Improved eigenanalysis of discrete subpopulations and admixture using the minimum average partial test

Principal components analysis of genetic data has benefited from advances in random matrix theory. The Tracy-Widom distribution has been identified as the limiting distribution of the lead eigenvalue, enabling formal hypothesis testing of population structure. Additionally, a phase change exists between small and large eigenvalues, such that population divergence below a threshold of F(ST) is impossible to detect and above which it is always detectable. I show that the plug-in estimate of the effective number of markers in the EIGENSOFT software often exceeds the rank of the sample covariance matrix, leading to a systematic overestimation of the number of significant principal components. I describe an alternative plug-in estimate that eliminates the problem. This improvement is not just an asymptotic result but is directly applicable to finite samples. The minimum average partial test, based on minimizing the average squared partial correlation between individuals, can detect population structure at smaller F(ST) values than the corrected test. The minimum average partial test is applicable to both unadmixed and admixed samples, with arbitrary numbers of discrete subpopulations or parental populations, respectively. Application of the minimum average partial test to the 11 HapMap Phase III samples, comprising 8 unadmixed samples and 3 admixed samples, revealed 13 significant principal components.     

Control of population stratification by correlation-selected principal components

In genome-wide association studies, population stratification is recognized as producing inflated type I error due to the inflation of test statistics. Principal component-based methods applied to genotypes provide information about population structure, and have been widely used to control for stratification. Here we explore the precise relationship between genotype principal components and inflation of association test statistics, thereby drawing a connection between principal component-based stratification control and the alternative approach of genomic control. Our results provide an inherent justification for the use of principal components, but call into question the popular practice of selecting principal components based on significance of eigenvalues alone. We propose a new approach, called EigenCorr, which selects principal components based on both their eigenvalues and their correlation with the (disease) phenotype. Our approach tends to select fewer principal components for stratification control than does testing of eigenvalues alone, providing substantial computational savings and improvements in power. Analyses of simulated and real data demonstrate the usefulness of the proposed approach.     

ATRIUM: Testing Untyped SNPs in Case-Control Association Studies with Related Individuals

In genome-wide association studies, only a subset of all genomic variants are typed by current, high-throughput, SNP-genotyping platforms. However, many of the untyped variants can be well predicted from typed variants, with linkage disequilibrium (LD) information among typed and untyped variants available from an external reference panel such as HapMap. Incorporation of such external information can allow one to perform tests of association between untyped variants and phenotype, thereby making more efficient use of the available genotype data. When related individuals are included in case-control samples, the dependence among their genotypes must be properly addressed for valid association testing. In the context of testing untyped variants, an additional analytical challenge is that the dependence, across related individuals, of the partial information on untyped-SNP genotypes must also be assessed and incorporated into the analysis for valid inference. We address this challenge with ATRIUM, a method for case-control association testing with untyped SNPs, based on genome screen data in samples in which some individuals are related. ATRIUM uses LD information from an external reference panel to specify a one-degree-of-freedom test of association with an untyped SNP. It properly accounts for dependence in the partial information on untyped-SNP genotypes across related individuals. We demonstrate that ATRIUM is robust in that it maintains the nominal type I error rate even when the external reference panel is not well matched to the case-control sample. We apply the method to detect association between type 2 diabetes and variants on chromosome 10 in the Framingham SHARe data.     

Maximizing the Power of Principal-Component Analysis of Correlated Phenotypes in Genome-wide Association Studies

Many human traits are highly correlated. This correlation can be leveraged to improve the power of genetic association tests to identify markers associated with one or more of the traits. Principal component analysis (PCA) is a useful tool that has been widely used for the multivariate analysis of correlated variables. PCA is usually applied as a dimension reduction method: the few top principal components (PCs) explaining most of total trait variance are tested for association with a predictor of interest, and the remaining components are not analyzed. In this study we review the theoretical basis of PCA and describe the behavior of PCA when testing for association between a SNP and correlated traits. We then use simulation to compare the power of various PCA-based strategies when analyzing up to 100 correlated traits. We show that contrary to widespread practice, testing only the top PCs often has low power, whereas combining signal across all PCs can have greater power. This power gain is primarily due to increased power to detect genetic variants with opposite effects on positively correlated traits and variants that are exclusively associated with a single trait. Relative to other methods, the combined-PC approach has close to optimal power in all scenarios considered while offering more flexibility and more robustness to potential confounders. Finally, we apply the proposed PCA strategy to the genome-wide association study of five correlated coagulation traits where we identify two candidate SNPs that were not found by the standard approach.     

