CROSSREFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 61/492,365 filed Jun. 1, 2011, which is hereby incorporated by reference in its entirety for all purposes.
STATEMENT OF GOVERNMENT SPONSORED SUPPORT

This invention was made with Government support under contracts GM073059 and HG002357 awarded by the National Institutes of Health. The Government has certain rights in this invention.
FIELD OF THE INVENTION

The present invention generally relates to the field of computcr diagnostics. More particularly, the present invention relates to methods for analyzing a genome.
BACKGROUND OF THE INVENTION

The term haplotype refers to the combination of alleles at multiple loci along a chromosome. In linkage disequilibrium (LD) mapping, haplotypebased tests are thought to improve power for detecting untyped variants. In population genetics studies of evolutionary histories, haplotype data have been used to detect recombination hotspots as well as regions that have undergone recent positive selection (Myers, S., Bottolo, L., Freeman, C., McVean, G. & Donnelly, P. A finescale map of recombination rates and hotspots across the human genome. Science 310, 321324 (2005); Sabeti, P. C. et al. Detecting recent positive selection in the human genome from haplotype structure. Nature 419, 8327 (2002); these and all other references cited herein are incorporated by reference for all purposes). Despite its usefulness, haplotypes cannot be directly assayed using existing highthroughput genomic or sequencing technologies which instead generate genotype dataunordered pairs of alleles. While reconstructing haplotype from genotypes is straightforward in some special settings (e.g. in the presence of relatives, in sperm, or for X chromosomes in males), statistical inference of haplotype from autosomal genotype data with no known relatives is challenging.

The paper by Kong et al (Kong, A. et al. Detection of sharing by descent, longrange phasing and haplotype imputation. Nature Genetics 40, 106875 (2008)) showed that distantly related individuals can be used accurately to infer haplotype phase from genotypes. Individuals sharing long haplotypes, “pseudo parents,” could be used to phase each other just as the two parents in a trio can be used to phase the unordered genotypes of their offspring. They showed an impressive performance improvement over an existing algorithm, FastPHASE (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 78, 629644 (2006)), but due to high computational burden could not compare against the related PHASE 2.1.1 algorithm (Stephens, M., Smith, N. & Donnelly, P. A new statistical method for haplotype reconstruction from population data. American Journal of Human Genetics 68, 97889 (2001)).

Numerous methods have been developed to infer haplotypes. The method of Clark, A. G. Inference of haplotypes from PCRamplified samples of diploid populations. Mol. Biol. Evol. 7, 111122 (1990) begins by identifying a pool of unambiguous (homozygous) individuals, and phases the remaining individuals based on a parsimony heuristic that seeks to minimize the total number of distinct haplotypes in the sample. For a small number of linked markers, multinomialbased model fit by the ExpectationMaximization (EM) algorithms can be quite effective (Excoffier, L. & Slatkin, M. Maximumlikelihood estimation of molecular haplotype frequencies in a diploid population. Mol Biol Evol 12, 921927 (1995); Hawley, M. E. & Kidd, K. K. Haplo: a program using the em algorithm to estimate the frequencies of multisite haplotypes. J Hered 86, 409411 (1995); Long, J. C., Williams, R. C. & Urbanek, M. An EM algorithm and testing strategy for multiplelocus haplotypes. Am J Hum Genet 56, 799810 (1995)). The partitionligation (PLEM) algorithm of (Niu, T., Qin, Z. S., Xu, X. & Liu, J. S. Bayesian haplotype inference for multiple linked single nucleotide polymorphisms. American Journal of Human Genetics 70, 157169 (2002)) was proposed to accelerate computation, and to keep the EM algorithm from becoming trapped in poor local modes. These methods identify common haplotypes. However, the multinomial model is inappropriate for rare haplotypes, which is a serious weakness because for any fixed sample size of individuals, a majority of haplotypes become rare or unique as the number of marker increases—either by increasing marker density or by expanding the genomic region.
SUMMARY OF THE INVENTION

An important feature of the phasing problem, which was ignored by the early methods, is that all haplotypes are related through a genealogy; as such a “rare” haplotype that resembles a common haplotype is more plausible than a “rare” haplotype that resembles no other observed haplotype. The coalescentbased likelihood function underlying the PHASE program has followed (Stephens, M., Smith, N. & Donnelly, P. A new statistical method for haplotype reconstruction from population data. American Journal of Human Genetics 68, 97889 (2001)). Subsequently, PHASE 2.1.1 incorporates intermarker distance to account for the linkage disequilibrium (LD) between linked markers (Stephens, M. & Scheet, P. Accounting for decay of linkage disequilibrium in haplotype inference and missingdata imputation. American Journal of Human Genetics 76, 449462 (2005)).

