ShapeIT: new rapid and accurate algorithm for haplotype inference
 7.3k Downloads
 28 Citations
Abstract
Background
We have developed a new computational algorithm, ShapeIT, to infer haplotypes under the genetic model of coalescence with recombination developed by Stephens et al in Phase v2.1. It runs much faster than Phase v2.1 while exhibiting the same accuracy. The major algorithmic improvements rely on the use of binary trees to represent the sets of candidate haplotypes for each individual. These binary tree representations: (1) speed up the computations of posterior probabilities of the haplotypes by avoiding the redundant operations made in Phase v2.1, and (2) overcome the exponential aspect of the haplotypes inference problem by the smart exploration of the most plausible pathways (ie. haplotypes) in the binary trees.
Results
Our results show that ShapeIT is several orders of magnitude faster than Phase v2.1 while being as accurate. For instance, ShapeIT runs 50 times faster than Phase v2.1 to compute the haplotypes of 200 subjects on 6,000 segments of 50 SNPs extracted from a standard Illumina 300 K chip (13 days instead of 630 days). We also compared ShapeIT with other widely used software, Gerbil, PLEM, Fastphase, 2SNP, and Ishape in various tests: ShapeIT and Phase v2.1 were the most accurate in all cases, followed by Ishape and Fastphase. As a matter of speed, ShapeIT was faster than Ishape and Fastphase for datasets smaller than 100 SNPs, but Fastphase became faster but still less accurate to infer haplotypes on larger SNP datasets.
Conclusion
ShapeIT deserves to be extensively used for regular haplotype inference but also in the context of the new highthroughput genotyping chips since it permits to fit the genetic model of Phase v2.1 on large datasets. This new algorithm based on tree representations could be used in other HMMbased haplotype inference software and may apply more largely to other fields using HMM.
Keywords
Hide Markov Model Single Nucleotide Polymorphism Binary Tree Hide State Forward AlgorithmBackground
The recent advent of genotyping chips, which can analyze up to 500,000 single nucleotide polymorphisms (SNP) per individual, offers a powerful tool for large scale association studies in human diseases. The most common approach to find genes possibly implicated in a disease relies on the comparison, in patients and controls, of the distributions of SNP markers. An approach to increase the power of such studies is to focus on more complex markers which capture implicitly the linkage disequilibrium (LD) between SNPs: the combination of SNP alleles on the same chromosome called haplotypes. Haplotypes are of great interest to study complex diseases since they are generally derived from chromosomal fragments which are transmitted from one generation to the next or which may have a biological meaning such as the promoter or the exons of a gene [1]. Beyond the biomedical applications, the comparison of haplotype distributions between populations also provides new insights in the diversity, the history and the migrations of human populations. For instance, several studies [2, 3, 4, 5, 6] have recently highlighted that genetic diversity of the human genome is organized in regions called haplotype blocks in which SNPs exhibit a high degree of LD and few common haplotypes. These haplotype blocks are delimited by recombination hotspots and chromosomes can thus be viewed as mosaics of common haplotypes. The recently developed HapMap project, dedicated to establish a dense map of SNPs and LD in various human populations [7, 8, 9], has emphasized the interest of haplotypes to study human diversity.
Regular genotyping (based on PCR/sequencing or on chips) provides the genotype for each SNP but does not allow the determination of the haplotypes (i.e. the combination of SNP alleles on each chromosome), and current experimental solutions to this problem are still expensive and timeconsuming [10, 11]. Clark was first to introduce a computational alternative [12]: the determination of haplotypes via a parsimony criterion which leads to a minimal set of haplotypes sufficient to explain the entire population. Since then, efficient statistical algorithms have been developed under the random mating assumption where the observed genotypes are formed by sampling independently two unknown haplotypes. This assumption, coupled with a probabilistic model for the haplotypes, permits to define the likelihood of the observed genotypes as a function of the model parameters. Thus, in order to infer haplotypes, the most likely parameter values are estimated via an Expectation Maximization algorithm (EM) or a Gibbs sampler algorithm (GS) on the observed genotypes.
The first EMbased model estimated the most likely haplotypes frequencies for observed genotypes without making any assumption on the mutation and recombination history of haplotypes [13]. Many software were built on this simple model and the bestknown is certainly PLEM [14]. Later on, two new models were developed based on the idea that the haplotypes were arising through mutation and recombination events from few founder haplotypes. In Gerbil [15], haplotype blocks are strictly defined by dynamic programming and in each block, the haplotypes are derived through mutations from founder haplotypes. On the other hand, in Fastphase [16], in HIT [17], and in HINT [18], both mutation and recombination events on founder haplotypes are simultaneously modeled through a hidden Markov model (HMM). All these methods estimate founder haplotypes from observed genotypes via EM algorithms.
For the GSbased algorithms, the general case relies on sampling haplotypes for a genotype in function of all the haplotypes currently assigned to the other genotypes. The model of Haplotyper [19] simply favors haplotypes which have been already assigned to many genotypes. In Phase v1.0 [20], the idea was to favor the sampling of haplotypes which likely coalesce with the already assigned ones. At last, in Phase v2.1 [21, 22], the sampled haplotypes are mosaics of the previously sampled ones modeled in a HMM.
