Genetic association mapping via evolution-based clustering of haplotypes

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.     

Haplotype sharing analysis using mantel statistics

OBJECTIVE: The potential value of haplotypes has attracted widespread interest in the mapping of complex traits. Haplotype sharing methods take the linkage disequilibrium information between multiple markers into account, and may have good power to detect predisposing genes. We present a new approach based on Mantel statistics for spacetime clustering, which is developed in order to improve the power of haplotype sharing analysis for gene mapping in complex disease. METHODS: The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes for case-only and case-control studies. The genetic similarity is measured as the shared length between haplotypes around a putative disease locus. The phenotypic similarity is measured as the mean-corrected cross-product based on the respective phenotypes. We analyzed two tests for statistical significance with respect to type I error: (1) assuming asymptotic normality, and (2) using a Monte Carlo permutation procedure. The results were compared to the chi(2) test for association based on 3-marker haplotypes. RESULTS: The results of the type I error rates for the Mantel statistics using the permutational procedure yielded pointwise valid tests. The approach based on the assumption of asymptotic normality was seriously liberal. CONCLUSION: Power comparisons showed that the Mantel statistics were better than or equal to the chi(2) test for all simulated disease models.     

Bayesian spatial modeling of haplotype associations

We review methods for relating the risk of disease to a collection of single nucleotide polymorphisms (SNPs) within a small region. Association studies using case-control designs with unrelated individuals could be used either to test for a direct effect of a candidate gene and characterize the responsible variant(s), or to fine map an unknown gene by exploiting the pattern of linkage disequilibrium (LD). We consider a flexible class of logistic penetrance models based on haplotypes and compare them with an alternative formulation based on unphased multilocus genotypes. The likelihood for haplotype-based models requires summation over all possible haplotype assignments consistent with the observed genotype data, and can be fitted using either Expectation-Maximization (E-M) or Markov chain Monte Carlo (MCMC) methods. Subtleties involving ascertainment correction for case-control studies are discussed. There has been great interest in methods for LD mapping based on the coalescent or ancestral recombination graphs as well as methods based on haplotype sharing, both of which we review briefly. Because of their computational complexity, we propose some alternative empirical modeling approaches using techniques borrowed from the Bayesian spatial statistics literature. Here, space is interpreted in terms of a distance metric describing the similarity of any pair of haplotypes to each other, and hence their presumed common ancestry. Specifically, we discuss the conditional autoregressive model and two spatial clustering models: Potts and Voronoi. We conclude with a discussion of the implications of these methods for modeling cryptic relatedness, haplotype blocks, and haplotype tagging SNPs, and suggest a Bayesian framework for the HapMap project.     

Haplotype-sharing analysis using Mantel statistics for combined genetic effects

We applied a new approach based on Mantel statistics to analyze the Genetic Analysis Workshop 14 simulated data with prior knowledge of the answers. The method was developed in order to improve the power of a haplotype sharing analysis for gene mapping in complex disease. The new statistic correlates genetic similarity and phenotypic similarity across pairs of haplotypes from case-control studies. The genetic similarity is measured as the shared length between haplotype pairs around a genetic marker. The phenotypic similarity is measured as the mean corrected cross-product based on the respective phenotypes. Cases with phenotype P1 and unrelated controls were drawn from the population of Danacaa. Power to detect main effects was compared to the X2-test for association based on 3-marker haplotypes and a global permutation test for haplotype association to test for main effects. Power to detect gene x gene interaction was compared to unconditional logistic regression. The results suggest that the Mantel statistics might be more powerful than alternative tests.     