In the embodiments described below, discussions pertaining to PHASE refer to the latest version, PHASE 2.1.1, unless otherwise specified. In comparisons using simulated and real data, it was found that PHASE consistently outperforms other existing methods. When implemented via Markov Chain Monte Carlo algorithms (MCMC), PHASE is computationally intensive where it can be difficult to perform analysis of largescale datasets, such as those generated in genomewide association studies (GWAS). It should, nonetheless, be understood that other programs beyond PHASE can be implemented consistent with the teachings of the present invention as would be understood by those of ordinary skill in the art. An embodiment of the present invention is described herein as PHASEEM. PHASEEM will be used to describe features of the present invention, however, the present invention is not limited to the PHASEEM embodiment.

In an embodiment of the present invention, a modified version of the PHASE model is implemented that is substantially more accurate than the FastPHASE model. Modifications in an embodiment of the present invention include using a parameterization EM algorithm similar to that of the FastPHASE model, and to perform optimization on haplotypes rather than MCMC sampling. In an embodiment, the imputed haplotypes themselves are used as hidden states in the HMM because this is believed to be important for the PHASE model's accuracy. This increase in accuracy becomes more pronounced with increasing sample size. This difference is attributed to the PHASE model's likelihood which produces long, shared haplotypes between pairs of individuals.

These and other embodiments and advantages can be more fully appreciated upon an understanding of the detailed description of the invention as disclosed below in conjunction with the attached Figures.
BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings will be used to more fully describe embodiments of the present invention.

FIGS. 1A and 1B are graphs of phasing error rate as a function of marker indexdistance according to an embodiment of the present invention.

FIGS. 2A and 2B are graphs of phasing error as a function of sample size and intermarker distance according to an embodiment of the present invention.

FIGS. 3A and 3B are graphs of error rate in the panel of 200 Mexican haplotypes using PHASEEM according to an embodiment of the present invention.

FIG. 4 is a representation of a Hidden Markov Model common to PHASE and FastPHASE according to an embodiment of the present invention.

FIG. 5 (Table 1) is a table of switch error rates corresponding to the three triopanels used in FIG. 1 according to an embodiment of the present invention.

FIG. 6 (Table 2) is a table of error rates for the Mexican panel as a function of sample size according to an embodiment of the present invention.

FIG. 7 is a block diagram of a computer system on which the present invention can be implemented.
DETAILED DESCRIPTION OF THE INVENTION

Among other things, the present invention relates to methods, techniques, and algorithms that are intended to be implemented in a digital computer system 100 such as generally shown in FIG. 7. Such a digital computer is wellknown in the art and may include the following.

Computer system 100 may include at least one central processing unit 102 but may include many processors or processing cores. Computer system 100 may further include memory 104 in different forms such as RAM, ROM, hard disk, optical drives, and removable drives that may further include drive controllers and other hardware. Auxiliary storage 112 may also be include that can be similar to memory 104 but may be more remotely incorporated such as in a distributed computer system with distributed memory capabilities.

Computer system 100 may further include at least one output device 108 such as a display unit, video hardware, or other peripherals (e.g., printer). At least one input device 106 may also be included in computer system 100 that may include a pointing device (e.g., mouse), a text input device (e.g., keyboard), or touch screen.

Communications interfaces 114 also form an important aspect of computer system 100 especially where computer system 100 is deployed as a distributed computer system. Computer interfaces 114 may include LAN network adapters, WAN network adapters, wireless interfaces, Bluetooth interfaces, modems and other networking interfaces as currently available and as may be developed in the future.

Computer system 100 may further include other components 116 that may be generally available components as well as specially developed components for implementation of the present invention. Importantly, computer system 100 incorporates various data buses 116 that are intended to allow for communication of the various components of computer system 100. Data buses 116 include, for example, input/output buses and bus controllers.