Recently, an alternative approach to the statistical algorithms was proposed in 2snp [23] which computes LD measures for all pairs of SNPs and then resolves genotypes by finding the maximum spanning trees.
Several studies have suggested that the HMMbased methods were the most accurate to infer the haplotypes [17, 18, 24], certainly because of the flexible definition of the haplotype blocks which depends generally on the physical distance between SNPs [16]. Among the HMMbased methods, Phase v2.1 is often considered as the most accurate developed so far [24, 25, 26, 27, 28, 29, 30] which explains why it is widely used in genetic association studies [31, 32, 33] and why it was used to phase the genotype data of the HapMap project [8]. The strength of Phase v2.1 probably comes from two particularities. First, the HMM is built during the GS iterations with a number of haplotypes proportional to the number of genotypes in opposition to other HMMbased methods which define a fixed number of founder haplotypes. Second, the haplotypes are inferred by summing over all the possible hidden state sequences of the HMM (Forward algorithm) whereas many other HMMbased methods infer haplotypes by sampling only the most probable hidden sequence in the HMM (Viterbi algorithm).
However, the required running time increases dramatically with the number of SNPs since the search space grows exponentially. This prevents the easy use of Phase v2.1 in the current highthroughput chips. This fact has previously motivated us to develop Ishape [27] which matches Phase v2.1 accuracy while maintaining feasible running times. For that, we have used a twostep strategy: 1. we defined a limited space of possible haplotypes with a rapid preprocessing algorithm based on bootstrapped EM haplotypes estimations 2. on this limited set of haplotypes, we then used an accurate Phaselike algorithm. The rapidity of the first step is made possible thanks to an iterative implementation of the EM algorithm which avoids any exponential growth of the space of possible haplotypes and includes the SNPs one after the other during the computations. In practice, Ishape runs up to 15 times faster than Phase 2.1 (for up to 100 SNPs) with a similar accuracy in populations with high LD, such as Caucasian genomes.
In this work, we present major improvements which greatly reduce the computational time of Phase v2.1. These improvements have been implemented in the software package ShapeIT and compared to the widely used competitor software.
Algorithm
Notations (Figure 1)
Let's assume we have a sample of n genotypes G = {G_{1},..., G_{ n }} describing the allelic content of n diploid individuals over s SNPs. A genotype is split into a haplotype pair by setting the phases between the z heterozygous SNPs (z ≤ s). The number of distinct haplotype pairs consistent with a genotype is then 2^{(z1)}. Let S = {S_{1},..., S_{ n }} denotes the total haplotype space where S_{ i }is the space of possible haplotype pairs associated with the ith genotype. Moreover, let's assume we have the recombination parameters ρ = {ρ_{1},..., ρ_{s1}} in the s1 intervals between the s SNPs of the sample as described by Stephens et al [22].
Gibbs sampler algorithm
The GS algorithm considers the haplotype reconstructions of n individuals as a set of n random variables H = {H_{1},..., H_{ n }} with sampling spaces in S and it estimates the conditional joint distribution of H given G and some recombination parameters ρ: Pr(H  G, ρ). In simple words, it computes a conditional probability for each haplotype pair of S in light of the observed genotypes G and the recombination pattern between the SNPs. Given these probabilities, the haplotype frequencies and the most likely haplotype pair for each genotype are straightforward to obtain. In practice, Pr(H  G, ρ) is estimated by sampling from the stationary distribution of a Gibbs sampler (GS) H^{(0)},..., H^{(t)},... where a state H^{(t)}is a particular realization of the random variables of H: n haplotype pairs from S which resolves the n genotypes of G. The GS starts with a random haplotype realization H^{(0)}, and goes from H^{(t)}to H^{(t+1)}by updating the haplotype pair of an individual i in light of the 2n2 other haplotypes found in H^{(t)}, that we call ${H}_{i}^{\left(t\right)}$. This "haplotypes update" step is done by sampling a new haplotype pair from the conditional distribution Pr(H_{ i } ${H}_{i}^{\left(t\right)}$, ρ) proposed by Fearnhead and Donnelly [34] and Li and Stephens [35]. This conditional distribution, called FDLS distribution in the following, is computed thanks to a hidden Markov model for haplotypes described in the next section. The important fact here is that computation of Pr(H_{ i } ${H}_{i}^{\left(t\right)}$, ρ) constitutes the most timeconsuming part of the GS since it has to be done on a space of possible haplotype pairs which grows exponentially with the number of heterozygous SNPs.
An iteration of the GS algorithm corresponds to update successively the haplotypes of the n individuals of G given a randomly initialized order of treatment. Between iterations, according to the Metropolis Hasting acceptance rates described by Stephens et al [22], we accept or reject (1) new values for the recombination parameters ρ = {ρ_{1},..., ρ_{s1}} in the s1 intervals between SNPs and (2) new treatment order of genotypes in the GS. To finally obtain Pr(H  G, ρ), we discard the first iterations of the GS as burnin iterations (typically 100) and for the n genotypes G_{ i }, we average the distribution Pr(H_{ i } ${H}_{i}^{\left(t\right)}$, ρ) on several main iterations (typically 100).
