An exact test for the association between the disease and alleles at highly polymorphic loci with particular interest in the haplotype analysis.

The association analysis between the disease and genetic alleles is one of the simple methods for localizing the susceptibility locus in the genes. For revealing the association, several statistical tests have been proposed without discussing explicitly the alternative hypotheses. We therefore specify two types of alternative hypotheses (i.e., there is only one susceptibility allele in the locus, and there is an extension or shortening of alleles associated with the disease) and derive exact tests for the respective hypotheses. We also propose to combine these two tests when the prior knowledge is not sufficient enough to specify one of these two hypotheses. In particular, these ideas are extended to the haplotype analysis of three-way association between the disease and bivariate allele frequencies at two closely linked loci. As a by-product, a factorization of the probability distribution of the three-way cell frequencies under the null hypothesis of no three-way interaction is obtained.