An application of common principal component analysis to cranial morphometry of Microtus californicus and M. ochrogaster(Mammalia, Rodentia)

Principal component analysis (PCA) is a one-group method. Its purpose is to transform correlated variables into uncorrelated ones and to find linear combinations accounting for a relatively large amount of the total variability, thus reducing the number of original variables to a few components only.
In the simultaneous analysis of different groups, similarities between the principal component structures can often be modelled by the methods of common principal components (CPCs) or partial CPCs. These methods assume that either all components or only some of them are common to all groups, the discrepancies being due mainly to sampling error.
Previous authors have dealt with the k-group situation either by pooling the data of all groups, or by pooling the within-group variance-covariance matrices before performing a PCA. The latter technique is known as multiple group principal component analysis or MGPCA (Thorpe, 1983a). We argue that CPC- or partial CPC-analysis is often more appropriate than these previous methods.
A morphometrical example using males and females of Microtus californicus and M. ochrogaster is presented, comparing PCA, CPC and partial CPC analyses. It is shown that the new methods yield estimated components having smaller standard errors than when groupwise analyses are performed. Formulas are given for estimating standard errors of the eigenvalues and eigenvectors, as well as for computing the likelihood ratio statistic used to test the appropriateness of the CPC- or partial CPC-model.     

Conditional Random Fields for Fast, Large-Scale Genome-Wide Association Studies

Understanding the role of genetic variation in human diseases remains an important problem to be solved in genomics. An important component of such variation consist of variations at single sites in DNA, or single nucleotide polymorphisms (SNPs). Typically, the problem of associating particular SNPs to phenotypes has been confounded by hidden factors such as the presence of population structure, family structure or cryptic relatedness in the sample of individuals being analyzed. Such confounding factors lead to a large number of spurious associations and missed associations. Various statistical methods have been proposed to account for such confounding factors such as linear mixed-effect models (LMMs) or methods that adjust data based on a principal components analysis (PCA), but these methods either suffer from low power or cease to be tractable for larger numbers of individuals in the sample. Here we present a statistical model for conducting genome-wide association studies (GWAS) that accounts for such confounding factors. Our method scales in runtime quadratic in the number of individuals being studied with only a modest loss in statistical power as compared to LMM-based and PCA-based methods when testing on synthetic data that was generated from a generalized LMM. Applying our method to both real and synthetic human genotype/phenotype data, we demonstrate the ability of our model to correct for confounding factors while requiring significantly less runtime relative to LMMs. We have implemented methods for fitting these models, which are available at http://www.microsoft.com/science.     

A principal-components approach based on heritability for combining phenotype information

For many traits, genetically relevant disease definition is unclear. For this reason, researchers applying linkage analysis often obtain information on a variety of items. With a large number of items, however, the test statistic from a multivariate analysis may require a prohibitively expensive correction for the multiple comparisons. The researcher is faced, therefore, with the issue of choosing which variables or combinations of variables to use in the linkage analysis. One approach to combining items is to first subject the data to a principal components analysis, and then perform the linkage analysis of the first few principal components. However, principal-components analyses do not take family structure into account. Here, an approach is developed in which family structure is taken into account when combining the data. The essence of the approach is to define principal components of heritability as the scores with maximum heritability in the data set, subject to being uncorrelated with each other. The principal components of heritability may be calculated as the solutions to a generalized eigensystem problem. Four simulation experiments are used to compare the power of linkage analyses based on the principal components of heritability and the usual principal components. The first of the experiments corresponds to the null hypothesis of no linkage. The second corresponds to a setting where the two kinds of principal components coincide. The third corresponds to a setting in which they are quite different and where the first of the usual principal components is not expected to have any power beyond the type I error rate. The fourth set of experiments corresponds to a setting where the usual principal components and the principal components of heritability differ, but where the first of the usual principal components is not without power. The results of the simulation experiments indicate that the principal components of heritability can be substantially different from the standard principal components and that when they are different, substantial gains in power can result by using the principal components of heritability in place of the standard principal components in linkage analyses.     

