Missing data imputation and haplotype phase inference for genome-wide association studies

Imputation of missing data and the use of haplotype-based association tests can improve the power of genome-wide association studies (GWAS). In this article, I review methods for haplotype inference and missing data imputation, and discuss their application to GWAS. I discuss common features of the best algorithms for haplotype phase inference and missing data imputation in large-scale data sets, as well as some important differences between classes of methods, and highlight the methods that provide the highest accuracy and fastest computational performance.     

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.     

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.     

Incorporating single-locus tests into haplotype cladistic analysis in case-control studies

In case-control studies, genetic associations for complex diseases may be probed either with single-locus tests or with haplotype-based tests. Although there are different views on the relative merits and preferences of the two test strategies, haplotype-based analyses are generally believed to be more powerful to detect genes with modest effects. However, a main drawback of haplotype-based association tests is the large number of distinct haplotypes, which increases the degrees of freedom for corresponding test statistics and thus reduces the statistical power. To decrease the degrees of freedom and enhance the efficiency and power of haplotype analysis, we propose an improved haplotype clustering method that is based on the haplotype cladistic analysis developed by Durrant et al. In our method, we attempt to combine the strengths of single-locus analysis and haplotype-based analysis into one single test framework. Novel in our method is that we develop a more informative haplotype similarity measurement by using p-values obtained from single-locus association tests to construct a measure of weight, which to some extent incorporates the information of disease outcomes. The weights are then used in computation of similarity measures to construct distance metrics between haplotype pairs in haplotype cladistic analysis. To assess our proposed new method, we performed simulation analyses to compare the relative performances of (1) conventional haplotype-based analysis using original haplotype, (2) single-locus allele-based analysis, (3) original haplotype cladistic analysis (CLADHC) by Durrant et al., and (4) our weighted haplotype cladistic analysis method, under different scenarios. Our weighted cladistic analysis method shows an increased statistical power and robustness, compared with the methods of haplotype cladistic analysis, single-locus test, and the traditional haplotype-based analyses. The real data analyses also show that our proposed method has practical significance in the human genetics field.     

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.     

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.     

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.     

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/     

Rapid and accurate haplotype phasing and missing-data inference for whole-genome association studies by use of localized haplotype clustering

Whole-genome association studies present many new statistical and computational challenges due to the large quantity of data obtained. One of these challenges is haplotype inference; methods for haplotype inference designed for small data sets from candidate-gene studies do not scale well to the large number of individuals genotyped in whole-genome association studies. We present a new method and software for inference of haplotype phase and missing data that can accurately phase data from whole-genome association studies, and we present the first comparison of haplotype-inference methods for real and simulated data sets with thousands of genotyped individuals. We find that our method outperforms existing methods in terms of both speed and accuracy for large data sets with thousands of individuals and densely spaced genetic markers, and we use our method to phase a real data set of 3,002 individuals genotyped for 490,032 markers in 3.1 days of computing time, with 99% of masked alleles imputed correctly. Our method is implemented in the Beagle software package, which is freely available.     

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.     

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 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.     

Comparison of population-based association study methods correcting for population stratification

Population stratification can cause spurious associations in population-based association studies. Several statistical methods have been proposed to reduce the impact of population stratification on population-based association studies. We simulated a set of stratified populations based on the real haplotype data from the HapMap ENCODE project, and compared the relative power, type I error rates, accuracy and positive prediction value of four prevailing population-based association study methods: traditional case-control tests, structured association (SA), genomic control (GC) and principal components analysis (PCA) under various population stratification levels. Additionally, we evaluated the effects of sample sizes and frequencies of disease susceptible allele on the performance of the four analytical methods in the presence of population stratification. We found that the performance of PCA was very stable under various scenarios. Our comparison results suggest that SA and PCA have comparable performance, if sufficient ancestral informative markers are used in SA analysis. GC appeared to be strongly conservative in significantly stratified populations. It may be better to apply GC in the stratified populations with low stratification level. Our study intends to provide a practical guideline for researchers to select proper study methods and make appropriate inference of the results in population-based association studies.     

Optimal use of regression models in genome-wide association studies

The performance of linear regression models in genome-wide association studies is influenced by how marker information is parameterized in the model. Considering the impact of parameterization is especially important when using information from multiple markers to test for association. Properties of the population, such as linkage disequilibrium (LD) and allele frequencies, will also affect the ability of a model to provide statistical support for an underlying quantitative trait locus (QTL). Thus, for a given location in the genome, the relationship between population properties and model parameterization is expected to influence the performance of the model in providing evidence for the position of a QTL. As LD and allele frequencies vary throughout the genome and between populations, understanding the relationship between these properties and model parameterization is of considerable importance in order to make optimal use of available genomic data. Here, we evaluate the performance of regression-based association models using genotype and haplotype information across the full spectrum of allele frequency and LD scenarios. Genetic marker data from 200 broiler chickens were used to simulate genomic conditions by selecting individual markers to act as surrogate QTL (sQTL) and then investigating the ability of surrounding markers to estimate sQTL genotypes and provide statistical support for their location. The LD and allele frequencies of markers and sQTL are shown to have a strong effect on the performance of models relative to one another. Our results provide an indication of the best choice of model parameterization given certain scenarios of marker and QTL LD and allele frequencies. We demonstrate a clear advantage of haplotype-based models, which account for phase uncertainty over other models tested, particularly for QTL with low minor allele frequencies. We show that the greatest advantage of haplotype models over single-marker models occurs when LD between markers and the causal locus is low. Under these situations, haplotype models have a greater accuracy of predicting the location of the QTL than other models tested.     

