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1.  Efficient whole-genome association mapping using local phylogenies for unphased genotype data 
Bioinformatics  2008;24(19):2215-2221.
Motivation: Recent advances in genotyping technology has made data acquisition for whole-genome association study cost effective, and a current active area of research is developing efficient methods to analyze such large-scale datasets. Most sophisticated association mapping methods that are currently available take phased haplotype data as input. However, phase information is not readily available from sequencing methods and inferring the phase via computational approaches is time-consuming, taking days to phase a single chromosome.
Results: In this article, we devise an efficient method for scanning unphased whole-genome data for association. Our approach combines a recently found linear-time algorithm for phasing genotypes on trees with a recently proposed tree-based method for association mapping. From unphased genotype data, our algorithm builds local phylogenies along the genome, and scores each tree according to the clustering of cases and controls. We assess the performance of our new method on both simulated and real biological datasets.
Availability The software described in this article is available at http://www.daimi.au.dk/~mailund/Blossoc and distributed under the GNU General Public License.
Contact:mailund@birc.au.dk
doi:10.1093/bioinformatics/btn406
PMCID: PMC2553438  PMID: 18667442
2.  Whole genome association mapping by incompatibilities and local perfect phylogenies 
BMC Bioinformatics  2006;7:454.
Background
With current technology, vast amounts of data can be cheaply and efficiently produced in association studies, and to prevent data analysis to become the bottleneck of studies, fast and efficient analysis methods that scale to such data set sizes must be developed.
Results
We present a fast method for accurate localisation of disease causing variants in high density case-control association mapping experiments with large numbers of cases and controls. The method searches for significant clustering of case chromosomes in the "perfect" phylogenetic tree defined by the largest region around each marker that is compatible with a single phylogenetic tree. This perfect phylogenetic tree is treated as a decision tree for determining disease status, and scored by its accuracy as a decision tree. The rationale for this is that the perfect phylogeny near a disease affecting mutation should provide more information about the affected/unaffected classification than random trees. If regions of compatibility contain few markers, due to e.g. large marker spacing, the algorithm can allow the inclusion of incompatibility markers in order to enlarge the regions prior to estimating their phylogeny. Haplotype data and phased genotype data can be analysed. The power and efficiency of the method is investigated on 1) simulated genotype data under different models of disease determination 2) artificial data sets created from the HapMap ressource, and 3) data sets used for testing of other methods in order to compare with these. Our method has the same accuracy as single marker association (SMA) in the simplest case of a single disease causing mutation and a constant recombination rate. However, when it comes to more complex scenarios of mutation heterogeneity and more complex haplotype structure such as found in the HapMap data our method outperforms SMA as well as other fast, data mining approaches such as HapMiner and Haplotype Pattern Mining (HPM) despite being significantly faster. For unphased genotype data, an initial step of estimating the phase only slightly decreases the power of the method. The method was also found to accurately localise the known susceptibility variants in an empirical data set – the ΔF508 mutation for cystic fibrosis – where the susceptibility variant is already known – and to find significant signals for association between the CYP2D6 gene and poor drug metabolism, although for this dataset the highest association score is about 60 kb from the CYP2D6 gene.
Conclusion
Our method has been implemented in the Blossoc (BLOck aSSOCiation) software. Using Blossoc, genome wide chip-based surveys of 3 million SNPs in 1000 cases and 1000 controls can be analysed in less than two CPU hours.
doi:10.1186/1471-2105-7-454
PMCID: PMC1624851  PMID: 17042942
3.  Direct maximum parsimony phylogeny reconstruction from genotype data 
BMC Bioinformatics  2007;8:472.
Background
Maximum parsimony phylogenetic tree reconstruction from genetic variation data is a fundamental problem in computational genetics with many practical applications in population genetics, whole genome analysis, and the search for genetic predictors of disease. Efficient methods are available for reconstruction of maximum parsimony trees from haplotype data, but such data are difficult to determine directly for autosomal DNA. Data more commonly is available in the form of genotypes, which consist of conflated combinations of pairs of haplotypes from homologous chromosomes. Currently, there are no general algorithms for the direct reconstruction of maximum parsimony phylogenies from genotype data. Hence phylogenetic applications for autosomal data must therefore rely on other methods for first computationally inferring haplotypes from genotypes.
Results
In this work, we develop the first practical method for computing maximum parsimony phylogenies directly from genotype data. We show that the standard practice of first inferring haplotypes from genotypes and then reconstructing a phylogeny on the haplotypes often substantially overestimates phylogeny size. As an immediate application, our method can be used to determine the minimum number of mutations required to explain a given set of observed genotypes.
Conclusion
Phylogeny reconstruction directly from unphased data is computationally feasible for moderate-sized problem instances and can lead to substantially more accurate tree size inferences than the standard practice of treating phasing and phylogeny construction as two separate analysis stages. The difference between the approaches is particularly important for downstream applications that require a lower-bound on the number of mutations that the genetic region has undergone.
doi:10.1186/1471-2105-8-472
PMCID: PMC2222657  PMID: 18053244
4.  Haplotype inference from unphased SNP data in heterozygous polyploids based on SAT 
BMC Genomics  2008;9:356.
Background
Haplotype inference based on unphased SNP markers is an important task in population genetics. Although there are different approaches to the inference of haplotypes in diploid species, the existing software is not suitable for inferring haplotypes from unphased SNP data in polyploid species, such as the cultivated potato (Solanum tuberosum). Potato species are tetraploid and highly heterozygous.