Indeed, the present invention is not limited to computer system 100 as known at the time of the invention. Instead, the present invention is intended to be deployed in future computer systems with more advanced technology that can make use of all aspects of the present invention. It is expected that computer technology will continue to advance but one of ordinary skill in the art will be able to take the present disclosure and implement the described teachings on the more advanced computers or other digital devices such as mobile telephones or “smart” televisions as they become available. Moreover, the present invention may be implemented on one or more distributed computers. Still further, the present invention may be implemented in various types of software languages including C, C++, and others. Also, one of ordinary skill in the art is familiar with compiling software source code into executable software that may be stored in various forms and in various media (e.g., magnetic, optical, solid state, etc.). One of ordinary skill in the art is familiar with the use of computers and software languages and, with ani understanding of the present disclosure, will be able to implement the present teachings for use on a wide variety of computers.

The present disclosure provides a detailed explanation of the present invention with detailed explanations that allow one of ordinary skill in the art to implement the present invention into a computerized method. Certain of these and other details are not included in the present disclosure so as not to detract from the teachings presented herein but it is understood that one of ordinary skill in the art would be familiar with such details.

Using data in a cohort of 35,528 Icelandic individuals genotyped by deCode, (Kong, A. et al. Detection of sharing by descent, longrange phasing and haplotype imputation. Nature Genetics 40, 106875 (2008)) demonstrated that the accuracy of haplotypes inferred by FastPHASE is limited to a short range: the error rate rise to 30% for phasing a region of 6.4 Mb. This error rate is comparable to the individual error rate reported in Scheet et al. (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 78, 629644 (2006)).

Kong et al. proposed longrange phasing method (LRP), which is based on the rationale that, in a large sample, some individuals may be closely related, such as second cousins. The LRP implements a heuristic algorithm that identifies “surrogatc” parents, who share at least one allele identicalbystate (IBS) with the proband over an extremely long region (e.g. 1,000 consecutive SNPs). The phasing of the proband is inferred by constructing the two obligatory haplotypes that must be shared by his/her surrogate parents. The LRP method was successful for the deCode sample considered in Kong et al.: for the 10 Mb MHC region on chromosome 6, 87% of the individuals can be fully phased, and 7% of the remaining individuals can be phased for 90% of the heterozygous sites; overall, 93.7% of the heterozygous sites can be phased unambiguously. But in many human populations, randomly sampled individuals are on average much less closely related than they are in the Icelandic population. As a result, the LRP method will not apply because many individuals will find no “surrogate” parents in the sample, unless a substantial fraction of the population is sampled.

Higasi et al. genotyped 100 haploid Japanese genomes from complete hydatidiform moles (CHM), which arise when an empty egg with no nucleus is fertilized by a normal sperm (Higasa, K. et al. Evaluation of haplotype inference using definitive haplotype data obtained from complete hydatidiform moles, and its significance for the analyses of positively selected regions. PLoS Genet 5, e1000468 (2009)). By pairing these haplotypes into pseudo individuals and using FastPHASE and Beagle to recover phasing information, the study provided and estimate of the error rate for the HapMap Japanese population. When applying the Extended Haplotype Homozygosity (EHH) test to either haplotypes inferred by FastPHASE or the true CHM haplotypes, the authors found evidence of positive selection using the true, but not the inferred, haplotypes. This result highlights the need to improve accuracy in existing statistical methods for haplotype inference.

The PHASE model consist of a score S(h_{1}, . . . , h_{N}; ρ, θ) on N imputed haplotypes h_{1}, . . . , h_{N }which are binary sequences of alleles and each is of the length l, and ρ and θ are parameters of a Hidden Markov Model (HMM) (Rabiner, L. R. A tutorial on hidden markov models and selected applications in speech recognition. In Proceedings of the IEEE, 257286 (1989)). This score decomposes as

Σ_{j=1} ^{N} S(h _{j} ;{h _{k}}_{k≠j},ρ,θ)

where

 S(h_{j};{h_{k}}_{k≠j},ρ,θ)
is large if h_{j }appears to be a mosaic of the other haplotypes (h_{k})_{k≠j}. The score when the imputed haplotypes share longer subsequences and will be particularly large if h_{j }and h_{k }(for some index k) are identical at every SNP. Given a large panel, the procedure of Kong et al. provides an excellent means of optimizing it in an embodiment of the present invention (Kong, A. et al. Detection of sharing by descent, longrange phasing and haplotype imputation. Nature Genetics 40, 106875 (2008)). Since panel sizes are generally much smaller, pseudo parents are not explicitly demarcated but recognize that this relationship is indeed present through the latent variables in the model.

