  Rapid research progress in genotyping techniques have allowed large
genome-wide association studies. Existing methods often focus on determining
associations between single loci and a specific phenotype. However, a
particular phenotype is usually the result of complex relationships between
multiple loci and the environment. In this paper, we describe a two-stage
method for detecting epistasis by combining the traditionally used single-locus
search with a search for multiway interactions. Our method is based on an
extended version of Fisher's exact test. To perform this test, a Markov chain
is constructed on the space of multidimensional contingency tables using the
elements of a Markov basis as moves. We test our method on simulated data and
compare it to a two-stage logistic regression method and to a fully Bayesian
method, showing that we are able to detect the interacting loci when other
methods fail to do so. Finally, we apply our method to a genome-wide data set
consisting of 685 dogs and identify epistasis associated with canine hair
length for four pairs of SNPs.