Results
Here we present the software SATlotyper which is able to handle polyploid and polyallelic data. SATlo-typer uses the Boolean satisfiability problem to formulate Haplotype Inference by Pure Parsimony. The software excludes existing haplotype inferences, thus allowing for calculation of alternative inferences. As it is not known which of the multiple haplotype inferences are best supported by the given unphased data set, we use a bootstrapping procedure that allows for scoring of alternative inferences. Finally, by means of the bootstrapping scores, it is possible to optimise the phased genotypes belonging to a given haplotype inference. The program is evaluated with simulated and experimental SNP data generated for heterozygous tetraploid populations of potato. We show that, instead of taking the first haplotype inference reported by the program, we can significantly improve the quality of the final result by applying additional methods that include scoring of the alternative haplotype inferences and genotype optimisation. For a sub-population of nineteen individuals, the predicted results computed by SATlotyper were directly compared with results obtained by experimental haplotype inference via sequencing of cloned amplicons. Prediction and experiment gave similar results regarding the inferred haplotypes and phased genotypes.
Conclusion
Our results suggest that Haplotype Inference by Pure Parsimony can be solved efficiently by the SAT approach, even for data sets of unphased SNP from heterozygous polyploids. SATlotyper is freeware and is distributed as a Java JAR file. The software can be downloaded from the webpage of the GABI Primary Database at . The application of SATlotyper will provide haplotype information, which can be used in haplotype association mapping studies of polyploid plants.
doi:10.1186/1471-2164-9-356
PMCID: PMC2566320  PMID: 18667059
5.  Linkage disequilibrium mapping via cladistic analysis of phase-unknown genotypes and inferred haplotypes in the Genetic Analysis Workshop 14 simulated data 
BMC Genetics  2005;6(Suppl 1):S100.
We recently described a method for linkage disequilibrium (LD) mapping, using cladistic analysis of phased single-nucleotide polymorphism (SNP) haplotypes in a logistic regression framework. However, haplotypes are often not available and cannot be deduced with certainty from the unphased genotypes. One possible two-stage approach is to infer the phase of multilocus genotype data and analyze the resulting haplotypes as if known. Here, haplotypes are inferred using the expectation-maximization (EM) algorithm and the best-guess phase assignment for each individual analyzed. However, inferring haplotypes from phase-unknown data is prone to error and this should be taken into account in the subsequent analysis. An alternative approach is to analyze the phase-unknown multilocus genotypes themselves. Here we present a generalization of the method for phase-known haplotype data to the case of unphased SNP genotypes. Our approach is designed for high-density SNP data, so we opted to analyze the simulated dataset. The marker spacing in the initial screen was too large for our method to be effective, so we used the answers provided to request further data in regions around the disease loci and in null regions. Power to detect the disease loci, accuracy in localizing the true site of the locus, and false-positive error rates are reported for the inferred-haplotype and unphased genotype methods. For this data, analyzing inferred haplotypes outperforms analysis of genotypes. As expected, our results suggest that when there is little or no LD between a disease locus and the flanking region, there will be no chance of detecting it unless the disease variant itself is genotyped.
doi:10.1186/1471-2156-6-S1-S100
PMCID: PMC1866839  PMID: 16451556
6.  HaploRec: efficient and accurate large-scale reconstruction of haplotypes 
BMC Bioinformatics  2006;7:542.
Background
Haplotypes extracted from human DNA can be used for gene mapping and other analysis of genetic patterns within and across populations. A fundamental problem is, however, that current practical laboratory methods do not give haplotype information. Estimation of phased haplotypes of unrelated individuals given their unphased genotypes is known as the haplotype reconstruction or phasing problem.
Results
We define three novel statistical models and give an efficient algorithm for haplotype reconstruction, jointly called HaploRec. HaploRec is based on exploiting local regularities conserved in haplotypes: it reconstructs haplotypes so that they have maximal local coherence. This approach – not assuming statistical dependence for remotely located markers – has two useful properties: it is well-suited for sparse marker maps, such as those used in gene mapping, and it can actually take advantage of long maps.
Conclusion
Our experimental results with simulated and real data show that HaploRec is a powerful method for the large scale haplotyping needed in association studies. With sample sizes large enough for gene mapping it appeared to be the best compared to all other tested methods (Phase, fastPhase, PL-EM, Snphap, Gerbil; simulated data), with small samples it was competitive with the best available methods (real data). HaploRec is several orders of magnitude faster than Phase and comparable to the other methods; the running times are roughly linear in the number of subjects and the number of markers. HaploRec is publicly available at .
doi:10.1186/1471-2105-7-542
PMCID: PMC1766938  PMID: 17187677
7.  Inferring haplotypes and parental genotypes in larger full sib-ships and other pedigrees with missing or erroneous genotype data 
BMC Genetics  2012;13:85.
Background
In many contexts, pedigrees for individuals are known even though not all individuals have been fully genotyped. In one extreme case, the genotypes for a set of full siblings are known, with no knowledge of parental genotypes. We propose a method for inferring phased haplotypes and genotypes for all individuals, even those with missing data, in such pedigrees, allowing a multitude of classic and recent methods for linkage and genome analysis to be used more efficiently.
Results
By artificially removing the founder generation genotype data from a well-studied simulated dataset, the quality of reconstructed genotypes in that generation can be verified. For the full structure of repeated matings with 15 offspring per mating, 10 dams per sire, 99.89% of all founder markers were phased correctly, given only the unphased genotypes for offspring. The accuracy was reduced only slightly, to 99.51%, when introducing a 2% error rate in offspring genotypes. When reduced to only 5 full-sib offspring in a single sire-dam mating, the corresponding percentage is 92.62%, which compares favorably with 89.28% from the leading Merlin package. Furthermore, Merlin is unable to handle more than approximately 10 sibs, as the number of states tracked rises exponentially with family size, while our approach has no such limit and handles 150 half-sibs with ease in our experiments.
