Bayesian logistic regression using a perfect phylogeny

Haplotype data capture the genetic variation among individuals in a population and among populations. An understanding of this variation and the ancestral history of haplotypes is important in genetic association studies of complex disease. We introduce a method for detecting associations between disease and haplotypes in a candidate gene region or candidate block with little or no recombination. A perfect phylogeny demonstrates the evolutionary relationship between single-nucleotide polymorphisms (SNPs) in the haplotype blocks. Our approach extends the logic regression technique of Ruczinski and others (2003) to a Bayesian framework, and constrains the model space to that of a perfect phylogeny. Environmental factors, as well as their interactions with SNPs, may be incorporated into the regression framework. We demonstrate our method on simulated data from a coalescent model, as well as data from a candidate gene study of sarcoidosis.     

Detecting selected haplotype blocks in evolve and resequence experiments

Shifting from the analysis of single nucleotide polymorphisms to the reconstruction of selected haplotypes greatly facilitates the interpretation of evolve and resequence (E&R) experiments. Merging highly correlated hitchhiker SNPs into haplotype blocks reduces thousands of candidates to few selected regions. Current methods of haplotype reconstruction from Pool‐seq data need a variety of data‐specific parameters that are typically defined ad hoc and require haplotype sequences for validation. Here, we introduce haplovalidate, a tool which detects selected haplotypes in Pool‐seq time series data without the need for sequenced haplotypes. Haplovalidate makes data‐driven choices of two key parameters for the clustering procedure, the minimum correlation between SNPs constituting a cluster and the window size. Applying haplovalidate to simulated E&R data reliably detects selected haplotype blocks with low false discovery rates. Importantly, our analyses identified a restriction of the haplotype block‐based approach to describe the genomic architecture of adaptation. We detected a substantial fraction of haplotypes containing multiple selection targets. These blocks were considered as one region of selection and therefore led to underestimation of the number of selection targets. We demonstrate that the separate analysis of earlier time points can significantly increase the separation of selection targets into individual haplotype blocks. We conclude that the analysis of selected haplotype blocks has great potential for the characterization of the adaptive architecture with E&R experiments.     

Linkage disequilibrium grouping of single nucleotide polymorphisms (SNPs) reflecting haplotype phylogeny for efficient selection of tag SNPs

Single nucleotide polymorphisms (SNPs) have been proposed to be grouped into haplotype blocks harboring a limited number of haplotypes. Within each block, the portion of haplotypes is expected to be tagged by a selected subset of SNPs; however, none of the proposed selection algorithms have been definitive. To address this issue, we developed a tag SNP selection algorithm based on grouping of SNPs by the linkage disequilibrium (LD) coefficient r(2) and examined five genes in three ethnic populations--the Japanese, African Americans, and Caucasians. Additionally, we investigated ethnic diversity by characterizing 979 SNPs distributed throughout the genome. Our algorithm could spare 60% of SNPs required for genotyping and limit the imprecision in allele-frequency estimation of nontag SNPs to 2% on average. We discovered the presence of a mosaic pattern of LD plots within a conventionally inferred haplotype block. This emerged because multiple groups of SNPs with strong intragroup LD were mingled in their physical positions. The pattern of LD plots showed some similarity, but the details of tag SNPs were not entirely concordant among three populations. Consequently, our algorithm utilizing LD grouping allows selection of a more faithful set of tag SNPs than do previous algorithms utilizing haplotype blocks.     