Computation of a haplotype pair probability in a HMM (Figure 2)
where δ_{h,h'}= 0 if h ≠ h' and δ_{h,h'}= 1 if h = h'. The conditional probability π of haplotype h reflects how likely h corresponds to an "imperfect mosaic" of the other haplotypes {h_{1}, ..., h_{2n2}} [22]. The underlying idea is that haplotype h has been probably created through the generations as a recombined sequence of haplotypes from the pool {h_{1}, ..., h_{2n2}}, possibly altered by some mutations. One models this by computing the probability of observing the sequence h = {o_{1}, ..., o_{ s }} in a hidden Markov model λ designed to represent all possible mosaics of {h_{1}, ..., h_{2n2}}: π(hh_{1}, ..., h_{2n2}, ρ) = Pr(o_{1}, ..., o_{ s }λ). Such HMM λ can be viewed as a trellis of s × (2n  2) hidden states q_{ j }(k) with 1 ≤ j ≤ s and 1 ≤ k ≤ 2n2. A hidden state q_{ j }(k) of λ corresponds to the allele of haplotype h_{ k }at SNP j and it is linked to all the hidden states q_{j+1}(l) (1 ≤ l ≤ 2n2) at SNP j+1 in order to model all the possible recombination jumps of haplotypes between SNPs j and j+1 (Figure 2). Then, a sequence of s hidden states in λ through the s SNPs corresponds to a particular mosaic of {h_{1}, ..., h_{2n2}}. The probability of observing h = {o_{1}, ..., o_{ s }} in λ is computed thanks to transition probabilities between hidden states which mimic recombination and thanks to emission probabilities from hidden alleles to observed alleles which mimic mutation. Similar hidden Markov models have been proposed, but they generally rely on a limited number of founder haplotypes where the most likely transition and emission probabilities are estimated from observed genotype data via an EM algorithm [17, 18]. Here, the emission and transition probabilities are defined with prior distributions depending respectively on a constant mutation parameter and on the variable recombination parameters ρ . The objective of this section is not to fully describe the probabilistic model of transitions and emissions since this has already been done by Stephens and Scheet [22]. Instead, we focus on how the haplotype probability is computed in such a HMM λ from transition and emission probabilities. We thus assume that the following quantities are known as set up by Stephens and Scheet:

The transition probability a_{ j }(l,k) from the state q_{ j }(l) of haplotype h_{ l }for SNP j to the state q_{j+1}(k) of haplotype h_{ k }for SNP j+1. If l ≠ k then a_{ j }(l,k) is the probability for h_{ l }to be recombined with h_{ k }between SNP j and SNP j+1 (large dashed arrows in Figure 2). And conversely, if l = k then a_{ j }(l,l) is the probability for h_{ l }to be not recombined between the two SNPs (plain arrows in Figure 2).

The emission probability b_{ j }(k) of the hidden allele of q_{ j }(k) in the observed allele o_{ j }of h (small dashed arrows in Figure 2). If the hidden allele is different from the observed one, then b_{ j }(k) corresponds to the probability that the hidden allele q_{ j }(k) has been altered in o_{ j }by a mutation event. Else, b_{ j }(k) corresponds to the probability that no mutation has occurred.
And the total probability of h over the s SNPs becomes:π(hh_{1}, ..., h_{2n2}, ρ) = π_{ s }(hh_{1}, ..., h_{2n2}, ρ)
The computations of α_{ j }(k) for k = 1,..., 2n2 and j = 1,..., s are efficiently done by a recursive algorithm for HMM called forward algorithm [36]. It starts from initial values:α_{1}(k) = b_{1}(k)/(2n  2)
Computing all the α values for a haplotype requires now running time in O(sn^{2}) instead of O(n^{ s }).
Computation of the FDLS distribution from a haplotype list by Phase v2.1 (Figure 3A)
The Phase v2.1 algorithm considers the haplotype space S_{ i }as a list of ${2}^{{z}_{i}}$ haplotypes compatibles with the genotype G_{ i }where z_{ i }is the number of heterozygous SNPs. And it computes the FDLS distribution over this list with equations (3) and (1) on the HMM λ. This approach is computationally intensive for two reasons. First, it performs many times the same computations of α values with the forward algorithm since the haplotypes of S_{ i }are derived from the same genotype and share thus identical allelic segments. For instance, as shown in Figure 3A, several haplotypes of S_{ i }differ only in the last SNPs while the computation of forward values α starts each time from the first SNP. Second, the list of haplotypes grows exponentially with the number of heterozygous SNPs which prevents any application with a high number of SNPs. To partially overcome this problem, a "divide for conquer" solution called "partitionligation" (PL) was first proposed by Niu et al [14, 19, 21]. It has been included in the Phase v2.1 algorithm as follows: it first divides the genotypes into segments of limited size (typically 5–8 SNPs), determines the most probable haplotypes on each segment with complete runs of the GS, and then progressively ligates haplotypes of the adjacent segments in several runs until completion. When two adjacent segments are ligated, the space S of candidate haplotype pairs is initialized from all combinations of the most probable haplotypes previously found in each segment. However, the PL procedure remains computationally expensive because it implies 2s/p  1 (where p is the size of the partitions) complete runs of the algorithm, each time on a quadratic number of combinations of adjacent plausible haplotypes.
