Genome-wide association studies (GWAS) explain a fraction of the underlying heritability of genetic diseases. Investigating epistatic interactions between two or more loci help to close this gap. Unfortunately, the sheer number of loci combinations to process and hypotheses prohibit the process both computationally and statistically. Epistasis test prioritization algorithms rank likely epistatic single nucleotide polymorphism (SNP) pairs to limit the number of tests. However, they still suffer from very low precision. It was shown in the literature that selecting SNPs that are individually correlated with the phenotype and also diverse with respect to genomic location leads to better phenotype prediction due to genetic complementation. Here, we propose that an algorithm that pairs SNPs from such diverse regions and ranks them can improve prediction power. We propose an epistasis test prioritization algorithm that optimizes a submodular set function to select a diverse and complementary set of genomic regions that span the underlying genome. The SNP pairs from these regions are then further ranked w.r.t. their co-coverage of the case cohort. We compare our algorithm with the state of the art on three GWAS and show that (1) we substantially improve precision (from 0.003 to 0.652) while maintaining the significance of selected pairs, (2) decrease the number of tests by 25-fold, and (3) decrease the runtime by 4-fold. We also show that promoting SNPs from regulatory/coding regions improves the performance (up to 0.8). Potpourri is available at http:/ciceklab.cs.bilkent.edu.tr/potpourri.
Keywords: complementation; diversification; epistasis test prioritization; population cover; submodular optimization.