SHEsis PCA: A GPU-Based Software to Correct for Population Stratification that Efficiently Accelerates the Process for Handling Genome-Wide Datasets

Population stratification is a problem in genetic association studies because it is likely to highlight loci that underlie the population structure rather than disease-related loci. At present, principal component analysis(PCA) has been proven to be an effective way to correct for population stratification. However, the conventional PCA algorithm is time-consuming when dealing with large datasets. We developed a Graphic processing unit(GPU)-based PCA software named SHEsis PCA(http://analysis.bio-x.cn/SHEsis Main.htm) that is highly parallel with a highest speedup greater than 100 compared with its CPU version. A cluster algorithm based on X-means was also implemented as a way to detect population subgroups and to obtain matched cases and controls in order to reduce the genomic inflation and increase the power. A study of both simulated and real datasets showed that SHEsis PCA ran at an extremely high speed while the accuracy was hardly reduced. Therefore, SHEsis PCA can help correct for population stratification much more efficiently than the conventional CPU-based algorithms.     

Model-free Estimation of Recent Genetic Relatedness

Genealogical inference from genetic data is essential for a variety of applications in human genetics. In genome-wide and sequencing association studies, for example, accurate inference on both recent genetic relatedness, such as family structure, and more distant genetic relatedness, such as population structure, is necessary for protection against spurious associations. Distinguishing familial relatedness from population structure with genotype data, however, is difficult because both manifest as genetic similarity through the sharing of alleles. Existing approaches for inference on recent genetic relatedness have limitations in the presence of population structure, where they either (1) make strong and simplifying assumptions about population structure, which are often untenable, or (2) require correct specification of and appropriate reference population panels for the ancestries in the sample, which might be unknown or not well defined. Here, we propose PC-Relate, a model-free approach for estimating commonly used measures of recent genetic relatedness, such as kinship coefficients and IBD sharing probabilities, in the presence of unspecified structure. PC-Relate uses principal components calculated from genome-screen data to partition genetic correlations among sampled individuals due to the sharing of recent ancestors and more distant common ancestry into two separate components, without requiring specification of the ancestral populations or reference population panels. In simulation studies with population structure, including admixture, we demonstrate that PC-Relate provides accurate estimates of genetic relatedness and improved relationship classification over widely used approaches. We further demonstrate the utility of PC-Relate in applications to three ancestrally diverse samples that vary in both size and genealogical complexity.     

A robust statistical method for association-based eQTL analysis

Background

It has been well established that theoretical kernel for recently surging genome-wide association study (GWAS) is statistical inference of linkage disequilibrium (LD) between a tested genetic marker and a putative locus affecting a disease trait. However, LD analysis is vulnerable to several confounding factors of which population stratification is the most prominent. Whilst many methods have been proposed to correct for the influence either through predicting the structure parameters or correcting inflation in the test statistic due to the stratification, these may not be feasible or may impose further statistical problems in practical implementation.

Methodology

We propose here a novel statistical method to control spurious LD in GWAS from population structure by incorporating a control marker into testing for significance of genetic association of a polymorphic marker with phenotypic variation of a complex trait. The method avoids the need of structure prediction which may be infeasible or inadequate in practice and accounts properly for a varying effect of population stratification on different regions of the genome under study. Utility and statistical properties of the new method were tested through an intensive computer simulation study and an association-based genome-wide mapping of expression quantitative trait loci in genetically divergent human populations.

Results/Conclusions

The analyses show that the new method confers an improved statistical power for detecting genuine genetic association in subpopulations and an effective control of spurious associations stemmed from population structure when compared with other two popularly implemented methods in the literature of GWAS.     