Method

Model and Notations.

Shown in FIG. 8 is a block diagram 800 describing features of a specialized model according to an embodiment of the present invention. As described below model 802 shown in FIG. 8 is substantially more accurate than the FastPHASE model. Modifications and improvements of an an embodiment of the present invention are further shown in FIG. 8. For example, a model according to an embodiment of the present invention includes a parameterization EM algorithm 804. Also, an embodiment of the present invention perform an optimization on haplotypes 806 rather than MCMC sampling (such as in the “wphase” approach described in Marchini et al. (Marchini, J., Howie, B., Myers, S., McVean, G. & Donnelly, P. A new multipoint method for genomewide association studies by imputation of genotypes. Nature Genetics 39, 90613 (2007))). In the model according to an embodiment of the present invention, imputed haplotypes are used as hidden states (808) in the specialized HMM (812) to improve accuracy. This increase in accuracy becomes more pronounced with increasing sample size. This difference is attributed to the PHASE model's likelihood which produces long, shared haplotypes between pairs of individuals.

In an embodiment of the present invention, every haplotype in the sample is modeled as an imperfect mosaic of haplotypes from a haplotype pool (810). This idea can be illustrated using the following example. The HapMap phase III project genotyped 50 parentoffspring trios from the Yoruba population in Nigeria (YRI); the trio relationship allows the accurate phasing of the 200 parental haplotypes. This panel was used to phase a new sample, unrelated to any of the HapMap trios. An embodiment of the present invention seeks the most plausible configuration where the new haplotypes are derived from recombination and mutation events on the known HapMap haplotypes. To phase multiple individuals in the absence of an appropriately known haplotype pool, a method according to an embodiment of the present invention aims to jointly model all unobserved haplotypes based on the observed LD patterns. Specifically, an embodiment of the present invention achieves this by iteratively optimizing the phasing configuration for one individual, treating all the other individuals in the sample as phased.

In developing the model, let G denote the N by L matrix of genotypes for N diploid individuals genotyped at L SNPmarkers; G_{jk}ε{0, 1, 2, ?} corresponds to genotypes AA, AB, BB, and missing, respectively. The 2N by L matrix A is composed of imputed, phased haplotypes, and the rows A_{2j−1 }and A_{2j }represent those from the jth individual. The matrix A is imputed data, but it also acts as model parameters. A^{−j }is used to denote the matrix A with the jth individual's imputed haplotypes “removed” (for simplicity of notation, the rowindexing is left unchanged), and this submatrix acts as model parameters for the jth individual's haplotypes. A Hidden Markov Model (HMM) is developed having a hidden state sequence H, an emitted sequence B, and jump variables J. The emitted sequence B_{k }is produced by taking the element of the current imputation A_{Hk,k }and changing its value with a small probability θ. The conditional probabilities of the HMM (for the jth individual's haplotypes) are

q _{j}(J _{k−1}=1;ρ_{k})=ρ_{k}=1−q _{j}(J _{k−1}=0;ρ_{k}) (1)

q _{j}(H _{k} =hJ _{k−1}=1,H _{k−1} =h′)=1{h⊂{2j,2j−1}}/(2N−2) (2)

q _{j}(H _{k} =hJ _{k−1}=0,H _{k−1} =h′)=1{h=h′} (3)

q _{j}(B _{k} =xH _{k} =h; θ _{k} ,A ^{−j})=1{x≠A _{h,k}}(1−θ_{k})+1{x=A _{h,k}} (4)

Model parameters are placed after the semicolon to distinguish them from random variables. The first equation says that the jump variables J_{k }are drawn as independent Bernoulli random variables. The next equations state that if the jump variable J_{k }is zero, H_{k+1}=H_{k }and the hidden state does not change. On the other hand if J_{k}=1, the next hidden state H_{k+1 }is drawn from a uniform distribution. As a result, the hidden state H_{k+1 }may “jump” but end up at H_{k }anyway. FIG. 4 shows this HMM model 400 as a Bayesian network but does not explicitly show that H_{k } 402 and H_{k−1 } 404 are independent conditional on {J_{k−1}(406)=1}.

At each site, a hidden state emits one allele with high probability while emitting the other allele at the mutation rate, θ. The probability of a jump in hidden states between two consecutive markers is proportional to the local recombination rate, ρ. Using the physical distance between markers and a coalescentbased population genetics model, PHASE puts a prior on ρ, and jointly infers all aspects of the HMM by MCMC. In PHASEEM as an embodiment of the present invention, the coalescentbased Bayesian prior is eliminated; as a consequence, the model parameters, ρ and θ, can be estimated by closedform EM updates.

