Accounting for decay of linkage disequilibrium in haplotype inference and missing-data imputation

Abstract

Although many algorithms exist for estimating haplotypes from genotype data, none of them take full account of both the decay of linkage disequilibrium (LD) with distance and the order and spacing of genotyped markers. Here, we describe an algorithm that does take these factors into account, using a flexible model for the decay of LD with distance that can handle both "blocklike" and "nonblocklike" patterns of LD. We compare the accuracy of this approach with a range of other available algorithms in three ways: for reconstruction of randomly paired, molecularly determined male X chromosome haplotypes; for reconstruction of haplotypes obtained from trios in an autosomal region; and for estimation of missing genotypes in 50 autosomal genes that have been completely resequenced in 24 African Americans and 23 individuals of European descent. For the autosomal data sets, our new approach clearly outperforms the best available methods, whereas its accuracy in inferring the X chromosome haplotypes is only slightly superior. For estimation of missing genotypes, our method performed slightly better when the two subsamples were combined than when they were analyzed separately, which illustrates its robustness to population stratification. Our method is implemented in the software package PHASE (v2.1.1), available from the Stephens Lab Web site.

Figure 1

Illustration of how π(h_k+1|h₁,…,h_k) builds h_k+1 as an imperfect mosaic of h₁,…,h_k. The figure illustrates the case k=3 and shows three possible values (h_4A, h_4B, and h_4C) for h₄, given h₁, h₂, and h₃. Each column of circles represents a SNP locus, with blackened and unblackened circles representing the two alleles. Each possible h₄ can be thought of as having been created by “copying” parts of h₁, h₂ and h₃. The shading in each case shows which haplotype was “copied” at each position along the chromosome and indicates whether the haplotype is most closely related to h₁, h₂, or h₃. Changes in the shading along a haplotype represent ancestral recombination events; these are more likely to occur between SNPs that are farther apart (e.g., SNPs 2 and 3 or 4 and 5) or that have a higher rate of recombination between them. The imperfect nature of the copying process is exemplified at the third and fourth locus, where h_4B has the blackened allele despite having “copied” h₂, which has the unblackened allele. The occurrence of several such “imperfections” on a single chunk indicate that the haplotype is relatively highly diverged from the one that it copied in that region (see text).