Inferences from Genomic Models in Stratified Populations

Unaccounted population stratification can lead to spurious associations in genome-wide association studies (GWAS) and in this context several methods have been proposed to deal with this problem. An alternative line of research uses whole-genome random regression (WGRR) models that fit all markers simultaneously. Important objectives in WGRR studies are to estimate the proportion of variance accounted for by the markers, the effect of individual markers, prediction of genetic values for complex traits, and prediction of genetic risk of diseases. Proposals to account for stratification in this context are unsatisfactory. Here we address this problem and describe a reparameterization of a WGRR model, based on an eigenvalue decomposition, for simultaneous inference of parameters and unobserved population structure. This allows estimation of genomic parameters with and without inclusion of marker-derived eigenvectors that account for stratification. The method is illustrated with grain yield in wheat typed for 1279 genetic markers, and with height, HDL cholesterol and systolic blood pressure from the British 1958 cohort study typed for 1 million SNP genotypes. Both sets of data show signs of population structure but with different consequences on inferences. The method is compared to an advocated approach consisting of including eigenvectors as fixed-effect covariates in a WGRR model. We show that this approach, used in the context of WGRR models, is ill posed and illustrate the advantages of the proposed model. In summary, our method permits a unified approach to the study of population structure and inference of parameters, is computationally efficient, and is easy to implement.     

CLIFF: clustering of high-dimensional microarray data via iterative feature filtering using normalized cuts

We present CLIFF, an algorithm for clustering biological samples using gene expression microarray data. This clustering problem is difficult for several reasons, in particular the sparsity of the data, the high dimensionality of the feature (gene) space, and the fact that many features are irrelevant or redundant. Our algorithm iterates between two computational processes, feature filtering and clustering. Given a reference partition that approximates the correct clustering of the samples, our feature filtering procedure ranks the features according to their intrinsic discriminability, relevance to the reference partition, and irredundancy to other relevant features, and uses this ranking to select the features to be used in the following round of clustering. Our clustering algorithm, which is based on the concept of a normalized cut, clusters the samples into a new reference partition on the basis of the selected features. On a well-studied problem involving 72 leukemia samples and 7130 genes, we demonstrate that CLIFF outperforms standard clustering approaches that do not consider the feature selection issue, and produces a result that is very close to the original expert labeling of the sample set.     

Molecular Reclassification of Crohn’s Disease: A Cautionary Note on Population Stratification

Complex human diseases commonly differ in their phenotypic characteristics, e.g., Crohn’s disease (CD) patients are heterogeneous with regard to disease location and disease extent. The genetic susceptibility to Crohn’s disease is widely acknowledged and has been demonstrated by identification of over 100 CD associated genetic loci. However, relating CD subphenotypes to disease susceptible loci has proven to be a difficult task. In this paper we discuss the use of cluster analysis on genetic markers to identify genetic-based subgroups while taking into account possible confounding by population stratification. We show that it is highly relevant to consider the confounding nature of population stratification in order to avoid that detected clusters are strongly related to population groups instead of disease-specific groups. Therefore, we explain the use of principal components to correct for population stratification while clustering affected individuals into genetic-based subgroups. The principal components are obtained using 30 ancestry informative markers (AIM), and the first two PCs are determined to discriminate between continental origins of the affected individuals. Genotypes on 51 CD associated single nucleotide polymorphisms (SNPs) are used to perform latent class analysis, hierarchical and Partitioning Around Medoids (PAM) cluster analysis within a sample of affected individuals with and without the use of principal components to adjust for population stratification. It is seen that without correction for population stratification clusters seem to be influenced by population stratification while with correction clusters are unrelated to continental origin of individuals.     

PSMIX: an R package for population structure inference via maximum likelihood method

Background  

Inference of population stratification and individual admixture from genetic markers is an integrative part of a study in diverse situations, such as association mapping and evolutionary studies. Bayesian methods have been proposed for population stratification and admixture inference using multilocus genotypes and widely used in practice. However, these Bayesian methods demand intensive computation resources and may run into convergence problem in Markov Chain Monte Carlo based posterior samplings.     