Multipoint linkage-disequilibrium mapping with haplotype-block structure

The HapMap Project is providing a great deal of new information on high-resolution haplotype structure in various human populations. This information has the potential to greatly increase the power of association mapping for a fixed amount of genotyping. A number of methods have been proposed for the identification of haplotype blocks, common haplotypes, and tagging single-nucleotide polymorphisms. Here, we build on this work by developing novel methods for case-control multipoint linkage-disequilibrium (LD) mapping that gain power and speed by making explicit use of the inferred block structure. Specifically, we developed a virtual-variant approach that uses the haplotype-block information to greatly increase power for detection of untyped common variants associated with a trait. Because full multipoint LD mapping can be slow, we exploited the haplotype-block information to develop a fast single-block multipoint mapping method. Our methods are appropriate for genotype data and take into account the uncertainty in phase. We describe the methods in the context of case-parents trios, although they are also applicable to unrelated cases and controls. Our simulations indicate that the most important gains from taking into account the haplotype-block structure at the analysis stage of multipoint LD mapping come from (1) greatly increased power to detect association with untyped variants and (2) greatly improved localization of untyped variants associated with the trait. More-modest gains are obtained in improving power to detect association with a variant that is typed with a moderate amount of missing data. The methods are applied to a Crohn disease data set.     

Inheritance mode of multiple sclerosis: the effect of <Emphasis Type="Italic">HLA</Emphasis> class II alleles is stronger than additive

We previously identified on chromosome 6 an interval of 51 kb as the most likely interval in the HLA region for a disease-susceptibility locus for multiple sclerosis (MS). The interval was located between markers G511525 and D6S1666 and identified by the haplotype sharing statistic (HSS). The study comprised 124 patients with ancestry within the northeastern part of the Netherlands. Haplotype clustering indicated that two different ancestral haplotypes likely include a polymorphism involved in susceptibility to MS. To investigate the dominance characteristics of the MS susceptibility locus in the HLA class II region, we reanalyzed our data, performing genotype association analyses for both marker loci separately and for the two-locus haplotype. The two-locus genotype association analysis showed that in individuals who carry only one of the risk haplotypes the risk for MS is moderately increased (odds ratio (OR) 2.82; 95% confidence interval (CI) 1.50–5.31). However, in individuals carrying two risk haplotypes the risk for MS is highly increased compared with individuals who carry no risk haplotypes (OR 37.00; 95% CI 8.31–164.74). This susceptibility locus for MS seems to follow an intermediate mode of inheritance. Fitting additive, multiplicative and third power risk models to the data, the effect appears to be significantly stronger than additive.     

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.     

Little loss of information due to unknown phase for fine-scale linkage-disequilibrium mapping with single-nucleotide-polymorphism genotype data

We present the results of a simulation study that indicate that true haplotypes at multiple, tightly linked loci often provide little extra information for linkage-disequilibrium fine mapping, compared with the information provided by corresponding genotypes, provided that an appropriate statistical analysis method is used. In contrast, a two-stage approach to analyzing genotype data, in which haplotypes are inferred and then analyzed as if they were true haplotypes, can lead to a substantial loss of information. The study uses our COLDMAP software for fine mapping, which implements a Markov chain-Monte Carlo algorithm that is based on the shattered coalescent model of genetic heterogeneity at a disease locus. We applied COLDMAP to 100 replicate data sets simulated under each of 18 disease models. Each data set consists of haplotype pairs (diplotypes) for 20 SNPs typed at equal 50-kb intervals in a 950-kb candidate region that includes a single disease locus located at random. The data sets were analyzed in three formats: (1). as true haplotypes; (2). as haplotypes inferred from genotypes using an expectation-maximization algorithm; and (3). as unphased genotypes. On average, true haplotypes gave a 6% gain in efficiency compared with the unphased genotypes, whereas inferring haplotypes from genotypes led to a 20% loss of efficiency, where efficiency is defined in terms of root mean integrated square error of the location of the disease locus. Furthermore, treating inferred haplotypes as if they were true haplotypes leads to considerable overconfidence in estimates, with nominal 50% credibility intervals achieving, on average, only 19% coverage. We conclude that (1). given appropriate statistical analyses, the costs of directly measuring haplotypes will rarely be justified by a gain in the efficiency of fine mapping and that (2). a two-stage approach of inferring haplotypes followed by a haplotype-based analysis can be very inefficient for fine mapping, compared with an analysis based directly on the genotypes.     

