Association mapping via regularized regression analysis of single-nucleotide-polymorphism haplotypes in variable-sized sliding windows

Large-scale haplotype association analysis, especially at the whole-genome level, is still a very challenging task without an optimal solution. In this study, we propose a new approach for haplotype association analysis that is based on a variable-sized sliding-window framework and employs regularized regression analysis to tackle the problem of multiple degrees of freedom in the haplotype test. Our method can handle a large number of haplotypes in association analyses more efficiently and effectively than do currently available approaches. We implement a procedure in which the maximum size of a sliding window is determined by local haplotype diversity and sample size, an attractive feature for large-scale haplotype analyses, such as a whole-genome scan, in which linkage disequilibrium patterns are expected to vary widely. We compare the performance of our method with that of three other methods--a test based on a single-nucleotide polymorphism, a cladistic analysis of haplotypes, and variable-length Markov chains--with use of both simulated and experimental data. By analyzing data sets simulated under different disease models, we demonstrate that our method consistently outperforms the other three methods, especially when the region under study has high haplotype diversity. Built on the regression analysis framework, our method can incorporate other risk-factor information into haplotype-based association analysis, which is becoming an increasingly necessary step for studying common disorders to which both genetic and environmental risk factors contribute.     

Powerful Haplotype-Based Hardy-Weinberg Equilibrium Tests for Tightly Linked Loci

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.     

Linkage disequilibrium mapping via cladistic analysis of single-nucleotide polymorphism haplotypes

We present a novel approach to disease-gene mapping via cladistic analysis of single-nucleotide polymorphism (SNP) haplotypes obtained from large-scale, population-based association studies, applicable to whole-genome screens, candidate-gene studies, or fine-scale mapping. Clades of haplotypes are tested for association with disease, exploiting the expected similarity of chromosomes with recent shared ancestry in the region flanking the disease gene. The method is developed in a logistic-regression framework and can easily incorporate covariates such as environmental risk factors or additional unlinked loci to allow for population structure. To evaluate the power of this approach to detect disease-marker association, we have developed a simulation algorithm to generate high-density SNP data with short-range linkage disequilibrium based on empirical patterns of haplotype diversity. The results of the simulation study highlight substantial gains in power over single-locus tests for a wide range of disease models, despite overcorrection for multiple testing.     

Statistical models for haplotype sharing in case-parent trio data

BACKGROUND: Haplotype sharing statistics have been introduced in an ad-hoc way, often relying heavily on permutation testing. As a result, applying these approaches to whole genome association studies or to evaluate their properties in extensive simulation experiments is problematic. Further, permutation testing may be inappropriate in the presence of phase ambiguity and population stratification. AIMS: To present a simple framework for a class of haplotype sharing statistics useful for association mapping in case-parent trio data. This framework allows derivation of novel haplotype sharing tests as well as simple variance estimators and asymptotic distributions for haplotype sharing tests. RESULTS AND CONCLUSIONS: We validated that our approach is appropriately sized using simulated data, and illustrate the methodology by analyzing a Crohn's disease dataset. We find that haplotype-based analyses are much more powerful than single-locus analyses for these data.     

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.     

Accelerating haplotype-based genome-wide association study using perfect phylogeny and phase-known reference data

The genome-wide association study (GWAS) has become a routine approach for mapping disease risk loci with the advent of large-scale genotyping technologies. Multi-allelic haplotype markers can provide superior power compared with single-SNP markers in mapping disease loci. However, the application of haplotype-based analysis to GWAS is usually bottlenecked by prohibitive time cost for haplotype inference, also known as phasing. In this study, we developed an efficient approach to haplotype-based analysis in GWAS. By using a reference panel, our method accelerated the phasing process and reduced the potential bias generated by unrealistic assumptions in phasing process. The haplotype-based approach delivers great power and no type I error inflation for association studies. With only a medium-size reference panel, phasing error in our method is comparable to the genotyping error afforded by commercial genotyping solutions.     

Effect of two- and three-locus linkage disequilibrium on the power to detect marker/phenotype associations

There has been much recent interest in describing the patterns of linkage disequilibrium (LD) along a chromosome. Most empirical studies that have examined this issue have concentrated on LD between collections of pairs of markers and have not considered the joint effect of a group of markers beyond these pairwise connections. Here, we examine many different patterns of LD defined by both pairwise and joint multilocus LD terms. The LD patterns we considered were chosen in part by examining those seen in real data. We examine how changes in these patterns affect the power to detect association when performing single-marker and haplotype-based case-control tests, including a novel haplotype test based on contrasting LD between affected and unaffected individuals. Through our studies we find that differences in power between single-marker tests and haplotype-based tests in general do not appear to be large. Where moderate to high levels of multilocus LD exist, haplotype tests tend to be more powerful. Single-marker tests tend to prevail when pairwise LD is high. For moderate pairwise values and weak multilocus LD, either testing strategy may come out ahead, although it is also quite likely that neither has much power.     

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.     