Conclusions
Our method is able to reconstruct genotypes for parents when genotype data is only available for offspring individuals, as well as haplotypes for all individuals. Compared to the Merlin package, we can handle larger pedigrees and produce superior results, mainly due to the fact that Merlin uses the Viterbi algorithm on the state space to infer the genotype sequence. Tracking of haplotype and allele origin can be used in any application where the marker set does not directly influence genotype variation influencing traits. Inference of genotypes can also reduce the effects of genotyping errors and missing data. The cnF2freq codebase implementing our approach is available under a BSD-style license.
doi:10.1186/1471-2156-13-85
PMCID: PMC3562206  PMID: 23046532
Haplotyping; Phasing; Genotype inference; Nuclear family data; Hidden Markov models
8.  Investigation of Inversion Polymorphisms in the Human Genome Using Principal Components Analysis 
PLoS ONE  2012;7(7):e40224.
Despite the significant advances made over the last few years in mapping inversions with the advent of paired-end sequencing approaches, our understanding of the prevalence and spectrum of inversions in the human genome has lagged behind other types of structural variants, mainly due to the lack of a cost-efficient method applicable to large-scale samples. We propose a novel method based on principal components analysis (PCA) to characterize inversion polymorphisms using high-density SNP genotype data. Our method applies to non-recurrent inversions for which recombination between the inverted and non-inverted segments in inversion heterozygotes is suppressed due to the loss of unbalanced gametes. Inside such an inversion region, an effect similar to population substructure is thus created: two distinct “populations” of inversion homozygotes of different orientations and their 1∶1 admixture, namely the inversion heterozygotes. This kind of substructure can be readily detected by performing PCA locally in the inversion regions. Using simulations, we demonstrated that the proposed method can be used to detect and genotype inversion polymorphisms using unphased genotype data. We applied our method to the phase III HapMap data and inferred the inversion genotypes of known inversion polymorphisms at 8p23.1 and 17q21.31. These inversion genotypes were validated by comparing with literature results and by checking Mendelian consistency using the family data whenever available. Based on the PCA-approach, we also performed a preliminary genome-wide scan for inversions using the HapMap data, which resulted in 2040 candidate inversions, 169 of which overlapped with previously reported inversions. Our method can be readily applied to the abundant SNP data, and is expected to play an important role in developing human genome maps of inversions and exploring associations between inversions and susceptibility of diseases.
doi:10.1371/journal.pone.0040224
PMCID: PMC3392271  PMID: 22808122
9.  Leveraging reads that span multiple single nucleotide polymorphisms for haplotype inference from sequencing data 
Bioinformatics  2013;29(18):2245-2252.
Motivation: Haplotypes, defined as the sequence of alleles on one chromosome, are crucial for many genetic analyses. As experimental determination of haplotypes is extremely expensive, haplotypes are traditionally inferred using computational approaches from genotype data, i.e. the mixture of the genetic information from both haplotypes. Best performing approaches for haplotype inference rely on Hidden Markov Models, with the underlying assumption that the haplotypes of a given individual can be represented as a mosaic of segments from other haplotypes in the same population. Such algorithms use this model to predict the most likely haplotypes that explain the observed genotype data conditional on reference panel of haplotypes. With rapid advances in short read sequencing technologies, sequencing is quickly establishing as a powerful approach for collecting genetic variation information. As opposed to traditional genotyping-array technologies that independently call genotypes at polymorphic sites, short read sequencing often collects haplotypic information; a read spanning more than one polymorphic locus (multi-single nucleotide polymorphic read) contains information on the haplotype from which the read originates. However, this information is generally ignored in existing approaches for haplotype phasing and genotype-calling from short read data.
Results: In this article, we propose a novel framework for haplotype inference from short read sequencing that leverages multi-single nucleotide polymorphic reads together with a reference panel of haplotypes. The basis of our approach is a new probabilistic model that finds the most likely haplotype segments from the reference panel to explain the short read sequencing data for a given individual. We devised an efficient sampling method within a probabilistic model to achieve superior performance than existing methods. Using simulated sequencing reads from real individual genotypes in the HapMap data and the 1000 Genomes projects, we show that our method is highly accurate and computationally efficient. Our haplotype predictions improve accuracy over the basic haplotype copying model by ∼20% with comparable computational time, and over another recently proposed approach Hap-SeqX by ∼10% with significantly reduced computational time and memory usage.
Availability: Publicly available software is available at http://genetics.cs.ucla.edu/harsh
Contact: bpasaniuc@mednet.ucla.edu or eeskin@cs.ucla.edu
doi:10.1093/bioinformatics/btt386
PMCID: PMC3753566  PMID: 23825370
10.  inPHAP: Interactive visualization of genotype and phased haplotype data 
BMC Bioinformatics  2014;15:200.
Background
To understand individual genomes it is necessary to look at the variations that lead to changes in phenotype and possibly to disease. However, genotype information alone is often not sufficient and additional knowledge regarding the phase of the variation is needed to make correct interpretations. Interactive visualizations, that allow the user to explore the data in various ways, can be of great assistance in the process of making well informed decisions. But, currently there is a lack for visualizations that are able to deal with phased haplotype data.
