A One-Degree-of-Freedom Test for Supra-Multiplicativity of SNP Effects

Deviation from multiplicativity of genetic risk factors is biologically plausible and might explain why Genome-wide association studies (GWAS) so far could unravel only a portion of disease heritability. Still, evidence for SNP-SNP epistasis has rarely been reported, suggesting that 2-SNP models are overly simplistic. In this context, it was recently proposed that the genetic architecture of complex diseases could follow limiting pathway models. These models are defined by a critical risk allele load and imply multiple high-dimensional interactions. Here, we present a computationally efficient one-degree-of-freedom “supra-multiplicativity-test” (SMT) for SNP sets of size 2 to 500 that is designed to detect risk alleles whose joint effect is fortified when they occur together in the same individual. Via a simulation study we show that the SMT is powerful in the presence of threshold models, even when only about 30–45% of the model SNPs are available. In addition, we demonstrate that the SMT outperforms standard interaction analysis under recessive models involving just a few SNPs. We apply our test to 10 consensus Alzheimer’s disease (AD) susceptibility SNPs that were previously identified by GWAS and obtain evidence for supra-multiplicativity ( ) that is not attributable to either two-way or three-way interaction.