Accounting for population stratification in practice: a comparison of the main strategies dedicated to genome-wide association studies

Genome-Wide Association Studies are powerful tools to detect genetic variants associated with diseases. Their results have, however, been questioned, in part because of the bias induced by population stratification. This is a consequence of systematic differences in allele frequencies due to the difference in sample ancestries that can lead to both false positive or false negative findings. Many strategies are available to account for stratification but their performances differ, for instance according to the type of population structure, the disease susceptibility locus minor allele frequency, the degree of sampling imbalanced, or the sample size. We focus on the type of population structure and propose a comparison of the most commonly used methods to deal with stratification that are the Genomic Control, Principal Component based methods such as implemented in Eigenstrat, adjusted Regressions and Meta-Analyses strategies. Our assessment of the methods is based on a large simulation study, involving several scenarios corresponding to many types of population structures. We focused on both false positive rate and power to determine which methods perform the best. Our analysis showed that if there is no population structure, none of the tests led to a bias nor decreased the power except for the Meta-Analyses. When the population is stratified, adjusted Logistic Regressions and Eigenstrat are the best solutions to account for stratification even though only the Logistic Regressions are able to constantly maintain correct false positive rates. This study provides more details about these methods. Their advantages and limitations in different stratification scenarios are highlighted in order to propose practical guidelines to account for population stratification in Genome-Wide Association Studies.     

A PCA-based method for ancestral informative markers selection in structured populations

Identification of population structure can help trace population histories and identify disease genes. Structured association (SA) is a commonly used approach for population structure identification and association mapping. A major issue with SA is that its performance greatly depends on the informativeness and the numbers of ancestral informative markers (AIMs). Present major AIM selection methods mostly require prior individual ancestry information, which is usually not available or uncertain in practice. To address this potential weakness, we herein develop a novel approach for AIM selection based on principle component analysis (PCA), which does not require prior ancestry information of study subjects. Our simulation and real genetic data analysis results suggest that, with equivalent AIMs, PCA-based selected AIMs can significantly increase the accuracy of inferred individual ancestries compared with traditionally randomly selected AIMs. Our method can easily be applied to whole genome data to select a set of highly informative AIMs in population structure, which can then be used to identify potential population structure and correct possible statistical biases caused by population stratification.     

Fine-scale estimation of location of birth from genome-wide single-nucleotide polymorphism data

Systematic nonrandom mating in populations results in genetic stratification and is predominantly caused by geographic separation, providing the opportunity to infer individuals' birthplace from genetic data. Such inference has been demonstrated for individuals' country of birth, but here we use data from the Northern Finland Birth Cohort 1966 (NFBC1966) to investigate the characteristics of genetic structure within a population and subsequently develop a method for inferring location to a finer scale. Principal component analysis (PCA) shows that while the first PCs are particularly informative for location, there is also location information in the higher-order PCs, but it cannot be captured by a linear model. We introduce a new method, pcLOCATE, which is able to exploit this information to improve the accuracy of location inference. pcLOCATE uses individuals' PC values to estimate the probability of birth in each town and then averages over all towns to give an estimated longitude and latitude of birth using a fully Bayesian model. We apply pcLOCATE to the NFBC1966 data to estimate parental birthplace, testing with successively more PCs and finding the model with the top 23 PCs most accurate, with a median distance of 23 km between the estimated and the true location. pcLOCATE predicts the most recent residence of NFBC1966 individuals to a median distance of 47 km. We also apply pcLOCATE to Indian individuals from the London Life Sciences Prospective Population Study (LOLIPOP) data, and find that birthplace is predicated to a median distance of 54 km from the true location. A method with such accuracy is potentially valuable in population genetics and forensics.     

SHIPS: Spectral Hierarchical Clustering for the Inference of Population Structure in Genetic Studies

Inferring the structure of populations has many applications for genetic research. In addition to providing information for evolutionary studies, it can be used to account for the bias induced by population stratification in association studies. To this end, many algorithms have been proposed to cluster individuals into genetically homogeneous sub-populations. The parametric algorithms, such as Structure, are very popular but their underlying complexity and their high computational cost led to the development of faster parametric alternatives such as Admixture. Alternatives to these methods are the non-parametric approaches. Among this category, AWclust has proven efficient but fails to properly identify population structure for complex datasets. We present in this article a new clustering algorithm called Spectral Hierarchical clustering for the Inference of Population Structure (SHIPS), based on a divisive hierarchical clustering strategy, allowing a progressive investigation of population structure. This method takes genetic data as input to cluster individuals into homogeneous sub-populations and with the use of the gap statistic estimates the optimal number of such sub-populations. SHIPS was applied to a set of simulated discrete and admixed datasets and to real SNP datasets, that are data from the HapMap and Pan-Asian SNP consortium. The programs Structure, Admixture, AWclust and PCAclust were also investigated in a comparison study. SHIPS and the parametric approach Structure were the most accurate when applied to simulated datasets both in terms of individual assignments and estimation of the correct number of clusters. The analysis of the results on the real datasets highlighted that the clusterings of SHIPS were the more consistent with the population labels or those produced by the Admixture program. The performances of SHIPS when applied to SNP data, along with its relatively low computational cost and its ease of use make this method a promising solution to infer fine-scale genetic patterns.     

