Measuring gene-gene interaction using Kullback-Leibler divergence

Genome-wide association studies (GWAS) are used to investigate genetic variants contributing to complex traits. Despite discovering many loci, a large proportion of "missing" heritability remains unexplained. Gene-gene interactions may help explain some of this gap. Traditionally, gene-gene interactions have been evaluated using parametric statistical methods such as linear and logistic regression, with multifactor dimensionality reduction (MDR) used to address sparseness of data in high dimensions. We propose a method for the analysis of gene-gene interactions across independent single-nucleotide polymorphisms (SNPs) in two genes. Typical methods for this problem use statistics based on an asymptotic chi-squared mixture distribution, which is not easy to use. Here, we propose a Kullback-Leibler-type statistic, which follows an asymptotic, positive, normal distribution under the null hypothesis of no relationship between SNPs in the two genes, and normally distributed under the alternative hypothesis. The performance of the proposed method is evaluated by simulation studies, which show promising results. The method is also used to analyze real data and identifies gene-gene interactions among RAB3A, MADD, and PTPRN on type 2 diabetes (T2D) status.