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

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 single‐nucleotide polymorphisms (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 (LRTs), 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 LRTs 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 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.