Paleo-population genetics

Two levels of population-genetic problems can be distinguished: (1) Distribution and population differences of monofactorial characters. In this connection, prehistoric physical anthropology is still very poor. (2) The study of processes which change the genetic structure of population. In this field also polyfactorial characters are important and may be used for analysis. Metric-morphological differentiations between and within skeletal populations are able to point at the following population genetic processes: migration and population mixture; genetic isolation and its effects; selection; social assortment, social stratification and assortative mating.     

Leveraging Multi-ethnic Evidence for Mapping Complex Traits in Minority Populations: An Empirical Bayes Approach

Elucidating the genetic basis of complex traits and diseases in non-European populations is particularly challenging because US minority populations have been under-represented in genetic association studies. We developed an empirical Bayes approach named XPEB (cross-population empirical Bayes), designed to improve the power for mapping complex-trait-associated loci in a minority population by exploiting information from genome-wide association studies (GWASs) from another ethnic population. Taking as input summary statistics from two GWASs—a target GWAS from an ethnic minority population of primary interest and an auxiliary base GWAS (such as a larger GWAS in Europeans)—our XPEB approach reprioritizes SNPs in the target population to compute local false-discovery rates. We demonstrated, through simulations, that whenever the base GWAS harbors relevant information, XPEB gains efficiency. Moreover, XPEB has the ability to discard irrelevant auxiliary information, providing a safeguard against inflated false-discovery rates due to genetic heterogeneity between populations. Applied to a blood-lipids study in African Americans, XPEB more than quadrupled the discoveries from the conventional approach, which used a target GWAS alone, bringing the number of significant loci from 14 to 65. Thus, XPEB offers a flexible framework for mapping complex traits in minority populations.     

Evaluating Methods to Correct for Population Stratification when Estimating Paternity Indexes

The statistical interpretation of the forensic genetic evidence requires the use of allelic frequency estimates in the reference population for the studied markers. Differences in the genetic make up of the populations can be reflected in statistically different allelic frequency distributions. One can easily figure out that collecting such information for any given population is not always possible. Therefore, alternative approaches are needed in these cases in order to compensate for the lack of information. A number of statistics have been proposed to control for population stratification in paternity testing and forensic casework, Fst correction being the only one recommended by the forensic community. In this study we aimed to evaluate the performance of Fst to correct for population stratification in forensics. By way of simulations, we first tested the dependence of Fst on the relative sizes of the sub-populations, and second, we measured the effect of the Fst corrections on the Paternity Index (PI) values compared to the ones obtained when using the local reference database. The results provide clear-cut evidence that (i) Fst values are strongly dependent on the sampling scheme, and therefore, for most situations it would be almost impossible to estimate real values of Fst; and (ii) Fst corrections might unfairly correct PI values for stratification, suggesting the use of local databases whenever possible to estimate the frequencies of genetic profiles and PI values.     

Quantitative similarity-based association tests using population samples

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification, such as family-based association designs, may be less powerful. Furthermore, it is often more feasible and less expensive to collect unrelated individuals. Recently, several statistical methods have been proposed for case-control association tests in a structured population; these methods may be robust to population stratification. In the present study, we propose a quantitative similarity-based association test (QSAT) to identify association between a candidate marker and a quantitative trait of interest, through use of unrelated individuals. For the QSAT, we first determine whether two individuals are from the same subpopulation or from different subpopulations, using genotype data at a set of independent markers. We then perform an association test between the candidate marker and the quantitative trait, through incorporation of such information. Simulation results based on either coalescent models or empirical population genetics data show that the QSAT has a correct type I error rate in the presence of population stratification and that the power of the QSAT is higher than that of family-based association designs.     