Computation of the FDLS distribution from a complete binary tree by ShapeIT (Figure 3B)
To compute the FDLS distribution while avoiding any redundant calculations of α values, our algorithm uses a complete binary tree (called haplotype tree in the following) instead of an exhaustive list to represent the haplotype pairs space S_{ i }. It can be viewed as an extension of the forward algorithm which computes the probabilities of observing in the HMM λ several pairs of sequences classified into a binary tree rather than observing a unique sequence.
Such a haplotype tree is easily derived from a partition of genotype G_{ i }into m unambiguous segments ${G}_{i}=\{({g}_{1},{{g}^{\prime}}_{1}),\mathrm{...},({g}_{m},{{g}^{\prime}}_{m})\}$ : each one starts from a heterozygous SNP, includes all the following homozygous SNPs, and ends before the next heterozygous SNP. A node of the haplotype tree corresponds to a genotype segment $({g}_{j},{{g}^{\prime}}_{j})$, and the two children nodes, to the two possible switch orientations with the following segment (g_{j+1}, ${{g}^{\prime}}_{j+1}$) and (${{g}^{\prime}}_{j+1}$, g_{j+1}). Then, a single path from the root to a leaf corresponds to a single possible haplotype pair of S_{ i }(Figure 3B).
This algorithm avoids all the unnecessary forward value computations made when using the representation by haplotype lists. However, the haplotype tree to be explored still grows exponentially with an increasing number of heterozygous SNPs. It results in a list L whose size is multiplied by two at each level explored (Figure 4). As with the classical haplotype list approach, this algorithm can be simply implemented in a PL strategy: first, a haplotype tree is derived for each segment of genotype, and then the most probable adjacent subtrees are determined and combined until completion. We have used an alternative strategy described in the next paragraph.
Computation of the FDLS distribution from an incomplete binary tree by ShapeIT (Figure 3C)
Methods
We have implemented our algorithm in the software package ShapeIT publicly available at http://www.griv.org/shapeit/. We have extensively compared ShapeIT with the widely used haplotype inference software 2snp [23], Gerbil [15], Fastphase [16], PLEM [14], Ishape [27] and Phase v2.1 [21, 22] on 3 kinds of datasets described hereafter. All the software were run with default parameters on a standard 2 GHz computer with 1 Go of RAM.
In the comparisons, we have tried to work as close as possible to real conditions: on the one hand, we have used tightly linked SNPs such as those used in a single gene fine mapping and on the other hand, we have used TagSNPs with a low level of LD which correspond to the worst conditions to infer haplotypes. At last, we have also made estimations of the running times required by the most accurate software to infer the haplotypes of a 300 K Illumina chips.
Single gene datasets
First, we have used genotypes for which the haplotypes have been completely determined experimentally: the GH1 [37] and ApoE [38] genes. The GH1 dataset contains 14 SNPs for 150 Caucasian individuals and the ApoE dataset contains 9 SNPs for 90 individuals of mixed ethnic origins. For each gene, we have additionally generated 100 replicates by randomly masking 5% of the alleles in order to simulate real experimental conditions (missing data). On these datasets, we have measured the IER (Individual Error Rate) and the MER (Missing data Error Rate) which corresponds respectively to the percentage of individuals incorrectly inferred and to the percentage of missing data incorrectly inferred. Although of limited size, these two genes are very useful to compare precisely the haplotype frequency estimations made by the algorithms via the I_{F} coefficient [25], since haplotype frequencies are commonly used by the geneticists in genetic association studies.
HapMap trio datasets
Hapmap trio datasets description
Datasets  Chromosome  #datasets  #SNP  #indiv  Details 

CEU Size  1 to 5  250  10 to 160  60  50 datasets of 10, 20, 40, 80 and 160 adjacent SNPs with MAF above 5% 
CEU Density  1 to 5  300  40  60  50 datasets with spanned distance between SNP above 0, 0.5, 1, 2, 4 and 8 kb (MAF 5%) 
CEU MAF  1 to 5  150  40  60  50 datasets with MAF above 1%, 5% and 10% 
YRI Size  1 to 5  250  10 to 160  60  50 datasets of 10, 20, 40, 80 and 160 adjacent SNPs with MAF above 5% 
YRI Density  1 to 5  300  40  60  50 datasets with spanned distance between SNP above 0, 0.5, 1, 2, 4 and 8 kb (MAF 5%) 
YRI MAF  1 to 5  150  40  60  50 datasets with MAF above 1%, 5% and 10% 
CEU illumina 50  12  300  50  60  15,000 illumina SNPs grouped by dataset of 50 SNPs 
CEU illumina 100  12  150  100  60  15,000 illumina SNPs grouped by dataset of 100 SNPs 
CEU illumina 200  12  75  200  60  15,000 illumina SNPs grouped by dataset of 200 SNPs 
GRIV  1  90  50 to 200  100 to 300  3,500 illumina SNPs grouped by dataset of 50, 100 and 200 SNPs 
To investigate on the impact of low LD in haplotype inference, we have also used a set of 15,000 adjacent Tag SNPs picked up from the large arm of chromosome 12 and found in the 300 K Illumina chips.