Inference of missing SNPs and information quantity measurements for haplotype blocks

MOTIVATION: Missing data in genotyping single nucleotide polymorphism (SNP) spots are common. High-throughput genotyping methods usually have a high rate of missing data. For example, the published human chromosome 21 data by Patil et al. contains about 20% missing SNPs. Inferring missing SNPs using the haplotype block structure is promising but difficult because the haplotype block boundaries are not well defined. Here we propose a global algorithm to overcome this difficulty. RESULTS: First, we propose to use entropy as a measure of haplotype diversity. We show that the entropy measure combined with a dynamic programming algorithm produces better haplotype block partitions than other measures. Second, based on the entropy measure, we propose a two-step iterative partition-inference algorithm for the inference of missing SNPs. At the first step, we apply the dynamic programming algorithm to partition haplotypes into blocks. At the second step, we use an iterative process similar to the expectation-maximization algorithm to infer missing SNPs in each haplotype block so as to minimize the block entropy. The algorithm iterates these two steps until the total block entropy is minimized. We test our algorithm in several experimental data sets. The results show that the global approach significantly improves the accuracy of the inference. AVAILABILITY: Upon request.     

Model-based inference of haplotype block variation.

The haplotype block structure of SNP variation in human DNA has been demonstrated by several recent studies. The presence of haplotype blocks can be used to dramatically increase the statistical power of genetic mapping. Several criteria have already been proposed for identifying these blocks, all of which require haplotypes as input. We propose a comprehensive statistical model of haplotype block variation and show how the parameters of this model can be learned from haplotypes and/or unphased genotype data. Using real-world SNP data, we demonstrate that our approach can be used to resolve genotypes into their constituent haplotypes with greater accuracy than previously known methods.     

The effect of single-nucleotide polymorphism marker selection on patterns of haplotype blocks and haplotype frequency estimates

The definition of haplotype blocks of single-nucleotide polymorphisms (SNPs) has been proposed so that the haplotypes can be used as markers in association studies and to efficiently describe human genetic variation. The International Haplotype Map (HapMap) project to construct a comprehensive catalog of haplotypic variation in humans is underway. However, a number of factors have already been shown to influence the definition of blocks, including the population studied and the sample SNP density. Here, we examine the effect that marker selection has on the definition of blocks and the pattern of haplotypes by using comparable but complementary SNP sets and a number of block definition methods in various genomic regions and populations that were provided by the Encyclopedia of DNA Elements (ENCODE) project. We find that the chosen SNP set has a profound effect on the block-covered sequence and block borders, even at high marker densities. Our results question the very concept of discrete haplotype blocks and the possibility of generalizing block findings from the HapMap project. We comparatively apply the block-free tagging-SNP approach and discuss both the haplotype approach and the tagging-SNP approach as means to efficiently catalog genetic variation.     

Bayesian association of haplotypes and non-genetic factors to regulatory and phenotypic variation in human populations

MOTIVATION: With the recent availability of large-scale data sets profiling single nucleotide polymorphisms (SNPs) and quantitative traits data across different human subpopulations, there has been much attention directed towards discovering patterns of genetic variation and their connection to gene regulation and the onset/progression of disease. While previous work has focused primarily on correlating individual SNP markers with gene expression and disease, it has been suggested that using haplotype blocks instead of individual markers can significantly increase statistical power. RESULTS: We present BlockMapper, a probabilistic generative model for genotype data and quantitative traits data, such as gene expression or phenotype measurements. BlockMapper discovers the block structure of genotype data and associates these inferred blocks to patterns of variation in quantitative traits data, whilst accounting for non-genetic factors. Our model achieves high accuracy for predicting Crohn's disease phenotype in Chromosome 5q31 and reveals novel cis-associations between two haplotype blocks in the ENm006 genomic region and GDI1, a gene implicated in X-linked mental retardation. Our results underscore the importance of accounting for the influence of large sets of SNPs on patterns of regulatory/phenotypic variation and represent a step towards an understanding of human genetic variation.     

The variable number of tandem repeats element in DAT1 regulates in vitro dopamine transporter density

Background

The selection of markers in association studies can be informed through the use of haplotype blocks. Recent reports have determined the genomic architecture of chromosomal segments through different haplotype block definitions based on linkage disequilibrium (LD) measures or haplotype diversity criteria. The relative applicability of distinct block definitions to association studies, however, remains unclear. We compared different block definitions in 6.1 Mb of chromosome 17q in 189 unrelated healthy individuals. Using 137 single nucleotide polymorphisms (SNPs), at a median spacing of 15.5 kb, we constructed haplotype block maps using published methods and additional methods we have developed. Haplotype tagging SNPs (htSNPs) were identified for each map.