To make the equations above defined for k=1, ρ_{1}=1 and H_{0}=1, so that the dummy jump variable J_{0 }always equals 1. A complete and marginal likelihoods are now obtained where the dependence on the current phasing A is stressed:

${q}_{j}\ue8a0\left(B,J,H:\rho ,\theta ,{A}^{j}\right)=\prod _{k=1}^{N}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{q}_{j}\ue8a0\left({H}_{k}{J}_{k1},{H}_{k1}\right)\ue89e{q}_{j}\ue8a0\left({B}_{k}{H}_{k}:{\theta}_{k},{A}^{j}\right)\ue89e{q}_{j}\ue8a0\left({J}_{k1}:{\rho}_{k}\right)$
${q}_{j}\ue8a0\left(B:\rho ,\theta ,{A}^{j}\right)=\sum _{J,H}\ue89e\prod _{k=1}^{N}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{q}_{j}\ue8a0\left({H}_{k}{J}_{k1};{H}_{k1}\right)\ue89e{q}_{j}\ue8a0\left({B}_{k}{H}_{k}:{\theta}_{k},{A}^{j}\right)\ue89e{q}_{j}\ue8a0\left({J}_{k1}:{\rho}_{k}\right)$

Following PHASE we will optimize the score

$\begin{array}{cc}S\ue8a0\left(A,\rho ,\theta \right):=\sum _{j=1}^{N}\ue89e\sum _{s=0}^{1}\ue89e\mathrm{log}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{q}_{j}\ue8a0\left(B={A}_{2\ue89ejs},.;\rho ,\theta ,{A}^{j}\right)& \left(5\right)\end{array}$

As implemented, the model above uses a simpler emission distribution, removes the divergence time variable T, and lacks Bayesian priors. In the model above as an embodiment of the present invention, the hidden states of the HMM are the imputed haploypes themselves. This is a primary difference between FastPHASE and the model above.

PHASE also has a random ordering v on the samples so that the parameters can be scored by a PAClikelihood (PAC stands for Product of Approximate Conditionals). By simplifying the PHASE model, the primary reason that PHASE would be more accurate than FastPHASE can be will optimize identified. The PHASE model can capture longer range sharing without the need for complex hierarchical models.

To learn ρ and θ, the EM algorithm is used as in FastPHASE in an embodiment of the present invention. The score is no longer the likelihood of a single model, but by applying Jensen's inequality, it can be verified that the parameter updates defined below still increase the score S and optimize a minorizing Qfunction as in the usual EM algorithm. The parameter updates are given as:

${\rho}_{k}\leftarrow \frac{\sum _{j=1}^{N}\ue89e\sum _{s=0}^{1}\ue89e{q}_{j}\ue8a0\left({J}_{k1}=1B={A}_{2\ue89ejs},.;{A}^{j},\theta ,\rho \right)}{2\ue89eN}$
${\theta}_{k}\leftarrow \frac{\begin{array}{c}\sum _{j=1}^{N}\ue89e\sum _{s=0}^{1}\ue89e\sum _{h=1}^{2\ue89eN}\ue89e1\ue89e\left\{{A}_{2\ue89ejs,k}\ne {A}_{h,k}\right\}\ue89e{q}_{j}\\ \left({H}_{k}=hB={A}_{2\ue89ejs},.;{A}^{j},\theta ,\rho \right)\end{array}}{2\ue89eN\ue8a0\left(2\ue89eN2\right)}$

Recall from equation (2) that

q _{j}(H _{k}=2j−sB=A _{2j−s.} .:A ^{−j},θ,ρ)

for s=0, 1.

