Two-locus association mapping in subquadratic time.

Genome-wide association studies (GWAS) have not been able to discover strong associations between many complex human diseases and single genetic loci. Mapping these phenotypes to pairs of genetic loci is hindered by the huge number of candidates leading to enormous computational and statistical problems. In GWAS on single nucleotide polymorphisms (SNPs), one has to consider in the order of 1010 to 1014 pairs, which is infeasible in practice. In this article, we give the first algorithm for 2-locus genome-wide association studies that is subquadratic in the number, n, of SNPs. The running time of our algorithm is data-dependent, but large experiments over real genomic data suggest that it scales empirically as n3/2. As a result, our algorithm can easily cope with n ~ 107, i.e., it can efficiently search all pairs of SNPs in the human genome.