Results
We present inPHAP, an interactive visualization tool for genotype and phased haplotype data. inPHAP features a variety of interaction possibilities such as zooming, sorting, filtering and aggregation of rows in order to explore patterns hidden in large genetic data sets. As a proof of concept, we apply inPHAP to the phased haplotype data set of Phase 1 of the 1000 Genomes Project. Thereby, inPHAP’s ability to show genetic variations on the population as well as on the individuals level is demonstrated for several disease related loci.
Conclusions
As of today, inPHAP is the only visual analytical tool that allows the user to explore unphased and phased haplotype data interactively. Due to its highly scalable design, inPHAP can be applied to large datasets with up to 100 GB of data, enabling users to visualize even large scale input data. inPHAP closes the gap between common visualization tools for unphased genotype data and introduces several new features, such as the visualization of phased data. inPHAP is available for download at http://bit.ly/1iJgKmX.
doi:10.1186/1471-2105-15-200
PMCID: PMC4083868  PMID: 25002076
Genotype data; Phased haplotype data; Interactive visualization; 1000 genomes project
11.  Generalized Linear Modeling with Regularization for Detecting Common Disease Rare Haplotype Association 
Genetic epidemiology  2009;33(4):308-316.
Whole genome association studies (WGAS) have surged in popularity in recent years as technological advances have made large-scale genotyping more feasible and as new exciting results offer tremendous hope and optimism. The logic of WGAS rests upon the common disease/common variant (CD/CV) hypothesis. Detection of association under the common disease/rare variant (CD/RV) scenario is much harder, and the current practices of WGAS may be under-power without large enough sample sizes. In this paper, we propose a generalized linear model with regularization (rGLM) approach for detecting disease-haplotype association using unphased single nucleotide polymorphisms data that is applicable to both CD/CV and CD/RV scenarios. We borrow a dimension-reduction method from the data mining and statistical learning literature, but use it for the purpose of weeding out haplotypes that are not associated with the disease so that the associated haplotypes, especially those that are rare, can stand out and be accounted for more precisely. By using high-dimensional data analysis techniques, which are frequently employed in microarray analyses, interacting effects among haplotypes in different blocks can be investigated without much concern about the sample size being overwhelmed by the number of haplotype combinations. Our simulation study demonstrates the gain in power for detecting associations with moderate sample sizes. For detecting association under CD/RV, regression type methods such as that implemented in hapassoc may fail to provide coefficient estimates for rare associated haplotypes, resulting in a loss of power compared to rGLM. Furthermore, our results indicate that rGLM can uncover the associated variants much more frequently than can hapassoc.
doi:10.1002/gepi.20382
PMCID: PMC2752471  PMID: 19025789
whole genome association study; interacting effects between haplotype blocks; dimension reduction; regularization/LASSO; case-control design
12.  Inference of the Haplotype Effect in a Matched Case-Control Study Using Unphased Genotype Data* 
Typically locus specific genotype data do not contain information regarding the gametic phase of haplotypes, especially when an individual is heterozygous at more than one locus among a large number of linked polymorphic loci. Thus, studying disease-haplotype association using unphased genotype data is essentially a problem of handling a missing covariate in a case-control design. There are several methods for estimating a disease-haplotype association parameter in a matched case-control study. Here we propose a conditional likelihood approach for inference regarding the disease-haplotype association using unphased genotype data arising from a matched case-control study design. The proposed method relies on a logistic disease risk model and a Hardy-Weinberg equilibrium (HWE) among the control population only. We develop an expectation and conditional maximization (ECM) algorithm for jointly estimating the haplotype frequency and the disease-haplotype association parameter(s). We apply the proposed method to analyze the data from the Alpha-Tocopherol, Beta-Carotene Cancer prevention study, and a matched case-control study of breast cancer patients conducted in Israel. The performance of the proposed method is evaluated via simulation studies.
doi:10.2202/1557-4679.1079
PMCID: PMC2835450  PMID: 20231916
13.  Viral diversity and clonal evolution from unphased genomic data 
BMC Genomics  2014;15(Suppl 6):S17.
Background
Clonal expansion is a process in which a single organism reproduces asexually, giving rise to a diversifying population. It is pervasive in nature, from within-host pathogen evolution to emergent infectious disease outbreaks. Standard phylogenetic tools rely on full-length genomes of individual pathogens or population consensus sequences (phased genotypes).
Although high-throughput sequencing technologies are able to sample population diversity, the short sequence reads inherent to them preclude assessing whether two reads originate from the same clone (unphased genotypes). This obstacle severely limits the application of phylogenetic methods and investigation of within-host dynamics of acute infections using this rich data source.
Methods
We introduce two measures of diversity to study the evolution of clonal populations using unphased genomic data, which eliminate the need to construct full-length genomes. Our method follows a maximum likelihood approach to estimate evolutionary rates and times to the most recent common ancestor, based on a relaxed molecular clock model; independent of a growth model. Deviations from neutral evolution indicate the presence of selection and bottleneck events.
Results
We evaluated our methods in silico and then compared it against existing approaches with the well-characterized 2009 H1N1 influenza pandemic. We then applied our method to high-throughput genomic data from marburgvirus-infected non-human primates and inferred the time of infection and the intra-host evolutionary rate, and identified purifying selection in viral populations.