Comparison of Methods to Account for Relatedness in Genome-Wide Association Studies with Family-Based Data

Approaches based on linear mixed models (LMMs) have recently gained popularity for modelling population substructure and relatedness in genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it is not always clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several LMM approaches (and software implementations, including EMMAX, GenABEL, FaST-LMM, Mendel, GEMMA and MMM) via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals (1972 genotyped). The implementations differ in precise details of methodology implemented and through various user-chosen options such as the method and number of SNPs used to estimate the kinship (relatedness) matrix. We investigate sensitivity to these choices and the success (or otherwise) of the approaches in controlling the overall genome-wide error-rate for both real and simulated phenotypes. We compare the LMM results to those obtained using traditional family-based association tests (based on transmission of alleles within pedigrees) and to alternative approaches implemented in the software packages MQLS, ROADTRIPS and MASTOR. We find strong concordance between the results from different LMM approaches, and all are successful in controlling the genome-wide error rate (except for some approaches when applied naively to longitudinal data with many repeated measures). We also find high correlation between LMMs and alternative approaches (apart from transmission-based approaches when applied to SNPs with small or non-existent effects). We conclude that LMM approaches perform well in comparison to competing approaches. Given their strong concordance, in most applications, the choice of precise LMM implementation cannot be based on power/type I error considerations but must instead be based on considerations such as speed and ease-of-use.     

Ultrahigh-dimensional variable selection method for whole-genome gene-gene interaction analysis

ABSTRACT: BACKGROUND: Genome-wide gene-gene interaction analysis using single nucleotide polymorphisms (SNPs) is an attractive way for identification of genetic components that confers susceptibility of human complex diseases. Individual hypothesis testing for SNP-SNP pairs as in common genome-wide association study (GWAS) however involves difficulty in setting overall p-value due to complicated correlation structure, namely, the multiple testing problem that causes unacceptable false negative results. A large number of SNP-SNP pairs than sample size, so-called the large p small n problem, precludes simultaneous analysis using multiple regression. The method that overcomes above issues is thus needed. RESULTS: We adopt an up-to-date method for ultrahigh-dimensional variable selection termed the sure independence screening (SIS) [17] for appropriate handling of numerous number of SNP-SNP interactions by including them as predictor variables in logistic regression. We propose ranking strategy using promising dummy coding methods and following variable selection procedure in the SIS method suitably modified for gene-gene interaction analysis. We also implemented the procedures in a software program, EPISIS, using the cost-effective GPGPU (General-purpose computing on graphics processing units) technology. EPISIS can complete exhaustive search for SNP-SNP interactions in standard GWAS dataset within several hours. The proposed method works successfully in simulation experiments and in application to real WTCCC (Wellcome Trust Case-Control Consortium) data. CONCLUSIONS: Based on the machine-learning principle, the proposed method gives powerful and flexible genome-wide search for various patterns of gene-gene interaction.     

A Kinship-Based Modification of the Armitage Trend Test to Address Hidden Population Structure and Small Differential Genotyping Errors

Background/Aims

We propose a modification of the well-known Armitage trend test to address the problems associated with hidden population structure and hidden relatedness in genome-wide case-control association studies.

Methods

The new test adopts beneficial traits from three existing testing strategies: the principal components, mixed model, and genomic control while avoiding some of their disadvantageous characteristics, such as the tendency of the principal components method to over-correct in certain situations or the failure of the genomic control approach to reorder the adjusted tests based on their degree of alignment with the underlying hidden structure. The new procedure is based on Gauss-Markov estimators derived from a straightforward linear model with an imposed variance structure proportional to an empirical relatedness matrix. Lastly, conceptual and analytical similarities to and distinctions from other approaches are emphasized throughout.

