Fast Sampling-Based Whole-Genome Haplotype Block Recognition

Abstract

Scaling linkage disequilibrium (LD) based haplotype block recognition to the entire human genome has always been a challenge. The best-known algorithm has quadratic runtime complexity and, even when sophisticated search space pruning is applied, still requires several days of computations. Here, we propose a novel sampling-based algorithm, called S-MIG (++), where the main idea is to estimate the area that most likely contains all haplotype blocks by sampling a very small number of SNP pairs. A subsequent refinement step computes the exact blocks by considering only the SNP pairs within the estimated area. This approach significantly reduces the number of computed LD statistics, making the recognition of haplotype blocks very fast. We theoretically and empirically prove that the area containing all haplotype blocks can be estimated with a very high degree of certainty. Through experiments on the 243,080 SNPs on chromosome 20 from the 1,000 Genomes Project, we compared our previous algorithm MIG (++) with the new S-MIG (++) and observed a runtime reduction from 2.8 weeks to 34.8 hours. In a parallelized version of the S-MIG (++) algorithm using 32 parallel processes, the runtime was further reduced to 5.1 hours.

Effects of Single Nucleotide Polymorphism Marker Density on Haplotype Block Partition

“…There have been several attempts to accelerates the speed and improve memory performance of the CI method in Haploview. Such attempts include MIG++ [ 12 ] and S-MIG++ [ 13 ] both of which can reduce the time/memory complexity by omitting unnecessary computations.…”

“…In addition, to improve the runtime/memory of the algorithm, the MIG++ uses a method based on an approximated estimator of the variance of D′ proposed by Zapata et al [ 18 ] instead of the likelihood-based method proposed by Wall and Pritchard [ 19 ] used in Haploview [ 10 ]. The MIG++ algorithm is now implemented in PLINK 1.9 [ 14 ], but in PLINK 1.9, the CI of D′ is estimated based on the maximum likelihood method by Wall and Pritchard [ 19 ] with improved efficiency in estimating diplotype frequencies [ 13 20 21 ]. In this study, we only obtain the haplotype block partition results of the PLINK-MIG++ implemented in PLINK 1.9 instead of the originally proposed version of MIG++.…”

“…The S-MIG++ algorithm improves the MIG++ by first sampling small fraction of all SNP pairs to estimate the upper limits of the LD block boundaries and then moving to the refinement step to determine exact haplotype boundaries [ 13 ]. In this way, S-MIG++ could reduce the search space much more than MIG++.…”

“…Among them, Haploview carries three different methods for haplotype block partitioning each of which adopts a different operational definition for haplotype blocks: confidence interval (CI) method by Gabriel et al [ 8 ], four gamete test (FGT) by Wang et al [ 9 ], and solid spine (SS) method [ 10 ]. More recently, following the haplotype block definition of Gabriel et al [ 8 ], some computationally efficient algorithms have been also released and these include MIG++ [ 12 ] and S-MIG++ [ 13 ]. MIG++ is also implemented in PLINK 1.9 with additional modification for computational efficiency [ 14 ].…”

“…We also investigate how these effects of the marker density work differently for different haplotype block partitioning methods. The haplotype block partition methods we investigate include three methods implemented in Haploview (CI, FGT, and SS) [ 10 ], MIG++ implemented in PLINK version 1.9 [ 12 14 ], and S-MIG++ [ 13 ]. For reference panel to construct experimental datasets we use the 1000 Genomes Projects phase 1 release 3 dataset [ 15 ] and HapMap phase III dataset [ 16 ].…”