Conclusions
Our method has the power to make use of minor variants present in less than 1% of the population and capture genomic diversification within days of infection, making it an ideal tool for the study of acute RNA viral infection dynamics.
doi:10.1186/1471-2164-15-S6-S17
PMCID: PMC4240099  PMID: 25573168
Clonal evolution; Evolutionary dynamics; Viral genomic diversity; Marburgvirus
14.  Multinomial logistic regression approach to haplotype association analysis in population-based case-control studies 
BMC Genetics  2006;7:43.
Background
The genetic association analysis using haplotypes as basic genetic units is anticipated to be a powerful strategy towards the discovery of genes predisposing human complex diseases. In particular, the increasing availability of high-resolution genetic markers such as the single-nucleotide polymorphisms (SNPs) has made haplotype-based association analysis an attractive alternative to single marker analysis.
Results
We consider haplotype association analysis under the population-based case-control study design. A multinomial logistic model is proposed for haplotype analysis with unphased genotype data, which can be decomposed into a prospective logistic model for disease risk as well as a model for the haplotype-pair distribution in the control population. Environmental factors can be readily incorporated and hence the haplotype-environment interaction can be assessed in the proposed model. The maximum likelihood estimation with unphased genotype data can be conveniently implemented in the proposed model by applying the EM algorithm to a prospective multinomial logistic regression model and ignoring the case-control design. We apply the proposed method to the hypertriglyceridemia study and identifies 3 haplotypes in the apolipoprotein A5 gene that are associated with increased risk for hypertriglyceridemia. A haplotype-age interaction effect is also identified. Simulation studies show that the proposed estimator has satisfactory finite-sample performances.
Conclusion
Our results suggest that the proposed method can serve as a useful alternative to existing methods and a reliable tool for the case-control haplotype-based association analysis.
doi:10.1186/1471-2156-7-43
PMCID: PMC1559715  PMID: 16907993
15.  HTreeQA: Using Semi-Perfect Phylogeny Trees in Quantitative Trait Loci Study on Genotype Data 
G3: Genes|Genomes|Genetics  2012;2(2):175-189.
With the advances in high-throughput genotyping technology, the study of quantitative trait loci (QTL) has emerged as a promising tool to understand the genetic basis of complex traits. Methodology development for the study of QTL recently has attracted significant research attention. Local phylogeny-based methods have been demonstrated to be powerful tools for uncovering significant associations between phenotypes and single-nucleotide polymorphism markers. However, most existing methods are designed for homozygous genotypes, and a separate haplotype reconstruction step is often needed to resolve heterozygous genotypes. This approach has limited power to detect nonadditive genetic effects and imposes an extensive computational burden. In this article, we propose a new method, HTreeQA, that uses a tristate semi-perfect phylogeny tree to approximate the perfect phylogeny used in existing methods. The semi-perfect phylogeny trees are used as high-level markers for association study. HTreeQA uses the genotype data as direct input without phasing. HTreeQA can handle complex local population structures. It is suitable for QTL mapping on any mouse populations, including the incipient Collaborative Cross lines. Applied HTreeQA, significant QTLs are found for two phenotypes of the PreCC lines, white head spot and running distance at day 5/6. These findings are consistent with known genes and QTL discovered in independent studies. Simulation studies under three different genetic models show that HTreeQA can detect a wider range of genetic effects and is more efficient than existing phylogeny-based approaches. We also provide rigorous theoretical analysis to show that HTreeQA has a lower error rate than alternative methods.
doi:10.1534/g3.111.001768
PMCID: PMC3284325  PMID: 22384396
phylogeny; quantitative trait loci (QTL); Mouse Collaborative Cross; Mouse Genetic Resource
16.  Genetic Association Mapping via Evolution-Based Clustering of Haplotypes 
PLoS Genetics  2007;3(7):e111.
Multilocus analysis of single nucleotide polymorphism haplotypes is a promising approach to dissecting the genetic basis of complex diseases. We propose a coalescent-based model for association mapping that potentially increases the power to detect disease-susceptibility variants in genetic association studies. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions with densely spaced markers and model chromosomal segments in high linkage disequilibrium therein assuming a perfect phylogeny. To make this assumption more realistic, we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium. The haplotype space is then partitioned into disjoint clusters, within which the phenotype–haplotype association is assumed to be the same. For example, in case-control studies, we expect chromosomal segments bearing the causal variant on a common ancestral background to be more frequent among cases than controls, giving rise to two separate haplotype clusters. The novelty of our approach arises from the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common ancestor. Our approach is fully Bayesian and we develop a Markov Chain Monte Carlo algorithm to sample efficiently over the space of possible partitions. We compare the proposed approach to both single-marker analyses and recently proposed multi-marker methods and show that the Bayesian partition modelling performs similarly in localizing the causal allele while yielding lower false-positive rates. Also, the method is computationally quicker than other multi-marker approaches. We present an application to real genotype data from the CYP2D6 gene region, which has a confirmed role in drug metabolism, where we succeed in mapping the location of the susceptibility variant within a small error.
Author Summary
Genetic association studies offer great promise in dissecting the genetic contribution to complex diseases. The underlying idea of such studies is to search for genetic variants along the genome that appear to be associated with a trait of interest, e.g., disease status for a binary trait. One then proceeds by genotyping unrelated individuals at several marker sites, searching for positions where single markers or combinations of multiple markers on the paternally and maternally inherited chromosomes (or haplotypes) appear to discriminate among affected and unaffected individuals, flagging genomic regions that may harbour disease susceptibility variants. The statistical analysis of such studies, however, poses several challenges, such as multiplicity and false-positives issue, due to the large number of markers considered. Focusing on case-control studies, we present a novel evolution-based Bayesian partition model that clusters haplotypes with similar disease risks. The novelty of this approach lies in the use of perfect phylogenies, which offers a sensible and computationally efficient approximation of the ancestry of a sample of chromosomes. We show that the incorporation of phylogenetic information leads to low false-positive rates, while our model fitting offers computational advantages over similar recently proposed coalescent-based haplotype clustering methods.
doi:10.1371/journal.pgen.0030111
PMCID: PMC1913101  PMID: 17616979
17.  HapTree: A Novel Bayesian Framework for Single Individual Polyplotyping Using NGS Data 
PLoS Computational Biology  2014;10(3):e1003502.