Results

Our simulations show that the power performance of the proposed test is quite promising compared to the considered competing strategies. The power gains are especially large when small differential differences between cases and controls are present; a likely scenario when public controls are used in multiple studies.

Conclusion

The proposed modified approach attains high power more consistently than that of the existing commonly implemented tests. Its performance improvement is most apparent when small but detectable systematic differences between cases and controls exist.     

On Quality Control Measures in Genome-Wide Association Studies: A Test to Assess the Genotyping Quality of Individual Probands in Family-Based Association Studies and an Application to the HapMap Data

Allele transmissions in pedigrees provide a natural way of evaluating the genotyping quality of a particular proband in a family-based, genome-wide association study. We propose a transmission test that is based on this feature and that can be used for quality control filtering of genome-wide genotype data for individual probands. The test has one degree of freedom and assesses the average genotyping error rate of the genotyped SNPs for a particular proband. As we show in simulation studies, the test is sufficiently powerful to identify probands with an unreliable genotyping quality that cannot be detected with standard quality control filters. This feature of the test is further exemplified by an application to the third release of the HapMap data. The test is ideally suited as the final layer of quality control filters in the cleaning process of genome-wide association studies. It identifies probands with insufficient genotyping quality that were not removed by standard quality control filtering.     

A two-stage random forest-based pathway analysis method

Pathway analysis provides a powerful approach for identifying the joint effect of genes grouped into biologically-based pathways on disease. Pathway analysis is also an attractive approach for a secondary analysis of genome-wide association study (GWAS) data that may still yield new results from these valuable datasets. Most of the current pathway analysis methods focused on testing the cumulative main effects of genes in a pathway. However, for complex diseases, gene-gene interactions are expected to play a critical role in disease etiology. We extended a random forest-based method for pathway analysis by incorporating a two-stage design. We used simulations to verify that the proposed method has the correct type I error rates. We also used simulations to show that the method is more powerful than the original random forest-based pathway approach and the set-based test implemented in PLINK in the presence of gene-gene interactions. Finally, we applied the method to a breast cancer GWAS dataset and a lung cancer GWAS dataset and interesting pathways were identified that have implications for breast and lung cancers.     

Case-Control Association Testing of Common Variants from Sequencing of DNA Pools

While genome-wide association studies (GWAS) have been successful in identifying a large number of variants associated with disease, the challenge of locating the underlying causal loci remains. Sequencing of case and control DNA pools provides an inexpensive method for assessing all variation in a genomic region surrounding a significant GWAS result. However, individual variants need to be ranked in terms of the strength of their association to disease in order to prioritise follow-up by individual genotyping. A simple method for testing for case-control association in sequence data from DNA pools is presented that allows the partitioning of the variance in allele frequency estimates into components due to the sampling of chromosomes from the pool during sequencing, sampling individuals from the population and unequal contribution from individuals during pool construction. The utility of this method is demonstrated on a sequence from the alcohol dehydrogenase (ADH) gene cluster on a case-control sample for heavy alcohol consumption.     

ROADTRIPS: Case-Control Association Testing with Partially or Completely Unknown Population and Pedigree Structure

Genome-wide association studies are routinely conducted to identify genetic variants that influence complex disorders. It is well known that failure to properly account for population or pedigree structure can lead to spurious association as well as reduced power. We propose a method, ROADTRIPS, for case-control association testing in samples with partially or completely unknown population and pedigree structure. ROADTRIPS uses a covariance matrix estimated from genome-screen data to correct for unknown population and pedigree structure while maintaining high power by taking advantage of known pedigree information when it is available. ROADTRIPS can incorporate data on arbitrary combinations of related and unrelated individuals and is computationally feasible for the analysis of genetic studies with millions of markers. In simulations with related individuals and population structure, including admixture, we demonstrate that ROADTRIPS provides a substantial improvement over existing methods in terms of power and type 1 error. The ROADTRIPS method can be used across a variety of study designs, ranging from studies that have a combination of unrelated individuals and small pedigrees to studies of isolated founder populations with partially known or completely unknown pedigrees. We apply the method to analyze two data sets: a study of rheumatoid arthritis in small UK pedigrees, from Genetic Analysis Workshop 15, and data from the Collaborative Study of the Genetics of Alcoholism on alcohol dependence in a sample of moderate-size pedigrees of European descent, from Genetic Analysis Workshop 14. We detect genome-wide significant association, after Bonferroni correction, in both studies.     

