Pedigree disequilibrium tests for multilocus haplotypes.

TLDR: A permutation procedure for the null hypothesis of interest is described, which controls for violation of the assumptions, and a likelihood‐ratio test is proposed, using the expectation‐maximization (E‐M) algorithm to account for haplotype ambiguities.

Abstract: Association tests of multilocus haplotypes are of interest both in linkage disequilibrium mapping and in candidate gene studies. For case-parent trios, I discuss the extension of existing multilocus methods to include ambiguous haplotypes in tests of models which distinguish between the cis and trans phase. A likelihood-ratio test is proposed, using the expectation-maximization (E-M) algorithm to account for haplotype ambiguities. Assumptions about the population structure are required, but realistic situations, including population stratification, which violate the assumptions lead to conservative tests. I describe a permutation procedure for the null hypothesis of interest, which controls for violation of the assumptions. For general pedigrees, I describe extensions of the pedigree disequilibrium test to include uncertain haplotypes. The summary statistics are replaced by their expected values over prior distributions of haplotype frequencies. If prior distributions are not available, a valid test is possible by using the E-M algorithm to estimate the null distribution of haplotype frequencies. Similar methods are available for quantitative traits. Exact permutation tests are difficult to construct in small samples, but an approximate procedure is appropriate in large samples, and can be used to account for dependencies between tests of multiple haplotypes and loci.