As the more recent next-generation sequencing (NGS) technologies provide longer read sequences, the use of sequencing datasets for complete haplotype phasing is fast becoming a reality, allowing haplotype reconstruction of a single sequenced genome. Nearly all previous haplotype reconstruction studies have focused on diploid genomes and are rarely scalable to genomes with higher ploidy. Yet computational investigations into polyploid genomes carry great importance, impacting plant, yeast and fish genomics, as well as the studies of the evolution of modern-day eukaryotes and (epi)genetic interactions between copies of genes. In this paper, we describe a novel maximum-likelihood estimation framework, HapTree, for polyploid haplotype assembly of an individual genome using NGS read datasets. We evaluate the performance of HapTree on simulated polyploid sequencing read data modeled after Illumina sequencing technologies. For triploid and higher ploidy genomes, we demonstrate that HapTree substantially improves haplotype assembly accuracy and efficiency over the state-of-the-art; moreover, HapTree is the first scalable polyplotyping method for higher ploidy. As a proof of concept, we also test our method on real sequencing data from NA12878 (1000 Genomes Project) and evaluate the quality of assembled haplotypes with respect to trio-based diplotype annotation as the ground truth. The results indicate that HapTree significantly improves the switch accuracy within phased haplotype blocks as compared to existing haplotype assembly methods, while producing comparable minimum error correction (MEC) values. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2–5.
Author Summary
While human and other eukaryotic genomes typically contain two copies of every chromosome, plants, yeast and fish such as salmon can have strictly more than two copies of each chromosome. By running standard genotype calling tools, it is possible to accurately identify the number of “wild type” and “mutant” alleles (A, C, G, or T) for each single-nucleotide polymorphism (SNP) site. However, in the case of two heterozygous SNP sites, genotype calling tools cannot determine whether “mutant” alleles from different SNP loci are on the same or different chromosomes. While the former would be healthy, in many cases the latter can cause loss of function; it is therefore necessary to identify the phase—the copies of a chromosome on which the mutant alleles occur—in addition to the genotype. This necessitates efficient algorithms to obtain accurate and comprehensive phase information directly from the next-generation-sequencing read data in higher ploidy species. We introduce an efficient statistical method for this task and show that our method significantly outperforms previous ones, in both accuracy and speed, for phasing triploid and higher ploidy genomes. Our method performs well on human diploid genomes as well, as demonstrated by our improved phasing of the well known NA12878 (1000 Genomes Project).
doi:10.1371/journal.pcbi.1003502
PMCID: PMC3967924  PMID: 24675685
18.  Empirical vs Bayesian approach for estimating haplotypes from genotypes of unrelated individuals 
BMC Genetics  2007;8:2.
Background
The completion of the HapMap project has stimulated further development of haplotype-based methodologies for disease associations. A key aspect of such development is the statistical inference of individual diplotypes from unphased genotypes. Several methodologies for inferring haplotypes have been developed, but they have not been evaluated extensively to determine which method not only performs well, but also can be easily incorporated in downstream haplotype-based association analyses. In this paper, we attempt to do so. Our evaluation was carried out by comparing the two leading Bayesian methods, implemented in PHASE and HAPLOTYPER, and the two leading empirical methods, implemented in PL-EM and HPlus. We used these methods to analyze real data, namely the dense genotypes on X-chromosome of 30 European and 30 African trios provided by the International HapMap Project, and simulated genotype data. Our conclusions are based on these analyses.
Results
All programs performed very well on X-chromosome data, with an average similarity index of 0.99 and an average prediction rate of 0.99 for both European and African trios. On simulated data with approximation of coalescence, PHASE implementing the Bayesian method based on the coalescence approximation outperformed other programs on small sample sizes. When the sample size increased, other programs performed as well as PHASE. PL-EM and HPlus implementing empirical methods required much less running time than the programs implementing the Bayesian methods. They required only one hundredth or thousandth of the running time required by PHASE, particularly when analyzing large sample sizes and large umber of SNPs.
Conclusion
For large sample sizes (hundreds or more), which most association studies require, the two empirical methods might be used since they infer the haplotypes as accurately as any Bayesian methods and can be incorporated easily into downstream haplotype-based analyses such as haplotype-association analyses.
doi:10.1186/1471-2156-8-2
PMCID: PMC1803795  PMID: 17261196
19.  Empirical evaluations of analytical issues arising from predicting HLA alleles using multiple SNPs 
BMC Genetics  2011;12:39.
Background
Numerous immune-mediated diseases have been associated with the class I and II HLA genes located within the major histocompatibility complex (MHC) consisting of highly polymorphic alleles encoded by the HLA-A, -B, -C, -DRB1, -DQB1 and -DPB1 loci. Genotyping for HLA alleles is complex and relatively expensive. Recent studies have demonstrated the feasibility of predicting HLA alleles, using MHC SNPs inside and outside of HLA that are typically included in SNP arrays and are commonly available in genome-wide association studies (GWAS). We have recently described a novel method that is complementary to the previous methods, for accurately predicting HLA alleles using unphased flanking SNPs genotypes. In this manuscript, we address several practical issues relevant to the application of this methodology.