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.     

Confounding from cryptic relatedness in case-control association studies

Case-control association studies are widely used in the search for genetic variants that contribute to human diseases. It has long been known that such studies may suffer from high rates of false positives if there is unrecognized population structure. It is perhaps less widely appreciated that so-called “cryptic relatedness” (i.e., kinship among the cases or controls that is not known to the investigator) might also potentially inflate the false positive rate. Until now there has been little work to assess how serious this problem is likely to be in practice. In this paper, we develop a formal model of cryptic relatedness, and study its impact on association studies. We provide simple expressions that predict the extent of confounding due to cryptic relatedness. Surprisingly, these expressions are functions of directly observable parameters. Our analytical results show that, for well-designed studies in outbred populations, the degree of confounding due to cryptic relatedness will usually be negligible. However, in contrast, studies where there is a sampling bias toward collecting relatives may indeed suffer from excessive rates of false positives. Furthermore, cryptic relatedness may be a serious concern in founder populations that have grown rapidly and recently from a small size. As an example, we analyze the impact of excess relatedness among cases for six phenotypes measured in the Hutterite population.     

The power comparison of the haplotype-based collapsing tests and the variant-based collapsing tests for detecting rare variants in pedigrees

Background

Both common and rare genetic variants have been shown to contribute to the etiology of complex diseases. Recent genome-wide association studies (GWAS) have successfully investigated how common variants contribute to the genetic factors associated with common human diseases. However, understanding the impact of rare variants, which are abundant in the human population (one in every 17 bases), remains challenging. A number of statistical tests have been developed to analyze collapsed rare variants identified by association tests. Here, we propose a haplotype-based approach. This work inspired by an existing statistical framework of the pedigree disequilibrium test (PDT), which uses genetic data to assess the effects of variants in general pedigrees. We aim to compare the performance between the haplotype-based approach and the rare variant-based approach for detecting rare causal variants in pedigrees.

Results

Extensive simulations in the sequencing setting were carried out to evaluate and compare the haplotype-based approach with the rare variant methods that drew on a more conventional collapsing strategy. As assessed through a variety of scenarios, the haplotype-based pedigree tests had enhanced statistical power compared with the rare variants based pedigree tests when the disease of interest was mainly caused by rare haplotypes (with multiple rare alleles), and vice versa when disease was caused by rare variants acting independently. For most of other situations when disease was caused both by haplotypes with multiple rare alleles and by rare variants with similar effects, these two approaches provided similar power in testing for association.

Conclusions

The haplotype-based approach was designed to assess the role of rare and potentially causal haplotypes. The proposed rare variants-based pedigree tests were designed to assess the role of rare and potentially causal variants. This study clearly documented the situations under which either method performs better than the other. All tests have been implemented in a software, which was submitted to the Comprehensive R Archive Network (CRAN) for general use as a computer program named rvHPDT.     

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.     

Haplotype inference for present-absent genotype data using previously identified haplotypes and haplotype patterns

MOTIVATION: Killer immunoglobulin-like receptor (KIR) genes vary considerably in their presence or absence on a specific regional haplotype. Because presence or absence of these genes is largely detected using locus-specific genotyping technology, the distinction between homozygosity and hemizygosity is often ambiguous. The performance of methods for haplotype inference (e.g. PL-EM, PHASE) for KIR genes may be compromised due to the large portion of ambiguous data. At the same time, many haplotypes or partial haplotype patterns have been previously identified and can be incorporated to facilitate haplotype inference for unphased genotype data. To accommodate the increased ambiguity of present-absent genotyping of KIR genes, we developed a hybrid approach combining a greedy algorithm with the Expectation-Maximization (EM) method for haplotype inference based on previously identified haplotypes and haplotype patterns. RESULTS: We implemented this algorithm in a software package named HAPLO-IHP (Haplotype inference using identified haplotype patterns) and compared its performance with that of HAPLORE and PHASE on simulated KIR genotypes. We compared five measures in order to evaluate the reliability of haplotype assignments and the accuracy in estimating haplotype frequency. Our method outperformed the two existing techniques by all five measures when either 60% or 25% of previously identified haplotypes were incorporated into the analyses. AVAILABILITY: The HAPLO-IHP is available at http://www.soph.uab.edu/Statgenetics/People/KZhang/HAPLO-IHP/index.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

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.