Results

Blocks were found to be shorter and coverage of the region limited with methods based on LD measures, compared to the method based on haplotype diversity. Although the distribution of blocks was highly variable, the number of SNPs that needed to be typed in order to capture the maximum number of haplotypes was consistent.

Conclusion

For the marker spacing used in this study, choice of block definition is not important when used as an initial screen of the region to identify htSNPs. However, choice of block definition has consequences for the downstream interpretation of association study results.     

Haplotype block structure and its applications to association studies: power and study designs

Recent studies have shown that the human genome has a haplotype block structure, such that it can be divided into discrete blocks of limited haplotype diversity. In each block, a small fraction of single-nucleotide polymorphisms (SNPs), referred to as "tag SNPs," can be used to distinguish a large fraction of the haplotypes. These tag SNPs can potentially be extremely useful for association studies, in that it may not be necessary to genotype all SNPs; however, this depends on how much power is lost. Here we develop a simulation study to quantitatively assess the power loss for a variety of study designs, including case-control designs and case-parental control designs. First, a number of data sets containing case-parental or case-control samples are generated on the basis of a disease model. Second, a small fraction of case and control individuals in each data set are genotyped at all the loci, and a dynamic programming algorithm is used to determine the haplotype blocks and the tag SNPs based on the genotypes of the sampled individuals. Third, the statistical power of tests was evaluated on the basis of three kinds of data: (1) all of the SNPs and the corresponding haplotypes, (2) the tag SNPs and the corresponding haplotypes, and (3) the same number of randomly chosen SNPs as the number of tag SNPs and the corresponding haplotypes. We study the power of different association tests with a variety of disease models and block-partitioning criteria. Our study indicates that the genotyping efforts can be significantly reduced by the tag SNPs, without much loss of power. Depending on the specific haplotype block-partitioning algorithm and the disease model, when the identified tag SNPs are only 25% of all the SNPs, the power is reduced by only 4%, on average, compared with a power loss of approximately 12% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. When the identified tag SNPs are approximately 14% of all the SNPs, the power is reduced by approximately 9%, compared with a power loss of approximately 21% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. Our study also indicates that haplotype-based analysis can be much more powerful than marker-by-marker analysis.     

Large-scale single-nucleotide polymorphism (SNP) and haplotype analyses, using dense SNP Maps, of 199 drug-related genes in 752 subjects: the analysis of the association between uncommon SNPs within haplotype blocks and the haplotypes constructed with haplotype-tagging SNPs

To optimize the strategies for population-based pharmacogenetic studies, we extensively analyzed single-nucleotide polymorphisms (SNPs) and haplotypes in 199 drug-related genes, through use of 4,190 SNPs in 752 control subjects. Drug-related genes, like other genes, have a haplotype-block structure, and a few haplotype-tagging SNPs (htSNPs) could represent most of the major haplotypes constructed with common SNPs in a block. Because our data included 860 uncommon (frequency <0.1) SNPs with frequencies that were accurately estimated, we analyzed the relationship between haplotypes and uncommon SNPs within the blocks (549 SNPs). We inferred haplotype frequencies through use of the data from all htSNPs and one of the uncommon SNPs within a block and calculated four joint probabilities for the haplotypes. We show that, irrespective of the minor-allele frequency of an uncommon SNP, the majority (mean +/- SD frequency 0.943+/-0.117) of the minor alleles were assigned to a single haplotype tagged by htSNPs if the uncommon SNP was within the block. These results support the hypothesis that recombinations occur only infrequently within blocks. The proportion of a single haplotype tagged by htSNPs to which the minor alleles of an uncommon SNP were assigned was positively correlated with the minor-allele frequency when the frequency was <0.03 (P<.000001; n=233 [Spearman's rank correlation coefficient]). The results of simulation studies suggested that haplotype analysis using htSNPs may be useful in the detection of uncommon SNPs associated with phenotypes if the frequencies of the SNPs are higher in affected than in control populations, the SNPs are within the blocks, and the frequencies of the SNPs are >0.03.     

