A measure of phase ambiguity in pairs of SNPs in the presence of linkage disequilibrium.

The extent of haplotype ambiguity in a string of single-nucleotide polymorphisms (SNPs) was quantified by Hodge et al. [Nat Genet 1999;21:360]. In their measure, the level of ambiguity increases with increasing numbers of loci and as loci become more polymorphic. That work assumed linkage equilibrium (LE). However, linkage disequilibrium (LD) provides additional information about the haplotypes at a site, thereby diluting the level of ambiguity. The ambiguity vanishes altogether when LD reaches its maximum value. Here, we introduce the ambiguity measure, Phi, to allow for LD (between pairs of SNPs). We derive the formula Phi = 4x(2)x(3) for ambiguity in individuals, where x(1), x(2), x(3) and x(4) are the probabilities of the A(1)A(2), A(1)B(2), B(1)A(2) and B(1)B(2) haplotypes, respectively, and w.l.o.g. x(1)x(4) > or = x(2)x(3). Alternatively, Phi can be expressed in terms of the allele frequencies and the LD parameter delta. We also extend the formula to triads of two parents plus one child. We estimate our measure Phi for relevant SNPs in the published lipoprotein lipase (LPL) gene dataset [Clark et al., Am J Hum Genet 1998;63:595; Nickerson et al., Nat Genet 1998;19:233], obtaining values ranging from a low of 0 to a high of 0.11 among adjacent pairs of sites. In genome-wide LD studies to map common disease genes, a dense map of SNPs may be utilized to detect association between a marker and disease. Therefore, the measurement of ambiguity can potentially help investigators to determine a more efficient map, designed to minimize ambiguity and subsequent information loss.