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 polymorp hisms (SNPs) was quantified by Hedge et al. [Nat Genet 1999;21:360]. In the ir measure, the level of ambiguity increases with increasing numbers of loc i and as loci become more polymorphic. That work assumed linkage equilibriu m (LE). However, linkage disequilibrium (LD) provides additional informatio n 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 B1B2 haptotypes, respectively, and w.l.o.g. x(1)x(2) gre ater than or equal to x(2)x(3) Alternatively, Phi can be expressed in terms of the allele frequencies and the LD parameter delta. We also extend the f ormula 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 a djacent pairs of sites. In genome-wide LD studies to map common disease gen es, a dense map of SNPs may be utilized to detect association between a mar ker and disease. Therefore, the measurement of ambiguity can potentially he lp investigators to determine a more efficient map, designed to minimize am biguity and subsequent information loss. Copyright (C) 2000 Karger AG, Base l.