Efficient reconstruction of haplotype structure via perfect phylogeny

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, and no recombination occurred at the given region. 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. Our webserver (http://www.cs.columbia.edu/compbio/hap/) is publicly available for predicting haplotypes from genotype data and partitioning genotype data into blocks.     

Distribution of recombination crossovers and the origin of haplotype blocks: the interplay of population history,recombination, and mutation

Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure.     

Haplotype diversity across 100 candidate genes for inflammation, lipid metabolism, and blood pressure regulation in two populations

Recent studies have suggested that a significant fraction of the human genome is contained in blocks of strong linkage disequilibrium, ranging from ~5 to >100 kb in length, and that within these blocks a few common haplotypes may account for >90% of the observed haplotypes. Furthermore, previous studies have suggested that common haplotypes in candidate genes are generally shared across populations and represent the majority of chromosomes in each population. The conclusions drawn from these preliminary studies, however, are based on an incomplete knowledge of the variation in the regions examined. To bridge this gap in knowledge, we have completely resequenced 100 candidate genes in a population of African descent and one of European descent. Although these genes have been well studied because of their medical importance, we demonstrate that a large amount of sequence variation has not yet been described. We also report that the average number of inferred haplotypes per gene, when complete data is used, is higher than in previous reports and that the number and proportion of all haplotypes represented by common haplotypes per gene is variable. Furthermore, we demonstrate that haplotypes shared between the two populations constitute only a fraction of the total number of haplotypes observed and that these shared haplotypes represent fewer of the African-descent chromosomes than was expected from previous studies. Finally, we show that restricting variation discovery to coding regions does not adequately describe all common haplotypes or the true haplotype block structure observed when all common variation is used to infer haplotypes. These data, derived from complete knowledge of genetic variation in these genes, suggest that the haplotype architecture of candidate genes across the human genome is more complex than previously suggested, with important implications for candidate gene and genomewide association studies.     

Performance of single nucleotide polymorphisms versus haplotypes for genome-wide association analysis in barley

Genome-wide association studies (GWAS) may benefit from utilizing haplotype information for making marker-phenotype associations. Several rationales for grouping single nucleotide polymorphisms (SNPs) into haplotype blocks exist, but any advantage may depend on such factors as genetic architecture of traits, patterns of linkage disequilibrium in the study population, and marker density. The objective of this study was to explore the utility of haplotypes for GWAS in barley (Hordeum vulgare) to offer a first detailed look at this approach for identifying agronomically important genes in crops. To accomplish this, we used genotype and phenotype data from the Barley Coordinated Agricultural Project and constructed haplotypes using three different methods. Marker-trait associations were tested by the efficient mixed-model association algorithm (EMMA). When QTL were simulated using single SNPs dropped from the marker dataset, a simple sliding window performed as well or better than single SNPs or the more sophisticated methods of blocking SNPs into haplotypes. Moreover, the haplotype analyses performed better 1) when QTL were simulated as polymorphisms that arose subsequent to marker variants, and 2) in analysis of empirical heading date data. These results demonstrate that the information content of haplotypes is dependent on the particular mutational and recombinational history of the QTL and nearby markers. Analysis of the empirical data also confirmed our intuition that the distribution of QTL alleles in nature is often unlike the distribution of marker variants, and hence utilizing haplotype information could capture associations that would elude single SNPs. We recommend routine use of both single SNP and haplotype markers for GWAS to take advantage of the full information content of the genotype data.     