The ForwardBackward algorithm is used to compute the conditional probabilities above. On the order often parameter updates using a phasing A found by FastPHASE can be used. After the parameters are at reasonable values, parameter updates are interleaved with haplotype optimization described now. The parameters are held fixed, and a current phasing A is obtained. New haplotypes C^{1}, C^{2 }are then accepted for the jth individual based on the change in score

$\begin{array}{cc}\Delta \ue8a0\left({C}^{1},{C}^{2},{A}_{2\ue89ej1},.,{A}_{2\ue89ej}\right):=\sum _{s=0}^{1}\ue89e\mathrm{log}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{q}_{j}\ue8a0\left(B={C}^{s};{\rho}_{j},\theta ,{A}^{j}\right)& \left(6\right)\\ \sum _{s=0}^{1}\ue89e\mathrm{log}\ue89e\phantom{\rule{0.3em}{0.3ex}}\ue89e{q}_{j}\ue8a0\left(B={A}_{2\ue89ejs},.;\rho ,\theta ,{A}^{j}\right)& \left(7\right)\end{array}$

If Δ(C^{1}, C^{2}, A_{2j−1}, . . . , A_{2j},.) exceeds a nominal threshold (e.g., set to 0.3 in the present implementation that is an embodiment of the present invention), A_{2j−1},.←C^{1 }and A_{2j},.←C^{2 }are updated. Just as in PHASE, this update is made before optimizing haplotypes for any other individuals.

There are two basic optimizations on haplotypes that are performed. The first is a single site move in which (A_{2j−1},A_{2j,t})=(a, b) are set to be the highest scoring pair (a, b) that is compatible with the observed genotype G_{jt}. The second move is a crossover in which new haplotypes C_{k} ^{1}=A_{2j−1{k>t},k }are created. The proposed haplotype C^{1 }is the same as A_{2j},. up to index t−1 and for larger indices it has the same sequence as A_{2j−1,}. Likewise the second haplotype C^{2 }in the proposed pair is identical A_{2j−1.}. at indices up to t−1 and to A_{2j,}. for larger indices. These moves are considered at every site t and are only made if they result in a nonnegligible increase in the score S( ) over the current configuration.

Data Analysis.

Two trio datasets are used to assess the performance of an embodiment of the present invention to be described here. The parentchild family structure allows for inferring the two haplotypes in the children unambiguously at most markers, except triple heterozygous sites (e.g., both parents and the child are heterozygous) and sites where one or more individuals have missing genotypes. Knowing the haplotypes in the children, all haplotypes are inferred in the parents. These haplotypes, excluding ambiguous sites, are treated as the standard.

In an embodiment of the present invention, phasing methods are applied to the parents, without using the children's genotype. Results from these analyses are comparable to analyzing unrelated individuals. These parents' genotype data are analyzed using FastPHASE and Beagle separately. FastPHASE was run with 20 hidden states, 10 restarts, and 35 EM iterations per restart. Twenty hidden states, instead of the default setting of 10, were chosen because this gave a lower error rate. For Beagle, the default setting was used and the program was allowed to run for 10 iterations and took n=1 sample. Using the output of either FastPHASE or Beagle as starting points, the method is applied by fitting the model parameters for 10 iterations without changing the inferred haplotypes, followed by three more iterations of both updating the parameters and optimizing the haplotypes.

The first dataset consists of 45 CEU trios and 50 YRI trios, genotyped on the Illumina HumanHap650Y arrays as part of the International HapMap Project, Phase III (Consortium, T. I. H. A second generation human haplotype map of over 3.1 million snps. Nature 449, 85161 (2007)). Specifically, focus is placed on the region of chromosome 9q, which included 13,976 SNPs. As a standard, the data that was used was the phased haplotype data generated by the HapMap consortium excluding ambiguous markers. In all analyses, the CEU and YRI trios were analyzed separately.

The second dataset includes 492 Mexican trios that were genotyped as part of an ongoing GWAS of asthma. The recruitment protocol was reviewed and approved by the Institute Review Boards of the Mexican National Institute of Public Health, the Hospital Infantil de Mexico, Federico Gomez, and the U.S. National Institute of Environmental Health Sciences. Parents provided the written informed consent for the child's participation. Children also gave their informed assent. The characteristics of this cohort are described previously (Hancock, D. B. et al. Genomewide association study implicates chromosome 9q21.31 as a susceptibility locus for asthma in mexican children. PLoS Genet. 5, e1000623 (2009)). This dataset is useful for two reasons. First, it allows for assessing the performance of various phasing methods in an genetically admixed population, a subject that has not been systematically studied. Second, as described below, the accuracy of haplotype inference depends on the sample size; therefore, as one of the largest triosample that has been genotyped to date (984 parents), analyzing this data provides a more realistic measure of the phasing accuracy expected in a GWAS study.

Assessment of Accuracy.

