Large Scale Recovery of Haplotypes from Genotype Data Using Imperfect Phylogeny

Halperin, Eran

doi:10.1007/978-3-540-24719-7_17

Cited by 4 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We examined the predictions of algorithm Build-Tree over their blocks by only using the children genotypes (see Table 3). We used the methods in [11] to fit the model to the coalescent model whenever needed. Our results show an extremely small error rate.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny

Eskin

Halperin

Karp

2003

J. Bioinform. Comput. Biol.

Self Cite

102

106

View full text Add to dashboard Cite

Each person's genome contains two copies of each chromosome, one inherited from the father and the other from the mother. A person's genotype specifies the pair of bases at each site, but does not specify which base occurs on which chromosome. The sequence of each chromosome separately is called a haplotype. The determination of the haplotypes within a population is essential for understanding genetic variation and the inheritance of complex diseases. The haplotype mapping project, a successor to the human genome project, seeks to determine the common haplotypes in the human population.Since experimental determination of a person's genotype is less expensive than determining its component haplotypes, algorithms are required for computing haplotypes from genotypes. Two observations aid in this process: first, the human genome contains short blocks within which only a few different haplotypes occur; second, as suggested by Gusfield, it is reasonable to assume that the haplotypes observed within a block have evolved according to a perfect phylogeny, in which at most one mutation event has occurred at any site.We present a simple and efficient polynomial-time algorithm for inferring haplotypes from the genotypes of a set of individuals assuming a perfect phylogeny. Using a reduction to 2-SAT we extend this algorithm to handle constraints that apply when we have genotypes from both parents and child. We also present a hardness result for the problem of removing the minimum number of individuals from a population to ensure that the genotypes of the remaining individuals are consistent with a perfect phylogeny.Our algorithms have been tested on real data and give biologically meaningful results.

show abstract

Section: Resultsmentioning

confidence: 99%

“…This experiment proves that using our algorithm, the study presented in [5] could have been done using the children alone. A more concise experimental work based on our algorithms and some extensions can be found in [11]. …”

Section: Resultsmentioning

confidence: 99%

Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny

Eskin

Halperin

Karp

2003

J. Bioinform. Comput. Biol.

Self Cite

102

106

View full text Add to dashboard Cite

show abstract

“…Instead, the phase is inferred statistically from a large population of SNP data. These phasing algorithms use assumptions such as parsimony in the total number of different haplotypes in the population, the Hardy-Weinberg equilibrium, perfect phylogeny to combinatorially constrain the possible haplotypes [5,9,10,12,14] or alternatively, use statistical approaches [19,21] (available as phase and haplotyper software packages). The statistical algorithms have tended to be bit more accurate, but unforgivingly slow.…”

Section: Introductionmentioning

confidence: 99%

Fast and Cheap Genome Wide Haplotype Construction via Optical Mapping

Anantharaman¹,

Mysore

Mishra

2004

Biocomputing 2005

View full text Add to dashboard Cite

We describe an efficient algorithm to construct genome wide haplotype restriction maps of an individual by aligning single molecule DNA fragments collected with Optical Mapping technology. Using this algorithm and small amount of genomic material, we can construct the parental haplotypes for each diploid chromosome for any individual, one from the father and the other from the mother. Since such haplotype maps reveal the polymorphisms due to single nucleotide differences (SNPs) and small insertions and deletions (RFLPs), they are useful in association studies, studies involving genomic instabilities in cancer, and genetics. For instance, such haplotype restriction maps of individuals in a population can be used in association studies to locate genes responsible for genetics diseases with relatively low cost and high throughput.If the underlying problem is formulated as a combinatorial optimization problem, it can be shown to be NP-complete (a special case of K-population problem). But by effectively exploiting the structure of the underlying error processes and using a novel analog of the Baum-Welch algorithm for HMM models, we devise a probabilistic algorithm with a time complexity that is linear in the number of markers.The algorithms were tested by constructing the first genome wide haplotype restriction map of the microbe T. Pseudoana, as well as constructing a haplotype restriction map of a 120 Megabase region of Human chromosome 4. The frequency of false positives and false negatives was estimated using simulated data. The empirical results were found very promising.

show abstract

HAPLOFREQ – Estimating Haplotype Frequencies Efficiently

Halperin

Hazan

2005

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

A commonly used tool in disease association studies is the search for discrepancies between the haplotype distribution in the case and control populations. In order to find this discrepancy, the haplotypes frequency in each of the populations is estimated from the genotypes.We present a new method HAPLOFREQ to estimate haplotype frequencies over a short genomic region given the genotypes or haplotypes with missing data or sequencing errors. Our approach incorporates a maximum likelihood model based on a simple random generative model which assumes that the genotypes are independently sampled from the population. We first show that if the phased haplotypes are given, possibly with missing data, we can estimate the frequency of the haplotypes in the population by finding the global optimum of the likelihood function in polynomial time. If the haplotypes are not phased, finding the maximum value of the likelihood function is NP-hard. In this case we define an alternative likelihood function which can be thought of as a relaxed likelihood function. We show that the maximum relaxed likelihood can be found in polynomial time, and that the optimal solution of the relaxed likelihood approaches asymptotically to the haplotype frequencies in the population.In contrast to previous approaches, our algorithms are guaranteed to converge in polynomial time to a global maximum of the different likelihood functions. We compared the performance of our algorithm to the widely used program PHASE, and we found that our estimates are at least 10% more accurate than PHASE and about ten times faster than PHASE.Our techniques involve new algorithms in convex optimization. These algorithms may be of independent interest. Particularly, they may be helpful in other maximum likelihood problems arising from survey sampling.

show abstract

Large Scale Recovery of Haplotypes from Genotype Data Using Imperfect Phylogeny

Cited by 4 publications

References 15 publications

Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny

Efficient Reconstruction of Haplotype Structure via Perfect Phylogeny

Fast and Cheap Genome Wide Haplotype Construction via Optical Mapping

HAPLOFREQ – Estimating Haplotype Frequencies Efficiently

Contact Info

Product

Resources

About