GRIV cohort datasets
Third, we have generated large SNP datasets from subjects of the GRIV (Genomics of Resistance to Immunodeficiency Virus) cohort genotyped with the 300 K Illumina chip. The GRIV cohort comprehends about 400 Caucasian subjects collected for genomic studies in AIDS [1, 40, 41, 42, 43]. These datasets were used to estimate the running times required by the most accurate software to infer the haplotypes of a 300 K Illumina chips. For that, we have generated 10 datasets from the GRIV cohort data for various numbers of markers (50, 100 and 200) and for various numbers of individuals (100, 200 and 300). Then the average running time over the 10 datasets of each combination of SNP number and genotype number was used to extrapolate the running time required to infer the haplotypes over the 300,000 SNPs.
Results
Empirical determination of the threshold f (Figure 6)
As discussed in the section Algorithm, ShapeIT relies on a threshold f to discard some branches of the haplotype binary trees. So, we have tested several values for f: the accuracy is clearly stable for values below 0.01. Since the running time was optimal for f = 0.01, we have used this value as default in all the following comparisons.
Comparisons on the single gene datasets (Table 2 and 3)
Results obtained by various haplotyping software on the experimentally determined ApoE dataset.
ApoE  0%MD  5%MD  

IER  IF  IER  MER  IF  
2snp  20.0  83.8  22.7  7.3  83.9 
Fastphase  11.3  89.4  17.4  6.1  87.5 
Gerbil  20.0  81.3  20.3  6.6  84.6 
Ishape  5.6  94.1  10.2  5.9  92.5 
ShapeIT  5.6  94.1  10.5  6.2  92.4 
Phase v2.1  5.8  94.0  10.2  5.8  92.4 
PLEM  12.5  89.8  16.0  6.5  88.7 
Results obtained by various haplotyping software on the experimentally determined GH1 dataset.
GH1  0%MD  5%MD  

IER  IF  IER  MER  IF  
2snp  15.7  88.2  22.0  7.5  88.3 
Fastphase  10.5  92.5  17.3  4.5  90.7 
Gerbil  11.8  92.8  16.7  4.2  91.6 
Ishape  10.1  93.8  15.0  4.5  92.6 
ShapeIT  10.3  93.6  14.9  4.5  92.5 
Phase v2.1  10.3  93.7  15.2  4.5  92.5 
PLEM  12.4  90.3  17.2  4.8  89.4 
On these datasets, ShapeIT, Ishape and Phase v2.1 give clearly the better haplotype reconstructions and frequency estimations compared to the other software. One can notice that Ishape seems to be slightly more accurate than ShapeIT and Phase v2.1. For the completion of missing data, all the methods (except 2snp) are closely related.
Comparisons on the HapMap trio datasets (Table 1 and 4)
Hapmap trio datasets results
Datasets  ShapeIT  Phase v2.1  Fastphase  Ishape  2snp  Gerbil  PLEM  

SER  Time  SER  Time  SER  Time  SER  Time  SER  Time  SER  Time  SER  Time  
CEU Size  1.1  1.1  1.5  1.1  2.2  2.3  2.0  
53  832  113  93  < 1  50  10  
YRI Size  1.7  1.7  2.3  1.8  4.5  3.9  4.2  
64  1,209  125  138  < 1  131  10  
CEU Density  2.3  2.3  2.7  2.4  4.2  4.0  4.1  
26  214  64  43  < 1  5  6  
YRI Density  3.7  3.7  4.9  3.9  8.5  7.5  8.8  
35  490  71  80  < 1  9  5  
CEU MAF  1.1  1.1  1.2  1.2  2.0  2.1  1.7  
19  104  71  22  < 1  2  4  
YRI MAF  1.5  1.5  2.0  1.5  4.5  3.8  3.2  
26  173  80  38  < 1  4  4  
CEU 50 illumina SNP  6.3  6.3  7.2  6.6  10.7  9.2  12.2  
51  1,214  60  161  < 1  22  5  
CEU 100 illumina SNP  6.7  6.8  7.7  9.2  11.3  9.7  N/A  
143  11,678  144  461  < 1  254  N/A  
CEU 200 illumina SNP  7.2  N/A  8.0  N/A  11.5  9.9  N/A  
372  N/A  198  N/A  < 1  2,038  N/A 
As a matter of accuracy, ShapeIT and Phase v2.1 outperform all the other methods. Ishape comes second but plunges when dealing with larger number of Tag SNPs. Fastphase comes third but it seems to work relatively better when the datasets get bigger. 2snp, Gerbil, and PLEM do not match the accuracy of the other software. All the software get higher error rates when the number of Tag SNPs increases which is probably the consequence of the increasing complexity of the LD pattern when dealing with limited numbers of individuals.
As a matter of speed, the fastest software is clearly 2snp. For relatively small numbers of SNPs, PLEM and Gerbil are also very fast, but become very slow when the number of SNPs increases or when the LD pattern gets more complex to capture. Among the 4 most accurate software (Phase v2.1, Fastphase, Ishape, and ShapeIT), Phase v2.1 is the slowest, ShapeIT is the fastest for small and mediumsized SNP samples (< 100 SNPs), and Fastphase becomes faster for larger numbers of SNPs (see additional file 1).
Running time on the GRIV cohort datasets (Table 5)
Comparison of the estimated running times of various software on 300 K Illunima genotyping chips datasets.