Results
Applying this new methodology to three large independent study cohorts, we have evaluated the performance of the predictive models in ethnically diverse populations. Specifically, we have found that utilizing imputed in addition to genotyped SNPs generally yields comparable if not better performance in prediction accuracies. Our evaluation also supports the idea that predictive models trained on one population are transferable to other populations of the same ethnicity. Further, when the training set includes multi-ethnic populations, the resulting models are reliable and perform well for the same subpopulations across all HLA genes. In contrast, the predictive models built from single ethnic populations have superior performance within the same ethnic population, but are not likely to perform well in other ethnic populations.
Conclusions
The empirical explorations reported here provide further evidence in support of the application of this approach for predicting HLA alleles with GWAS-derived SNP data. Utilizing all available samples, we have built "state of the art" predictive models for HLA-A, -B, -C, -DRB1, -DQB1 and -DPB1. The HLA allele predictive models, along with the program used to carry out the prediction, are available on our website.
doi:10.1186/1471-2156-12-39
PMCID: PMC3111398  PMID: 21518453
20.  Powerful Haplotype-Based Hardy-Weinberg Equilibrium Tests for Tightly Linked Loci 
PLoS ONE  2013;8(10):e77399.
Recently, there have been many case-control studies proposed to test for association between haplotypes and disease, which require the Hardy-Weinberg equilibrium (HWE) assumption of haplotype frequencies. As such, haplotype inference of unphased genotypes and development of haplotype-based HWE tests are crucial prior to fine mapping. The goodness-of-fit test is a frequently-used method to test for HWE for multiple tightly-linked loci. However, its degrees of freedom dramatically increase with the increase of the number of loci, which may lack the test power. Therefore, in this paper, to improve the test power for haplotype-based HWE, we first write out two likelihood functions of the observed data based on the Niu's model (NM) and inbreeding model (IM), respectively, which can cause the departure from HWE. Then, we use two expectation-maximization algorithms and one expectation-conditional-maximization algorithm to estimate the model parameters under the HWE, IM and NM models, respectively. Finally, we propose the likelihood ratio tests LRT and LRT for haplotype-based HWE under the NM and IM models, respectively. We simulate the HWE, Niu's, inbreeding and population stratification models to assess the validity and compare the performance of these two LRT tests. The simulation results show that both of the tests control the type I error rates well in testing for haplotype-based HWE. If the NM model is true, then LRT is more powerful. While, if the true model is the IM model, then LRT has better performance in power. Under the population stratification model, LRT is still more powerful. To this end, LRT is generally recommended. Application of the proposed methods to a rheumatoid arthritis data set further illustrates their utility for real data analysis.
doi:10.1371/journal.pone.0077399
PMCID: PMC3805574  PMID: 24167573
21.  Application of the Linux cluster for exhaustive window haplotype analysis using the FBAT and Unphased programs 
BMC Bioinformatics  2008;9(Suppl 6):S10.
Background
Genetic association studies have been used to map disease-causing genes. A newly introduced statistical method, called exhaustive haplotype association study, analyzes genetic information consisting of different numbers and combinations of DNA sequence variations along a chromosome. Such studies involve a large number of statistical calculations and subsequently high computing power. It is possible to develop parallel algorithms and codes to perform the calculations on a high performance computing (HPC) system. However, most existing commonly-used statistic packages for genetic studies are non-parallel versions. Alternatively, one may use the cutting-edge technology of grid computing and its packages to conduct non-parallel genetic statistical packages on a centralized HPC system or distributed computing systems. In this paper, we report the utilization of a queuing scheduler built on the Grid Engine and run on a Rocks Linux cluster for our genetic statistical studies.
Results
Analysis of both consecutive and combinational window haplotypes was conducted by the FBAT (Laird et al., 2000) and Unphased (Dudbridge, 2003) programs. The dataset consisted of 26 loci from 277 extended families (1484 persons). Using the Rocks Linux cluster with 22 compute-nodes, FBAT jobs performed about 14.4–15.9 times faster, while Unphased jobs performed 1.1–18.6 times faster compared to the accumulated computation duration.
Conclusion
Execution of exhaustive haplotype analysis using non-parallel software packages on a Linux-based system is an effective and efficient approach in terms of cost and performance.
doi:10.1186/1471-2105-9-S6-S10
PMCID: PMC2423433  PMID: 18541045
22.  Assessment of global phase uncertainty in case-control studies 
BMC Genetics  2009;10:54.
Background
In haplotype-based candidate gene studies a problem is that the genotype data are unphased, which results in haplotype ambiguity. The measure [1] quantifies haplotype predictability from genotype data. It is computed for each individual haplotype, and for a measure of global relative efficiency a minimum value is suggested. Alternatively, we developed methods directly based on the information content of haplotype frequency estimates to obtain global relative efficiency measures: and based on A- and D-optimality, respectively. All three methods are designed for single populations; they can be applied in cases only, controls only or the whole data. Therefore they are not necessarily optimal for haplotype testing in case-control studies.
Results
A new global relative efficiency measure was derived to maximize power of a simple test statistic that compares haplotype frequencies in cases and controls. Application to real data showed that our proposed method gave a clear and summarizing measure for the case-control study conducted. Additionally this measure might be used for selection of individuals, who have the highest potential for improving power by resolving phase ambiguity.