Single nucleotide polymorphism haplotypes in the cholesteryl-ester transfer protein (CETP) gene and lipid phenotypes

We studied the association between high (HDL) and low-density (LDL) cholesterol concentrations and family-derived haplotypes based on six common SNPs in the cholesteryl-ester transfer protein (CETP) gene. We based our analysis on 201 founders from families recruited throughout Germany. The analysis revealed one subhaplotype block with complete, pairwise, linkage disequilibrium between 5 SNPs located in the promoter and intron 1. The sixth SNP was the well known 1405V polymorphism in exon 14, close to the 3' end of the gene. Four haplotypes accounted for 86% of the entire sample. We found that haplotype associations with HDL, LDL, and the LDL/HDL ratio were more robust than associations with individual SNPs. Moreover, the associations were robust for men, but not for women. Our data suggest an interaction between gender and genetic variation within the CETP gene.     

Evolutionary signatures of common human cis-regulatory haplotypes

Variation in gene expression may give rise to a significant fraction of inter-individual phenotypic variation. Studies searching for the underlying genetic controls for such variation have been conducted in model organisms and humans in recent years. In our previous effort of assessing conserved underlying haplotype patterns across ethnic populations, we constructed common haplotypes using SNPs having conserved linkage disequilibrium (LD) across ethnic populations. These common haplotypes cluster into a simple evolutionary structure based on their frequencies, defining only up to three conserved clusters termed 'haplotype frameworks'. One intriguing preliminary finding was that a significant portion of reported variants strongly associated with cis-regulation tags these globally conserved haplotype frameworks. Here we expand the investigation by collecting genes showing stringently determined cis-association between genotypes and expression phenotypes from major studies. We conducted phylogenetic analysis of current major haplotypes along with the corresponding haplotypes derived from chimpanzee reference sequences. Our analysis reveals that, for the vast majority of such cis-regulatory genes, the tagging SNPs showing the strongest association also tag the haplotype lineages directly separated from ancestry, inferred from either chimpanzee reference sequences or the allele frequency-derived haplotype frameworks, suggesting that the differentially expressed phenotypes were evolved relatively early in human history. Such evolutionary signatures provide keys for a more effective identification of globally-conserved candidate regulatory haplotypes across human genes in future epidemiologic and pharmacogenetic studies.     

A double classification tree search algorithm for index SNP selection

Background  

In population-based studies, it is generally recognized that single nucleotide polymorphism (SNP) markers are not independent. Rather, they are carried by haplotypes, groups of SNPs that tend to be coinherited. It is thus possible to choose a much smaller number of SNPs to use as indices for identifying haplotypes or haplotype blocks in genetic association studies. We refer to these characteristic SNPs as index SNPs. In order to reduce costs and work, a minimum number of index SNPs that can distinguish all SNP and haplotype patterns should be chosen. Unfortunately, this is an NP-complete problem, requiring brute force algorithms that are not feasible for large data sets.     

Finding associations in dense genetic maps: a genetic algorithm approach

Large-scale association studies hold promise for discovering the genetic basis of common human disease. These studies will consist of a large number of individuals, as well as large number of genetic markers, such as single nucleotide polymorphisms (SNPs). The potential size of the data and the resulting model space require the development of efficient methodology to unravel associations between phenotypes and SNPs in dense genetic maps. Our approach uses a genetic algorithm (GA) to construct logic trees consisting of Boolean expressions involving strings or blocks of SNPs. These blocks or nodes of the logic trees consist of SNPs in high linkage disequilibrium (LD), that is, SNPs that are highly correlated with each other due to evolutionary processes. At each generation of our GA, a population of logic tree models is modified using selection, cross-over and mutation moves. Logic trees are selected for the next generation using a fitness function based on the marginal likelihood in a Bayesian regression frame-work. Mutation and cross-over moves use LD measures to pro pose changes to the trees, and facilitate the movement through the model space. We demonstrate our method and the flexibility of logic tree structure with variable nodal lengths on simulated data from a coalescent model, as well as data from a candidate gene study of quantitative genetic variation.