#SNPs  #genotypes  Fastphase  Ishape  ShapeIT  Phase v2.1 

50  100  10  29  10  151 
100  100  6  37  12  519 
200  100  6  41  19  3,137 
50  200  21  34  13  443 
100  200  21  119  29  2,739 
200  200  21  124  37  7,601 
50  300  37  113  28  1,372 
100  300  41  268  52  6,514 
200  300  42  261  81  12,757 
On these datasets, ShapeIT runs between 15 to 150 times faster that Phase v2.1, depending on the segmentation strategy used (50, 100 or 200 SNPs) and the number of genotypes in the population (100, 200 or 300). Fastphase remains the fastest software but closely followed by ShapeIT. The increase of SNP and genotype numbers strongly cripples Phase v2.1 and Ishape, while it is better handled by ShapeIT and Fastphase.
Discussion and conclusion
We have developed a new algorithm derived from the Phase v2.1 Gibbs sampler scheme. We have improved the most timeconsuming steps by using binary tree representations and by avoiding the PL procedure thanks to an incomplete exploration of binary trees. The resulting software, ShapeIT, is extremely accurate like Phase v2.1, but may run up to 150 times faster as shown in our tests. These results have an impact for the computation of haplotypes in genome scans as shown in Table 5. As an example, for the 300,000 SNPs of an Illumina genotyping chip, inferring haplotypes on 6,000 segments of 50 SNPs with a regular 2 GHz computer would take for ShapeIT about 10 days for 100 individuals, 13 days for 200 individuals, 28 days for 300 individuals while it would take for Phase v2.1 151 days for 100 individuals (15 times more), 443 days for 200 individuals (34 times more) and 1372 days for 300 individuals (49 times more). The gain of time using ShapeIT is thus considerable and practically very useful to exploit datasets derived from largescale genotyping chips.
An important aspect of this work is that other haplotype inference software relying on HMM may gain to implement this new binary tree representation of the observed genotypes. Moreover, we have not found in the literature the description of this algorithm whereas it might be useful for other fields using HMM.
Availability and requirements
Project name: ShapeIT v1.0
Project home page: http://www.griv.org/shapeit/
Operating systems: MacOS, Windows, Linux32bits and Linux64bits.
Programming language: C++
Do not forget to read the manual file, manual_ShapeITv1.0.pdf, to get the detailed information. The software remains confidential until publication of the work. It will be freely available to academics, and a licence will be needed for nonacademics (patented for business and commercial applications).
Notes
Acknowledgements
OD has a fellowship from the French Ministry of Education, Research and technology, and CC has a fellowship from Conservatoire National des Arts et Métiers. This work was supported by ACV development foundation, by Vaxconsulting, and by the Innovation 2007 program of Conservatoire National des Arts et Métiers. The authors thank Dr Adkins and Dr Orzack for providing respectively the GH1 and ApoE gene datasets.
Supplementary material
References
 1.Vasilescu A, Terashima Y, Enomoto M, Heath S, Poonpiriya V, Gatanaga H, Do H, Diop G, Hirtzig T, Auewarakul P, et al.: A haplotype of the human CXCR1 gene protective against rapid disease progression in HIV1+ patients. Proceedings of the National Academy of Sciences of the United States of America 2007, 104(9):3354–3359. 10.1073/pnas.0611670104PubMedCentralCrossRefPubMedGoogle Scholar
 2.Daly MJ, Rioux JD, Schaffner SF, Hudson TJ, Lander ES: Highresolution haplotype structure in the human genome. Nature genetics 2001, 29(2):229–232. 10.1038/ng1001229CrossRefPubMedGoogle Scholar
 3.Dawson E, Abecasis GR, Bumpstead S, Chen Y, Hunt S, Beare DM, Pabial J, Dibling T, Tinsley E, Kirby S, et al.: A firstgeneration linkage disequilibrium map of human chromosome 22. Nature 2002, 418(6897):544–548. 10.1038/nature00864CrossRefPubMedGoogle Scholar
 4.Gabriel SB, Schaffner SF, Nguyen H, Moore JM, Roy J, Blumenstiel B, Higgins J, DeFelice M, Lochner A, Faggart M, et al.: The structure of haplotype blocks in the human genome. Science 2002, 296(5576):2225–2229. 10.1126/science.1069424CrossRefPubMedGoogle Scholar
 5.Johnson GC, Esposito L, Barratt BJ, Smith AN, Heward J, Di Genova G, Ueda H, Cordell HJ, Eaves IA, Dudbridge F, et al.: Haplotype tagging for the identification of common disease genes. Nature genetics 2001, 29(2):233–237. 10.1038/ng1001233CrossRefPubMedGoogle Scholar
