (SNPs) are marginally significant leads to more significant interactions when compared to focusing on pairs where at least one SNP is marginally significant; and (2) parsimonious parameterization of interaction effects might decrease, rather than increase, statistical power.

Performance of epistasis detection methods in semi-simulated GWAS

“…[ 12 ] compared their methods on simulated datasets with independant SNPs. Emily [ 13 ], Goudey et al [ 14 ], and Yu et al [ 15 ] compared their methods to PLINK, χ 2 , and BOOST on simulated contingency tables with two SNPs including linkage disequilibrium (LD). Wan et al [ 16 ] compared BOOST and PLINK under H 0 using evolutionary simulations [ 17 ] to generate datasets of 38836 SNPs with simulated LD.…”

A new method for exploring gene-gene and gene-environment interactions in GWAS with tree ensemble methods and SHAP values

“…For the testing of the interactions we apply the likelihood ratio test (LRT) to test the null hypothesis that ν = 0 for SNP-SNP interactions or φ = 0 for SNP-environment interactions [19,54]. The LRT assumes independence between the samples, and so we need to make sure the individuals included in the test are not related to any significant degree.…”

Fast and general tests of genetic interaction for genome-wide association studies

“…However, these tests typically depend on strong assumptions about the main effects, marginal effects or LD to reduce the computational complexity [ 15 , 19 , 20 ]. Recently Yu et al introduced a closed-form Wald test restricted to a specific parameterization of the logistic regression model [ 21 ]. Here, we introduce a general class of computationally efficient Wald tests, that enables analysis of case-control traits, quantitative traits, and in fact any trait modeled by a member in the exponential family.…”