It should be pointed out that most previous studies comparing haplotype inference methods have focused on the rate of switching error, which is the error probability between consecutive pairs of heterozygous sites. The switching error rate measures the shortrange phasing accuracy and is useful in some applications such as estimation of local recombination rate. But other analyses, such as the extended haplotype homozygosity (EHH) test used for detecting recent positive selection, depend on accurate phasing over a longer range (see Sabeti, P. C. et al. Detecting recent positive selection in the human genome from haplotype structure. Nature 419, 8327 (2002)). In these settings, the error rate between a random pair of SNPs, referred to as the individual error rate, is the relevant quantity. Furthermore, because a higher error rate is expected between markers that are far apart, it is useful to characterize the error rate as a function of distance.

In an embodiment, SNPs were indexed according to their physical positions, 1, 2, . . . , N, and define the distance between a pair of SNPs, i and j, by the difference in their indices, i−j. This metric was chosen because none of the methods otherwise considered here, FastPHASE, Beagle, and PHASEEM, take into account physical or recombination distance. The error rate at distance, d, is then computed over all pairs of markers that are d SNPs apart.

Results

Two software packages are used to analyze largescale highdensity SNP data: FastPHASE (see 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 78, 629644 (2006)), and Beagle (see Browning, B. L. & Browning, S. R. A unified approach to genotype imputation and haplotype phase inference for large data sets of trios and unrelated individuals. American Journal of Human Genetics 84, 21023 (2009)). Both programs employ Hidden Markov Models (HMM's), which can be computed efficiently via the EM algorithm and without lengthy MCMC runs.

FastPHASE implements a Markov Jump Model, in which the hidden states represent clusters of “similar” haplotypes. The number of hidden states is fixed and constant, and is usually set to a small number (e.g., 1020) in practice. Similarly, Beagle represents local haplotype clusters by a directed acyclic graph (DAG). This graph is learned through a greedy algorithm and allows the number of hidden states to vary from region to region. Although the Beagle HMM typically has many more hidden states than that in FastPHASE, the computation in Beagle is not hampered because most hiddenstate transition and emission probabilities are exactly zero.

To assess the accuracy of PHASEEM, haplotypes were inferred for the HapMap CEU and YRI parents as unrelated individuals, first using FastPHASE and subsequently updating the FastPHASE results with PHASEEM. FIG. 1A compares the error rates generated by FastPHASE and PHASEEM using triobased phasing as the standard. As expected, the error rate increases with intermarker distance, with the limit approaching the random guess error rate of 50%. On the CEU trio data, the error rate incurred by FastPHASE rises from 0.0165 to 0.0646 to 0.391 at snp's with index distance of 1, 5, and 50 respectively. Applying PHASEEM to the output of FastPHASE, phasing accuracy improves regardless of marker distance; the reduction in error rate ranges between 10%20% (see FIG. 1B), and is comparable with the difference between PHASE and FastPHASE found in (Lai, T. L., Xing, H. & Zhang, N. Stochastic segmentation models for array based comparative genomic hybridization data analysis. Biostatistics 9, 290307 (2008)).

Analysis of the HapMap YRI dataset yields qualitatively similar results. But PHASEEM achieves a greater error reduction on this set: between 20%35% depending on the index distance. Even for adjacent SNP pairs, the PHASEEM error rate is 26% lower than the FastPHASE error (0.031%). The greater improvement is due mainly to the higher error rate FastPHASE produces on the YRI data, which suggests that FastPHASE model with 20 states may be insufficient to model the level of haplotype diversity in an African population. In contrast, PHASEEM achieves similar accuracy on the two datasets despite a poorer YRI starting configuration.

The difference between PHASEEM and FastPHASE becomes more pronounced as the sample size is increased. In the subsample of 100 Mexican parents, a decrease in error rate is seen by about 1020%. When PHASEEM is run on larger data sets (400, 800, 1200 and 1968 chromosomes), this gap in performance widens considerably. Using the entire dataset, PHASEEM nearly halved the error rate compared to FastPHASE. Increasing the sample size from 100 to 984, the switch error rate of FastPHASE dropped from 0.0477% to 0.0413% whereas PHASEEM (initialized from these phasings) decreased from 0.0413% to 0.0236%. Beagle had an error rate of 0.0363% which also represents a significant gain in accuracy. However, despite the difference in switch error, almost no difference was found in the final PHASEEM errorrate when initializing from Beagle rather than FastPHASE. This indicates that model refinements (such as the addition of the divergence time variable of PHASE) may be more important than better optimization moves. Table 2, shown in FIG. 6, shows the effect of sample size on the switch error rates.