 6.Patil N, Berno AJ, Hinds DA, Barrett WA, Doshi JM, Hacker CR, Kautzer CR, Lee DH, Marjoribanks C, McDonough DP, et al.: Blocks of limited haplotype diversity revealed by highresolution scanning of human chromosome 21. Science 2001, 294(5547):1719–1723. 10.1126/science.1065573CrossRefPubMedGoogle Scholar
 7.The International HapMap Project Nature 2003, 426(6968):789–796. 10.1038/nature02168Google Scholar
 8.A haplotype map of the human genome Nature 2005, 437(7063):1299–1320. 10.1038/nature04226Google Scholar
 9.Frazer KA, Ballinger DG, Cox DR, Hinds DA, Stuve LL, Gibbs RA, Belmont JW, Boudreau A, Hardenbol P, Leal SM, et al.: A second generation human haplotype map of over 3.1 million SNPs. Nature 2007, 449(7164):851–861. 10.1038/nature06258CrossRefPubMedGoogle Scholar
 10.Burgtorf C, Kepper P, Hoehe M, Schmitt C, Reinhardt R, Lehrach H, Sauer S: Clonebased systematic haplotyping (CSH): a procedure for physical haplotyping of whole genomes. Genome research 2003, 13(12):2717–2724. 10.1101/gr.1442303PubMedCentralCrossRefPubMedGoogle Scholar
 11.Ding C, Cantor CR: Direct molecular haplotyping of longrange genomic DNA with M1PCR. Proceedings of the National Academy of Sciences of the United States of America 2003, 100(13):7449–7453. 10.1073/pnas.1232475100PubMedCentralCrossRefPubMedGoogle Scholar
 12.Clark AG: Inference of haplotypes from PCRamplified samples of diploid populations. Mol Biol Evol 1990, 7(2):111–122.PubMedGoogle Scholar
 13.Excoffier L, Slatkin M: Maximumlikelihood estimation of molecular haplotype frequencies in a diploid population. Mol Biol Evol 1995, 12(5):921–927.PubMedGoogle Scholar
 14.Qin ZS, Niu T, Liu JS: Partitionligationexpectationmaximization algorithm for haplotype inference with singlenucleotide polymorphisms. American journal of human genetics 2002, 71(5):1242–1247. 10.1086/344207PubMedCentralCrossRefPubMedGoogle Scholar
 15.Kimmel G, Shamir R: GERBIL: Genotype resolution and block identification using likelihood. Proceedings of the National Academy of Sciences of the United States of America 2005, 102(1):158–162. 10.1073/pnas.0404730102PubMedCentralCrossRefPubMedGoogle Scholar
 16.Scheet P, Stephens M: A fast and flexible statistical model for largescale population genotype data: applications to inferring missing genotypes and haplotypic phase. American journal of human genetics 2006, 78(4):629–644. 10.1086/502802PubMedCentralCrossRefPubMedGoogle Scholar
 17.Rastas P, Koivisto M, Mannila H, Ukkonen E: A Hidden Markov Technique for Haplotype Reconstruction. 5th Workshop on Algorithms in Bioinformatics: 2005 2005.Google Scholar
 18.Kimmel G, Shamir R: A blockfree hidden Markov model for genotypes and its application to disease association. J Comput Biol 2005, 12(10):1243–1260. 10.1089/cmb.2005.12.1243CrossRefPubMedGoogle Scholar
 19.Niu T, Qin ZS, Xu X, Liu JS: Bayesian haplotype inference for multiple linked singlenucleotide polymorphisms. American journal of human genetics 2002, 70(1):157–169. 10.1086/338446PubMedCentralCrossRefPubMedGoogle Scholar
 20.Stephens M, Smith NJ, Donnelly P: A new statistical method for haplotype reconstruction from population data. American journal of human genetics 2001, 68(4):978–989. 10.1086/319501PubMedCentralCrossRefPubMedGoogle Scholar
 21.Stephens M, Donnelly P: A comparison of bayesian methods for haplotype reconstruction from population genotype data. American journal of human genetics 2003, 73(5):1162–1169. 10.1086/379378PubMedCentralCrossRefPubMedGoogle Scholar
 22.Stephens M, Scheet P: Accounting for decay of linkage disequilibrium in haplotype inference and missingdata imputation. American journal of human genetics 2005, 76(3):449–462. 10.1086/428594PubMedCentralCrossRefPubMedGoogle Scholar
 23.Brinza D, Zelikovsky A: 2SNP: scalable phasing based on 2SNP haplotypes. Bioinformatics (Oxford, England) 2006, 22(3):371–373. 10.1093/bioinformatics/bti785CrossRefGoogle Scholar
 24.Marchini J, Cutler D, Patterson N, Stephens M, Eskin E, Halperin E, Lin S, Qin ZS, Munro HM, Abecasis GR, et al.: A comparison of phasing algorithms for trios and unrelated individuals. American journal of human genetics 2006, 78(3):437–450. 10.1086/500808PubMedCentralCrossRefPubMedGoogle Scholar
 25.Adkins RM: Comparison of the accuracy of methods of computational haplotype inference using a large empirical dataset. BMC genetics 2004, 5: 22. 10.1186/14712156522PubMedCentralCrossRefPubMedGoogle Scholar
 26.Bettencourt BF, Santos MR, Fialho RN, Couto AR, Peixoto MJ, Pinheiro JP, Spinola H, Mora MG, Santos C, Brehm A, et al.: Evaluation of two methods for computational HLA haplotypes inference using a real dataset. BMC bioinformatics 2008, 9: 68. 10.1186/14712105968PubMedCentralCrossRefPubMedGoogle Scholar