Improved power by use of a weighted score test for linkage disequilibrium mapping

Association studies offer an exciting approach to finding underlying genetic variants of complex human diseases. However, identification of genetic variants still includes difficult challenges, and it is important to develop powerful new statistical methods. Currently, association methods may depend on single-locus analysis--that is, analysis of the association of one locus, which is typically a single-nucleotide polymorphism (SNP), at a time--or on multilocus analysis, in which multiple SNPs are used to allow extraction of maximum information about linkage disequilibrium (LD). It has been shown that single-locus analysis may have low power because a single SNP often has limited LD information. Multilocus analysis, which is more informative, can be performed on the basis of either haplotypes or genotypes. It may lose power because of the often large number of degrees of freedom involved. The ideal method must make full use of important information from multiple loci but avoid increasing the degrees of freedom. Therefore, we propose a method to capture information from multiple SNPs but with the use of fewer degrees of freedom. When a set of SNPs in a block are correlated because of LD, we might expect that the genotype variation among the different phenotypic groups would extend across all the SNPs, and this information could be compressed into the low-frequency components of a Fourier transform. Therefore, we develop a test based on weighted Fourier transformation coefficients, with more weight given to the low-frequency components. Our simulation results demonstrate the validity and substantially higher power of the proposed method compared with other common methods. This method provides an additional tool to existing methods for identification of causative genetic variants underlying complex diseases.     

Screening for recently selected alleles by analysis of human haplotype similarity

There is growing interest in the use of haplotype-based methods for detecting recent selection. Here, we describe a method that uses a sliding window to estimate similarity among the haplotypes associated with any given single-nucleotide polymorphism (SNP) allele. We used simulations of natural selection to provide estimates of the empirical power of the method to detect recently selected alleles and found it to be comparable in power to the popular long-range haplotype test and more powerful than methods based on nucleotide diversity. We then applied the method to a recently selected allele--the sickle mutation at the HBB locus--and found it to have a signal of selection that was significantly stronger than that of simulated models both with and without strong selection. Using this method, we also evaluated >4,000 SNPs on chromosome 20, indicating the applicability of the method to regional data sets.     

Confounding from cryptic relatedness in haplotype-based association studies

Cryptic relatedness was suggested to be an important source of confounding in population-based association studies (PBAS). The impact of cryptic relatedness on the performance of haplotype phase inference and haplotype-based association tests is not clear. In this study, we used the Hapmap genetic data to simulate a set of related samples. We evaluated the accuracy of haplotype phase inferred by PHASE 2.1 and calculated the power, type I error rates, accuracy and positive prediction value (PPV) of haplotype frequency-based association tests (HFAT) and haplotype similarity-based association tests (HSAT) under various scenarios, considering relatedness levels, disease models and sample sizes. Cryptic relatedness appeared to slightly increase the accuracy of haplotype phase inference. We observed significant negative effect of cryptic relatedness on the performance of HFAT and HSAT. Ignoring cryptic relatedness may increase spurious association results in haplotype-based PBAS.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.     

Powerful testing via hierarchical linkage disequilibrium in haplotype association studies

Marginal tests based on individual SNPs are routinely used in genetic association studies. Studies have shown that haplotype‐based methods may provide more power in disease mapping than methods based on single markers when, for example, multiple disease‐susceptibility variants occur within the same gene. A limitation of haplotype‐based methods is that the number of parameters increases exponentially with the number of SNPs, inducing a commensurate increase in the degrees of freedom and weakening the power to detect associations. To address this limitation, we introduce a hierarchical linkage disequilibrium model for disease mapping, based on a reparametrization of the multinomial haplotype distribution, where every parameter corresponds to the cumulant of each possible subset of a set of loci. This hierarchy present in the parameters enables us to employ flexible testing strategies over a range of parameter sets: from standard single SNP analyses through the full haplotype distribution tests, reducing degrees of freedom and increasing the power to detect associations. We show via extensive simulations that our approach maintains the type I error at nominal level and has increased power under many realistic scenarios, as compared to single SNP and standard haplotype‐based studies. To evaluate the performance of our proposed methodology in real data, we analyze genome‐wide data from the Wellcome Trust Case‐Control Consortium.     

Genetic association analysis of human longevity in cohort studies of elderly subjects: an example of the PON1 gene in the Danish 1905 birth cohort

Although the case-control or the cross-sectional design has been popular in genetic association studies of human longevity, such a design is prone to false positive results due to sampling bias and a potential secular trend in gene-environment interactions. To avoid these problems, the cohort or follow-up study design has been recommended. With the observed individual survival information, the Cox regression model has been used for single-locus data analysis. In this article, we present a novel survival analysis model that combines population survival with individual genotype and phenotype information in assessing the genetic association with human longevity in cohort studies. By monitoring the changes in the observed genotype frequencies over the follow-up period in a birth cohort, we are able to assess the effects of the genotypes and/or haplotypes on individual survival. With the estimated parameters, genotype- and/or haplotype-specific survival and hazard functions can be calculated without any parametric assumption on the survival distribution. In addition, our model estimates haplotype frequencies in a birth cohort over the follow-up time, which is not observable in the multilocus genotype data. A computer simulation study was conducted to specifically assess the performance and power of our haplotype-based approach for given risk and frequency parameters under different sample sizes. Application of our method to paraoxonase 1 genotype data detected a haplotype that significantly reduces carriers' hazard of death and thus reveals and stresses the important role of genetic variation in maintaining human survival at advanced ages.     

