Detecting epistasis via Markov bases

Rapid research progress in genotyping techniques have allowed large genome-wide associationstudies. Existing methods often focus on determining associations between single loci anda specic phenotype. However, a particular phenotype is usually the result of complex relationshipsbetween multiple loci and the environment. In this paper, we describe a two-stage methodfor detecting epistasis by combining the traditionally used single-locus search with a search formultiway interactions. Our method is based on an extended version of Fisher's exact test. Toperform this test, a Markov chain is constructed on the space of multidimensional contingencytables using the elements of a Markov basis as moves. We test our method on simulated data andcompare it to a two-stage logistic regression method and to a fully Bayesian method, showing thatwe are able to detect the interacting loci when other methods fail to do so. Finally, we apply ourmethod to a genome-wide data set consisting of 685 dogs and identify epistasis associated withcanine hair length for four pairs of single nucleotide polymorphisms (SNPs).