 27.Delaneau O, Coulonges C, Boelle PY, Nelson G, Spadoni JL, Zagury JF: ISHAPE: new rapid and accurate software for haplotyping. BMC bioinformatics 2007, 8: 205. 10.1186/147121058205PubMedCentralCrossRefPubMedGoogle Scholar
 28.Marroni F, Toni C, Pennato B, Tsai YY, Duggal P, BaileyWilson JE, Presciuttini S: Haplotypic structure of the X chromosome in the COGA population sample and the quality of its reconstruction by extant software packages. BMC genetics 2005, 6(Suppl 1):S77. 10.1186/147121566S1S77PubMedCentralCrossRefPubMedGoogle Scholar
 29.Xu H, Wu X, Spitz MR, Shete S: Comparison of haplotype inference methods using genotypic data from unrelated individuals. Human heredity 2004, 58(2):63–68. 10.1159/000083026CrossRefPubMedGoogle Scholar
 30.Zaitlen NA, Kang HM, Feolo ML, Sherry ST, Halperin E, Eskin E: Inference and analysis of haplotypes from combined genotyping studies deposited in dbSNP. Genome research 2005, 15(11):1594–1600. 10.1101/gr.4297805PubMedCentralCrossRefPubMedGoogle Scholar
 31.Do H, Vasilescu A, Carpentier W, Meyer L, Diop G, Hirtzig T, Coulonges C, Labib T, Spadoni JL, Therwath A, et al.: Exhaustive genotyping of the interleukin1 family genes and associations with AIDS progression in a French cohort. The Journal of infectious diseases 2006, 194(11):1492–1504. 10.1086/508545CrossRefPubMedGoogle Scholar
 32.Do H, Vasilescu A, Diop G, Hirtzig T, Coulonges C, Labib T, Heath SC, Spadoni JL, Therwath A, Lathrop M, et al.: Associations of the IL2Ralpha, IL4Ralpha, IL10Ralpha, and IFN (gamma) R1 cytokine receptor genes with AIDS progression in a French AIDS cohort. Immunogenetics 2006, 58: 2–3. 10.1007/s0025100500723CrossRefGoogle Scholar
 33.Kamarainen OP, Solovieva S, Vehmas T, Luoma K, Riihimaki H, AlaKokko L, Mannikko M, LeinoArjas P: Common interleukin6 promoter variants associate with the more severe forms of distal interphalangeal osteoarthritis. Arthritis research & therapy 2008, 10(1):R21. 10.1186/ar2374CrossRefGoogle Scholar
 34.Fearnhead P, Donnelly P: Estimating recombination rates from population genetic data. Genetics 2001, 159(3):1299–1318.PubMedCentralPubMedGoogle Scholar
 35.Li N, Stephens M: Modeling linkage disequilibrium and identifying recombination hotspots using singlenucleotide polymorphism data. Genetics 2003, 165(4):2213–2233.PubMedCentralPubMedGoogle Scholar
 36.Rabiner LR: A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 1989, 77(2):257–286. 10.1109/5.18626CrossRefGoogle Scholar
 37.Horan M, Millar DS, Hedderich J, Lewis G, Newsway V, Mo N, Fryklund L, Procter AM, Krawczak M, Cooper DN: Human growth hormone 1 (GH1) gene expression: complex haplotypedependent influence of polymorphic variation in the proximal promoter and locus control region. Human mutation 2003, 21(4):408–423. 10.1002/humu.10167CrossRefPubMedGoogle Scholar
 38.Orzack SH, Gusfield D, Olson J, Nesbitt S, Subrahmanyan L, Stanton VP Jr: Analysis and exploration of the use of rulebased algorithms and consensus methods for the inferral of haplotypes. Genetics 2003, 165(2):915–928.PubMedCentralPubMedGoogle Scholar
 39.Barrett JC, Fry B, Maller J, Daly MJ: Haploview: analysis and visualization of LD and haplotype maps. Bioinformatics (Oxford, England) 2005, 21(2):263–265. 10.1093/bioinformatics/bth457CrossRefGoogle Scholar
 40.Hendel H, CaillatZucman S, Lebuanec H, Carrington M, O'Brien S, Andrieu JM, Schachter F, Zagury D, Rappaport J, Winkler C, et al.: New class I and II HLA alleles strongly associated with opposite patterns of progression to AIDS. J Immunol 1999, 162(11):6942–6946.PubMedGoogle Scholar
 41.Rappaport J, Cho YY, Hendel H, Schwartz EJ, Schachter F, Zagury JF: 32 bp CCR5 gene deletion and resistance to fast progression in HIV1 infected heterozygotes. Lancet 1997, 349(9056):922–923. 10.1016/S01406736(05)626979CrossRefPubMedGoogle Scholar
 42.Vasilescu A, Heath SC, Ivanova R, Hendel H, Do H, Mazoyer A, Khadivpour E, Goutalier FX, Khalili K, Rappaport J, et al.: Genomic analysis of Th1Th2 cytokine genes in an AIDS cohort: identification of IL4 and IL10 haplotypes associated with the disease progression. Genes and immunity 2003, 4(6):441–449. 10.1038/sj.gene.6363983CrossRefPubMedGoogle Scholar
 43.Winkler CA, Hendel H, Carrington M, Smith MW, Nelson GW, O'Brien SJ, Phair J, Vlahov D, Jacobson LP, Rappaport J, et al.: Dominant effects of CCR2CCR5 haplotypes in HIV1 disease progression. Journal of acquired immune deficiency syndromes (1999) 2004, 37(4):1534–1538. 10.1097/01.qai.0000127353.01578.63CrossRefGoogle Scholar
Copyright information
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.