A comparison of linkage disequilibrium measures for fine-scale mapping

Linkage mapping generally localizes disease genes to 1- to 2-cM regions of chromosomes. In theory, further refinement of location can be achieved by population-based studies of linkage disequilibrium between disease locus alleles and alleles at adjacent markers. One approach to localization, dubbed simple disequilibrium mapping, is to determine the relative location of the disease locus by plotting disequilibrium values against marker locations. We investigate the simple mapping properties of five disequilibrium measures, the correlation coefficient delta, Lewontin's D', the robust formulation of the population attributable risk delta, Yule's Q, and Kaplan and Weir's proportional difference d under the assumption of initial complete disequilibrium between disease and marker loci. The studies indicate that delta is a superior measure for fine mapping because it is directly related to the recombination fraction between the disease and the marker loci, and it is invariant when disease haplotypes are sampled at a rate higher than their population frequencies, as in a case-control study. D' yields results comparable to those of delta in many realistic settings. Of the remaining three measures, Q, delta, and d, Q yields the best results. From simulations of short-term evolution, all measures show some sensitivity to marker allele frequencies; however, as predicted by analytic results, Q, delta, and d exhibit the greatest sensitivity to variation in marker allele frequencies across loci.