Unsupervised feature selection via two-way ordering in gene expression analysis

MOTIVATION: Selection of genes most relevant and informative for certain phenotypes is an important aspect in gene expression analysis. Most current methods select genes based on known phenotype information. However, certain set of genes may correspond to new phenotypes which are yet unknown, and it is important to develop novel effective selection methods for their discovery without using any prior phenotype information. RESULTS: We propose and study a new method to select relevant genes based on their similarity information only. The method relies on a mechanism for discarding irrelevant genes. A two-way ordering of gene expression data can force irrelevant genes towards the middle in the ordering and thus can be discarded. Mechanisms based on variance and principal component analysis are also studied. When applied to expression profiles of colon cancer and leukemia, the unsupervised method outperforms the baseline algorithm that simply uses all genes, and it also selects relevant genes close to those selected using supervised methods. SUPPLEMENT: More results and software are online: http://www.nersc.gov/~cding/2way.     

fastSTRUCTURE: Variational Inference of Population Structure in Large SNP Data Sets

Tools for estimating population structure from genetic data are now used in a wide variety of applications in population genetics. However, inferring population structure in large modern data sets imposes severe computational challenges. Here, we develop efficient algorithms for approximate inference of the model underlying the STRUCTURE program using a variational Bayesian framework. Variational methods pose the problem of computing relevant posterior distributions as an optimization problem, allowing us to build on recent advances in optimization theory to develop fast inference tools. In addition, we propose useful heuristic scores to identify the number of populations represented in a data set and a new hierarchical prior to detect weak population structure in the data. We test the variational algorithms on simulated data and illustrate using genotype data from the CEPH–Human Genome Diversity Panel. The variational algorithms are almost two orders of magnitude faster than STRUCTURE and achieve accuracies comparable to those of ADMIXTURE. Furthermore, our results show that the heuristic scores for choosing model complexity provide a reasonable range of values for the number of populations represented in the data, with minimal bias toward detecting structure when it is very weak. Our algorithm, fastSTRUCTURE, is freely available online at http://pritchardlab.stanford.edu/structure.html.     

Discerning the ancestry of European Americans in genetic association studies

European Americans are often treated as a homogeneous group, but in fact form a structured population due to historical immigration of diverse source populations. Discerning the ancestry of European Americans genotyped in association studies is important in order to prevent false-positive or false-negative associations due to population stratification and to identify genetic variants whose contribution to disease risk differs across European ancestries. Here, we investigate empirical patterns of population structure in European Americans, analyzing 4,198 samples from four genome-wide association studies to show that components roughly corresponding to northwest European, southeast European, and Ashkenazi Jewish ancestry are the main sources of European American population structure. Building on this insight, we constructed a panel of 300 validated markers that are highly informative for distinguishing these ancestries. We demonstrate that this panel of markers can be used to correct for stratification in association studies that do not generate dense genotype data.     

Likelihood-based association analysis for nuclear families and unrelated subjects with missing genotype data

Missing data occur in genetic association studies for several reasons including missing family members and uncertain haplotype phase. Maximum likelihood is a commonly used approach to accommodate missing data, but it can be difficult to apply to family-based association studies, because of possible loss of robustness to confounding by population stratification. Here a novel likelihood for nuclear families is proposed, in which distinct sets of association parameters are used to model the parental genotypes and the offspring genotypes. This approach is robust to population structure when the data are complete, and has only minor loss of robustness when there are missing data. It also allows a novel conditioning step that gives valid analysis for multiple offspring in the presence of linkage. Unrelated subjects are included by regarding them as the children of two missing parents. Simulations and theory indicate similar operating characteristics to TRANSMIT, but with no bias with missing data in the presence of linkage. In comparison with FBAT and PCPH, the proposed model is slightly less robust to population structure but has greater power to detect strong effects. In comparison to APL and MITDT, the model is more robust to stratification and can accommodate sibships of any size. The methods are implemented for binary and continuous traits in software, UNPHASED, available from the author.