Incorporating genotyping uncertainty in haplotype inference for single-nucleotide polymorphisms

The accuracy of the vast amount of genotypic information generated by high-throughput genotyping technologies is crucial in haplotype analyses and linkage-disequilibrium mapping for complex diseases. To date, most automated programs lack quality measures for the allele calls; therefore, human interventions, which are both labor intensive and error prone, have to be performed. Here, we propose a novel genotype clustering algorithm, GeneScore, based on a bivariate t-mixture model, which assigns a set of probabilities for each data point belonging to the candidate genotype clusters. Furthermore, we describe an expectation-maximization (EM) algorithm for haplotype phasing, GenoSpectrum (GS)-EM, which can use probabilistic multilocus genotype matrices (called "GenoSpectrum") as inputs. Combining these two model-based algorithms, we can perform haplotype inference directly on raw readouts from a genotyping machine, such as the TaqMan assay. By using both simulated and real data sets, we demonstrate the advantages of our probabilistic approach over the current genotype scoring methods, in terms of both the accuracy of haplotype inference and the statistical power of haplotype-based association analyses.     

ParaHaplo 2.0: a program package for haplotype-estimation and haplotype-based whole-genome association study using parallel computing

Background  

The use of haplotype-based association tests can improve the power of genome-wide association studies. Since the observed genotypes are unordered pairs of alleles, haplotype phase must be inferred. However, estimating haplotype phase is time consuming. When millions of single-nucleotide polymorphisms (SNPs) are analyzed in genome-wide association study, faster methods for haplotype estimation are required.     

Leveraging the HapMap correlation structure in association studies

Recent high-throughput genotyping technologies, such as the Affymetrix 500k array and the Illumina HumanHap 550 beadchip, have driven down the costs of association studies and have enabled the measurement of single-nucleotide polymorphism (SNP) allele frequency differences between case and control populations on a genomewide scale. A key aspect in the efficiency of association studies is the notion of "indirect association," where only a subset of SNPs are collected to serve as proxies for the uncollected SNPs, taking advantage of the correlation structure between SNPs. Recently, a new class of methods for indirect association, multimarker methods, has been proposed. Although the multimarker methods are a considerable advancement, current methods do not fully take advantage of the correlation structure between SNPs and their multimarker proxies. In this article, we propose a novel multimarker indirect-association method, WHAP, that is based on a weighted sum of the haplotype frequency differences. In contrast to traditional indirect-association methods, we show analytically that there is a considerable gain in power achieved by our method compared with both single-marker and multimarker tests, as well as traditional haplotype-based tests. Our results are supported by empirical evaluation across the HapMap reference panel data sets, and a software implementation for the Affymetrix 500k and Illumina HumanHap 550 chips is available for download.     

Transmission/disequilibrium test meets measured haplotype analysis: family-based association analysis guided by evolution of haplotypes

Family data teamed with the transmission/disequilibrium test (TDT), which simultaneously evaluates linkage and association, is a powerful means of detecting disease-liability alleles. To increase the information provided by the test, various researchers have proposed TDT-based methods for haplotype transmission. Haplotypes indeed produce more-definitive transmissions than do the alleles comprising them, and this tends to increase power. However, the larger number of haplotypes, relative to alleles at individual loci, tends to decrease power, because of the additional degrees of freedom required for the test. An optimal strategy would focus the test on particular haplotypes or groups of haplotypes. In this report we develop such an approach by combining the theory of TDT with that of measured haplotype analysis (MHA). MHA uses the evolutionary relationships among haplotypes to produce a limited set of hypothesis tests and to increase the interpretability of these tests. The theory of our approach, called the "evolutionary tree" (ET)-TDT, is developed for two cases: when haplotype transmission is certain and when it is not. Simulations show the ET-TDT can be more powerful than other proposed methods under reasonable conditions. More importantly, our results show that, when multiple polymorphisms are found within the gene, the ET-TDT can be useful for determining which polymorphisms affect liability.     

WHAP: haplotype-based association analysis

We describe a software tool to perform haplotype-based association analysis, for quantitative and qualitative traits, in population and family samples, using single nucleotide polymorphism or multiallelic marker data. A range of tests is offered: omnibus and haplotype-specific tests; prospective and retrospective likelihoods; covariates and moderators; sliding window analyses; permutation P-values. We focus on the ability to flexibly impose constraints on haplotype effects, which allows for a range of conditional haplotype-based likelihood ratio tests: for example, whether an allele has an effect independent of its haplotypic background, or whether a single variant can explain the overall association at a locus. We illustrate using these tests to dissect a multi-locus association. AVAILABILITY: WHAP is a C/C++ program, freely available from the author's website: http://pngu.mgh.harvard.edu/purcell/whap/