In addition to inferring the most likely haplotype configurations, PHASEEM produces two confidence measures as a biproduct of its optimization. Let

Δ_{jkk′} ^{CR},

be a measure of uncertainty for the contiguous set of SNPs indexed k, k+1, . . . , k′ in the jth imputed haplotype. This is the log likelihood of the imputed phasing minus the maximum log likelihood of a phasing after a single crossover is performed somewhere between SNPs k and k′. To illustrate, shown in FIG. 3A is the switch error rate stratified by this confidence measure in the left panel. The error rate of FastPHASE is shown for comparison. Shown are the pairs of SNP's with index distance given on the x axis and whose confidence measure falls in the intervals (−1, ∞), (−5, −1] and (−∞, −5], respectively. A very negative number means that all crossovers resulted in significantly lower likelihood and so a switch error is less likely, and this is reflected in the error rates.

In FIG. 3, the dotted line indicates that fewer SNPpairs fall in the highconfidence crossover stratum as the intermarker distance increases; in the Mexican data, half of the SNPpairs can be phased with high crossover confidence at a distance of 37 SNPs apart. The crossover measure allows for identifying a large set of long haplotypcs that are still accurately phased. The usual switch error is also provided for these three panels in Table 1 shown in FIG. 5.

Discussion

The ability to accurately construct haplotypes from unphased genotype data plays pivotal roles in population and medical genetics studies. Previous studies have largely focused on accuracy over short range, such as the error rate between consecutive heterozygous sites (switching error), although some downstream analyses relies on accurate phasing over a long range (see Sabeti, P. C. et al. Detecting recent positive selection in the human genome from haplotype structure. Nature 419, 8327 (2002)). In the present disclosure, a new method is disclosed, implemented in program PHASEEM, with a goal to improve the long range phasing accuracy over FastPHASE and Beagle. The error rate is characterized as a function of marker spacing and observed that the error rate of FastPHASE, Beagle and PHASEEM increase rapidly as a function of marker spacing. It is likely that a similar pattern holds for most other existing phasing algorithms with the exception of the heuristicdrive LRP method proposed in Kong et al. This latter method, however, relies on substantial pairs of individuals in the sample sharing haplotypes on the order of 1000. For this to hold, either the underlying population is extremely inbred or the sample size needs to be very large. The allele sharing is examined in 10 windows of 1000 SNPs in the HapMap CEU and YRI parents as well as the 984 Mexican parents and found no individualpair sharing a haplotype at this length. Therefore, it is unlikely that LRP can be directly applied to data collected on nonfounder populations.

Given that the error rate increases with an increase in distance between SNPs, it is can be important to account for the uncertainties in the downstream analysis. Two measures are disclosed: crossover confidence and singlesite confidence. The crossover confidence was found to be highly informative while singlesite confidence offers additional information. An analysis, such as the EHH, can be improved by accounting for the uncertainties.

The presently disclosed method relates to several other approaches. Like FastPHASE, Beagle, PHASE and many other methods, PHASEEM, as an embodiment of the present invention, adopts an HMM model. A key feature in PHASEEM is the hidden states of the HMM is every putative haplotype in the sample. There is a connection between this idea and the heuristic notion of “surrogate” parents that underlies LRP: the hidden state can be thought as the best “surrogate” parent; the optimization in PHASEEM, which favors staying in a hidden state for long segments, coincides with features in LRP where long range allele sharing is a hallmark for “surrogate” parents. In other words, the HMM in PHASEEM aims to choose the mostlikely “surrogate” parents in the sample.

The success of the parameterization presented here indicates that the use of other haplotypes as hidden states for the HMM likelihood is an important difference between FastPHASE and PHASE. The PHASE model can simultaneously capture shared haplotypes at both local and large scales, and yet the model is not hierarchical. Some aspects of PHASE have been omitted which may improve performance (the divergencetime variable, for example), but it is useful to illustrate that the single retained aspect of PHASE produces more accurate phasings than FastPHASE.

It should be appreciated by those skilled in the art that the specific embodiments disclosed above may be readily utilized as a basis for modifying or designing other algorithms or systems. It should also be appreciated by those skilled in the art that such modifications do not depart from the scope of the invention as set forth in the appended claims.