A note on the optimal measure of allelic association

Association of pairs of loci due to departure of gamete frequencies from expected frequencies is called allelic association. This measure is useful for fine-scale mapping. There are several measures of allelic association in the literature. With the availability of a SNP map, the use of linkage disequilibrium to map genes is one of the central issues in the human genome project. The size of linkage disequilibrium blocks is of considerable interest. In this note, we investigate the statistical properties of a measure which is known to have the strongest theoretical population basis and be least sensitive to the marker allele frequencies. In particular, we have shown that this measure has intuitive appeal and the estimator for this measure has several statistically optimal properties such as consistency, asymptotic unbiasedness and asymptotic efficiency.