Likelihood-based disequilibrium mapping for two-marker haplotype data

We report a theory that gives the sampling distribution of two-marker haplotypes that are linked to a rare disease mutation. The sampling distribution is generated with successive Monte Carlo realizations of the coalescence of the disease mutation having recombination and marker mutation events placed along the lineage. Given a sample of mutation-bearing, two-marker haplotypes, the maximum likelihood estimate of the location of the disease mutation can be calculated from the generated sampling distribution, provided that one knows enough about the population history in order to model it. The two-marker likelihood method is compared to a single-marker likelihood and a composite likelihood. The two-marker maximum likelihood gives smaller confidence intervals for the location of the disease locus than a comparable single-marker maximum likelihood. The composite likelihood can give biased results and the bias increases as the extent of linkage disequilibrium on mutation-bearing chromosomes decreases. Haplotype configurations exist for which the composite likelihood will fail to place the disease locus in the correct marker interval.