A haplotype-based test of association using data from cohort and nested case-control epidemiologic studies

Haplotype-based risk models can lead to powerful methods for detecting the association of a disease with a genomic region of interest. In population-based studies of unrelated individuals, however, the haplotype status of some subjects may not be discernible without ambiguity from available locus-specific genotype data. A score test for detecting haplotype-based association using genotype data has been developed in the context of generalized linear models for analysis of data from cross-sectional and retrospective studies. In this article, we develop a test for association using genotype data from cohort and nested case-control studies where subjects are prospectively followed until disease incidence or censoring (end of follow-up) occurs. Assuming a proportional hazard model for the haplotype effects, we derive an induced hazard function of the disease given the genotype data, and hence propose a test statistic based on the associated partial likelihood. The proposed test procedure can account for differential follow-up of subjects, can adjust for possibly time-dependent environmental co-factors and can make efficient use of valuable age-at-onset information that is available on cases. We provide an algorithm for computing the test statistic using readily available statistical software. Utilizing simulated data in the context of two genomic regions GPX1 and GPX3, we evaluate the validity of the proposed test for small sample sizes and study its power in the presence and absence of missing genotype data.     

Testing association of statistically inferred haplotypes with discrete and continuous traits in samples of unrelated individuals

There have been increasing efforts to relate drug efficacy and disease predisposition with genetic polymorphisms. We present statistical tests for association of haplotype frequencies with discrete and continuous traits in samples of unrelated individuals. Haplotype frequencies are estimated through the expectation-maximization algorithm, and each individual in the sample is expanded into all possible haplotype configurations with corresponding probabilities, conditional on their genotype. A regression-based approach is then used to relate inferred haplotype probabilities to the response. The relationship of this technique to commonly used approaches developed for case-control data is discussed. We confirm the proper size of the test under H(0) and find an increase in power under the alternative by comparing test results using inferred haplotypes with single-marker tests using simulated data. More importantly, analysis of real data comprised of a dense map of single nucleotide polymorphisms spaced along a 12-cM chromosomal region allows us to confirm the utility of the haplotype approach as well as the validity and usefulness of the proposed statistical technique. The method appears to be successful in relating data from multiple, correlated markers to response.     

Inference on haplotype effects in case-control studies using unphased genotype data

A variety of statistical methods exist for detecting haplotype-disease association through use of genetic data from a case-control study. Since such data often consist of unphased genotypes (resulting in haplotype ambiguity), such statistical methods typically apply the expectation-maximization (EM) algorithm for inference. However, the majority of these methods fail to perform inference on the effect of particular haplotypes or haplotype features on disease risk. Since such inference is valuable, we develop a retrospective likelihood for estimating and testing the effects of specific features of single-nucleotide polymorphism (SNP)-based haplotypes on disease risk using unphased genotype data from a case-control study. Our proposed method has a flexible structure that allows, among other choices, modeling of multiplicative, dominant, and recessive effects of specific haplotype features on disease risk. In addition, our method relaxes the requirement of Hardy-Weinberg equilibrium of haplotype frequencies in case subjects, which is typically required of EM-based haplotype methods. Also, our method easily accommodates missing SNP information. Finally, our method allows for asymptotic, permutation-based, or bootstrap inference. We apply our method to case-control SNP genotype data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus (FUSION) Genetics study and identify two haplotypes that appear to be significantly associated with type 2 diabetes. Using the FUSION data, we assess the accuracy of asymptotic P values by comparing them with P values obtained from a permutation procedure. We also assess the accuracy of asymptotic confidence intervals for relative-risk parameters for haplotype effects, by a simulation study based on the FUSION data.     

A block-free hidden Markov model for genotypes and its application to disease association.

