Closed-form Wald tests for genome-wide analysis of gene-gene interactions

Despite the successful discovery of hundreds of variants for complex human traits using genomewide association studies, the degree to which genes jointly affect disease risk is largely unknown. One obstacle toward this goal is that the computational effort required for testing gene-gene interactions is enormous. As a result, numerous computationally efficient tests were recently proposed, such as PLINK [1], Boost [2], and a joint test [3]. However, the validity of these methods often relies on unrealistic assumptions such as additive main effects, main effects at only one SNP, and no linkage disequilibrium. Here we propose to use closed-form Wald tests. The Wald tests are asymptotically equivalent to the corresponding 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 Wald tests have very similar performance with their computationally intensive counterparts. 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 found 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.