Conclusion
Instead of using relative efficiency measure for cases only, controls only or their combined data, we link uncertainty measure to case-control studies directly. Hence, our global efficiency measure might be useful to assess whether data are informative or have enough power for estimation of a specific haplotype risk.
doi:10.1186/1471-2156-10-54
PMCID: PMC2760579  PMID: 19751505
23.  Inferring species trees from incongruent multi-copy gene trees using the Robinson-Foulds distance 
Background
Constructing species trees from multi-copy gene trees remains a challenging problem in phylogenetics. One difficulty is that the underlying genes can be incongruent due to evolutionary processes such as gene duplication and loss, deep coalescence, or lateral gene transfer. Gene tree estimation errors may further exacerbate the difficulties of species tree estimation.
Results
We present a new approach for inferring species trees from incongruent multi-copy gene trees that is based on a generalization of the Robinson-Foulds (RF) distance measure to multi-labeled trees (mul-trees). We prove that it is NP-hard to compute the RF distance between two mul-trees; however, it is easy to calculate this distance between a mul-tree and a singly-labeled species tree. Motivated by this, we formulate the RF problem for mul-trees (MulRF) as follows: Given a collection of multi-copy gene trees, find a singly-labeled species tree that minimizes the total RF distance from the input mul-trees. We develop and implement a fast SPR-based heuristic algorithm for the NP-hard MulRF problem.
We compare the performance of the MulRF method (available at http://genome.cs.iastate.edu/CBL/MulRF/) with several gene tree parsimony approaches using gene tree simulations that incorporate gene tree error, gene duplications and losses, and/or lateral transfer. The MulRF method produces more accurate species trees than gene tree parsimony approaches. We also demonstrate that the MulRF method infers in minutes a credible plant species tree from a collection of nearly 2,000 gene trees.
Conclusions
Our new phylogenetic inference method, based on a generalized RF distance, makes it possible to quickly estimate species trees from large genomic data sets. Since the MulRF method, unlike gene tree parsimony, is based on a generic tree distance measure, it is appealing for analyses of genomic data sets, in which many processes such as deep coalescence, recombination, gene duplication and losses as well as phylogenetic error may contribute to gene tree discord. In experiments, the MulRF method estimated species trees accurately and quickly, demonstrating MulRF as an efficient alternative approach for phylogenetic inference from large-scale genomic data sets.
doi:10.1186/1748-7188-8-28
PMCID: PMC3874668  PMID: 24180377
24.  Are Molecular Haplotypes Worth the Time and Expense? A Cost-Effective Method for Applying Molecular Haplotypes 
PLoS Genetics  2006;2(8):e127.
Because current molecular haplotyping methods are expensive and not amenable to automation, many researchers rely on statistical methods to infer haplotype pairs from multilocus genotypes, and subsequently treat these inferred haplotype pairs as observations. These procedures are prone to haplotype misclassification. We examine the effect of these misclassification errors on the false-positive rate and power for two association tests. These tests include the standard likelihood ratio test (LRTstd) and a likelihood ratio test that employs a double-sampling approach to allow for the misclassification inherent in the haplotype inference procedure (LRTae). We aim to determine the cost–benefit relationship of increasing the proportion of individuals with molecular haplotype measurements in addition to genotypes to raise the power gain of the LRTae over the LRTstd. This analysis should provide a guideline for determining the minimum number of molecular haplotypes required for desired power. Our simulations under the null hypothesis of equal haplotype frequencies in cases and controls indicate that (1) for each statistic, permutation methods maintain the correct type I error; (2) specific multilocus genotypes that are misclassified as the incorrect haplotype pair are consistently misclassified throughout each entire dataset; and (3) our simulations under the alternative hypothesis showed a significant power gain for the LRTae over the LRTstd for a subset of the parameter settings. Permutation methods should be used exclusively to determine significance for each statistic. For fixed cost, the power gain of the LRTae over the LRTstd varied depending on the relative costs of genotyping, molecular haplotyping, and phenotyping. The LRTae showed the greatest benefit over the LRTstd when the cost of phenotyping was very high relative to the cost of genotyping. This situation is likely to occur in a replication study as opposed to a whole-genome association study.
Synopsis
Localizing genes for complex genetic diseases presents a major challenge. Recent technological advances such as genotyping arrays containing hundreds of thousands of genomic “landmarks,” and databases cataloging these “landmarks” and the levels of correlation between them, have aided in these endeavors. To utilize these resources most effectively, many researchers employ a gene-mapping technique called haplotype-based association in order to examine the variation present at multiple genomic sites jointly for a role in and/or an association with the disease state. Although methods that determine haplotype pairs directly by biological assays are currently available, they rarely are used due to their expense and incongruity to automation. Statistical methods provide an inexpensive, relatively accurate means to determine haplotype pairs. However, these statistical methods can provide erroneous results. In this article, the authors compare a standard statistical method for performing a haplotype-based association test with a method that accounts for the misclassification of haplotype pairs as part of the test. Under a number of feasible scenarios, the performance of the new test exceeded that of the standard test.
doi:10.1371/journal.pgen.0020127
PMCID: PMC1550282  PMID: 16933998
25.  Likelihood-Based Association Analysis for Nuclear Families and Unrelated Subjects with Missing Genotype Data 
Human heredity  2008;66(2):87-98.
Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.
doi:10.1159/000119108
PMCID: PMC2386559  PMID: 18382088
Conditional likelihood; Family-based association tests; Missing data; Population stratification; Transmission/disequilibrium test; Unphased genotype data

Results 1-25 (1426762)