We present a new stochastic model for genotype generation. The model offers a compromise between rigid block structure and no structure altogether: It reflects a general blocky structure of haplotypes, but also allows for "exchange" of haplotypes at nonboundary SNP sites; it also accommodates rare haplotypes and mutations. We use a hidden Markov model and infer its parameters by an expectation-maximization algorithm. The algorithm was implemented in a software package called HINT (haplotype inference tool) and tested on 58 datasets of genotypes. To evaluate the utility of the model in association studies, we used biological human data to create a simple disease association search scenario. When comparing HINT to three other models, HINT predicted association most accurately.     

Accuracy of haplotype reconstruction from haplotype-tagging single-nucleotide polymorphisms

Many investigators are now using haplotype-tagging single-nucleotide polymorphism (htSNPs) as a way of screening regions of the genome for association with disease. A common approach is to genotype htSNPs in a study population and to use this information to draw inferences about each individual's haplotypic makeup, including SNPs that were not directly genotyped. To test the validity of this approach, we simulated the exercise of typing htSNPs in a large sample of individuals and compared the true and inferred haplotypes. The accuracy of haplotype inference varied, depending on the method of selecting htSNPs, the linkage-disequilibrium structure of the region, and the amount of missing data. At the stage of selection of htSNPs, haplotype-block-based methods required a larger number of htSNPs than did unstructured methods but gave lower levels of error in haplotype inference, particularly when there was a significant amount of missing data. We present a Web-based utility that allows investigators to compare the likely error rates of different sets of htSNPs and to arrive at an economical set of htSNPs that provides acceptable levels of accuracy in haplotype inference.     

Haplotype association analysis of human disease traits using genotype data of unrelated individuals

Haplotype inference has become an important part of human genetic data analysis due to its functional and statistical advantages over the single-locus approach in linkage disequilibrium mapping. Different statistical methods have been proposed for detecting haplotype - disease associations using unphased multi-locus genotype data, ranging from the early approach by the simple gene-counting method to the recent work using the generalized linear model. However, these methods are either confined to case - control design or unable to yield unbiased point and interval estimates of haplotype effects. Based on the popular logistic regression model, we present a new approach for haplotype association analysis of human disease traits. Using haplotype-based parameterization, our model infers the effects of specific haplotypes (point estimation) and constructs confidence interval for the risks of haplotypes (interval estimation). Based on the estimated parameters, the model calculates haplotype frequency conditional on the trait value for both discrete and continuous traits. Moreover, our model provides an overall significance level for the association between the disease trait and a group or all of the haplotypes. Featured by the direct maximization in haplotype estimation, our method also facilitates a computer simulation approach for correcting the significance level of individual haplotype to adjust for multiple testing. We show, by applying the model to an empirical data set, that our method based on the well-known logistic regression model is a useful tool for haplotype association analysis of human disease traits.     

Impact of missing genotype data on Monte-Carlo simulation based haplotype analysis

In the context of haplotype association analysis of unphased genotype data, methods based on Monte-Carlo simulations are often used to compensate for missing or inappropriate asymptotic theory. Moreover, such methods are an indispensable means to deal with multiple testing problems. We want to call attention to a potential trap in this usually useful approach: The simulation approach may lead to strongly inflated type I errors in the presence of different missing rates between cases and controls, depending on the chosen test statistic. Here, we consider four different testing strategies for haplotype analysis of case-control data. We recommend to interpret results for data sets with non-comparable distributions of missing genotypes with special caution, in case the test statistic is based on inferred haplotypes per individual. Moreover, our results are important for the conduction and interpretation of genome-wide association studies.     

Haplotype-based association analysis via variance-components score test

Haplotypes provide a more informative format of polymorphisms for genetic association analysis than do individual single-nucleotide polymorphisms. However, the practical efficacy of haplotype-based association analysis is challenged by a trade-off between the benefits of modeling abundant variation and the cost of the extra degrees of freedom. To reduce the degrees of freedom, several strategies have been considered in the literature. They include (1) clustering evolutionarily close haplotypes, (2) modeling the level of haplotype sharing, and (3) smoothing haplotype effects by introducing a correlation structure for haplotype effects and studying the variance components (VC) for association. Although the first two strategies enjoy a fair extent of power gain, empirical evidence showed that VC methods may exhibit only similar or less power than the standard haplotype regression method, even in cases of many haplotypes. In this study, we report possible reasons that cause the underpowered phenomenon and show how the power of the VC strategy can be improved. We construct a score test based on the restricted maximum likelihood or the marginal likelihood function of the VC and identify its nontypical limiting distribution. Through simulation, we demonstrate the validity of the test and investigate the power performance of the VC approach and that of the standard haplotype regression approach. With suitable choices for the correlation structure, the proposed method can be directly applied to unphased genotypic data. Our method is applicable to a wide-ranging class of models and is computationally efficient and easy to implement. The broad coverage and the fast and easy implementation of this method make the VC strategy an effective tool for haplotype analysis, even in modern genomewide association studies.     

Haplotype-based association analysis in cohort and nested case-control studies

Genetic epidemiologic studies often collect genotype data at multiple loci within a genomic region of interest from a sample of unrelated individuals. One popular method for analyzing such data is to assess whether haplotypes, i.e., the arrangements of alleles along individual chromosomes, are associated with the disease phenotype or not. For many study subjects, however, the exact haplotype configuration on the pair of homologous chromosomes cannot be derived with certainty from the available locus-specific genotype data (phase ambiguity). In this article, we consider estimating haplotype-specific association parameters in the Cox proportional hazards model, using genotype, environmental exposure, and the disease endpoint data collected from cohort or nested case-control studies. We study alternative Expectation-Maximization algorithms for estimating haplotype frequencies from cohort and nested case-control studies. Based on a hazard function of the disease derived from the observed genotype data, we then propose a semiparametric method for joint estimation of relative-risk parameters and the cumulative baseline hazard function. The method is greatly simplified under a rare disease assumption, for which an asymptotic variance estimator is also proposed. The performance of the proposed estimators is assessed via simulation studies. An application of the proposed method is presented, using data from the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study.     

Linked vs unlinked markers: multilocus microsatellite haplotype-sharing as a tool to estimate gene flow and introgression

We have explored the use of multilocus microsatellite haplotypes to study introgression from cultivated (Malus domestica) into wild apple (Malus sylvestris), and to study gene flow among remnant populations of M. sylvestris. A haplotype consisted of alleles at microsatellite loci along one chromosome. As destruction of haplotypes through recombination occurs much faster than loss of alleles due to genetic drift, the lifespan of a multilocus haplotype is much shorter than that of the underlying alleles. When different populations share the same haplotype, this may indicate recent gene flow between populations. Similarly, haplotypes shared between two species would be a strong signal for introgression. As the expected lifespan of a haplotype depends on the strength of the linkage, the length [in centiMorgans (cM)] of the haplotype shared contains information on the number of generations passed. This application of shared haplotypes is distinct from using haplotype-sharing to detect association between markers and a certain trait. We inferred haplotypes for four to eight microsatellite loci on Linkage Group 10 of apple from genotype data using the program phase, and then identified those haplotypes shared between populations and species. Compared with a Bayesian analysis of unlinked microsatellite loci using the program structure, haplotype-sharing detected a partially different set of putative hybrids. Cultivated haplotypes present in M. sylvestris were short (< 1.5 cM), indicating that introgression had taken place many generations ago, except for two Belgian plants that contained a haplotype of 47.1 cM, indicating recent introgression. In the estimation of gene flow, F(ST) based on unlinked loci indicated small (0.032-0.058) but statistically significant differentiation between some populations only. However, various M. sylvestris haplotypes were shared in nearly all pairwise comparisons of populations, and their length indicated recent gene flow. Hence, all Dutch populations should be considered as one conservation unit. The added value of using sharing of multilocus microsatellite haplotypes as a source of population genetic information is discussed.     

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.