DASH: a method for identical-by-descent haplotype mapping uncovers association with recent variation

Rare variants affecting phenotype pose a unique challenge for human genetics. Although genome-wide association studies have successfully detected many common causal variants, they are underpowered in identifying disease variants that are too rare or population-specific to be imputed from a general reference panel and thus are poorly represented on commercial SNP arrays. We set out to overcome these challenges and detect association between disease and rare alleles using SNP arrays by relying on long stretches of genomic sharing that are identical by descent. We have developed an algorithm, DASH, which builds upon pairwise identical-by-descent shared segments to infer clusters of individuals likely to be sharing a single haplotype. DASH constructs a graph with nodes representing individuals and links on the basis of such segments spanning a locus and uses an iterative minimum cut algorithm to identify densely connected components. We have applied DASH to simulated data and diverse GWAS data sets by constructing haplotype clusters and testing them for association. In simulations we show this approach to be significantly more powerful than single-marker testing in an isolated population that is from Kosrae, Federated States of Micronesia and has abundant IBD, and we provide orthogonal information for rare, recent variants in the outbred Wellcome Trust Case-Control Consortium (WTCCC) data. In both cohorts, we identified a number of haplotype associations, five such loci in the WTCCC data and ten in the isolated, that were conditionally significant beyond any individual nearby markers. We have replicated one of these loci in an independent European cohort and identified putative structural changes in low-pass whole-genome sequence of the cluster carriers.     

Retrospective Binary-Trait Association Test Elucidates Genetic Architecture of Crohn Disease

In genetic association testing, failure to properly control for population structure can lead to severely inflated type 1 error and power loss. Meanwhile, adjustment for relevant covariates is often desirable and sometimes necessary to protect against spurious association and to improve power. Many recent methods to account for population structure and covariates are based on linear mixed models (LMMs), which are primarily designed for quantitative traits. For binary traits, however, LMM is a misspecified model and can lead to deteriorated performance. We propose CARAT, a binary-trait association testing approach based on a mixed-effects quasi-likelihood framework, which exploits the dichotomous nature of the trait and achieves computational efficiency through estimating equations. We show in simulation studies that CARAT consistently outperforms existing methods and maintains high power in a wide range of population structure settings and trait models. Furthermore, CARAT is based on a retrospective approach, which is robust to misspecification of the phenotype model. We apply our approach to a genome-wide analysis of Crohn disease, in which we replicate association with 17 previously identified regions. Moreover, our analysis on 5p13.1, an extensively reported region of association, shows evidence for the presence of multiple independent association signals in the region. This example shows how CARAT can leverage known disease risk factors to shed light on the genetic architecture of complex traits.     

A note on interobserver error in multivariate analyses of populations

The effect of interobserver error on a principal components analysis of a small sample of human crania is examined. A comparison of individual specimen scores for components is made to find rotated principal components which identify interobserver error. The individual variables which load highly on such components are then tested for interobserver error univariately. Multivariate components which must identify interobserver error contain no high loadings for variables which demonstrate interobserver error in the univariate case. Principal component analysis, in defining new component variables, extracts such error in an easily identified way which makes comparison of samples measured by more than one anthropometrist more reliable.     

Identifying the Genetic Variation of Gene Expression Using Gene Sets: Application of Novel Gene Set eQTL Approach to PharmGKB and KEGG

Genetic variation underlying the regulation of mRNA gene expression in humans may provide key insights into the molecular mechanisms of human traits and complex diseases. Current statistical methods to map genetic variation associated with mRNA gene expression have typically applied standard linkage and/or association methods; however, when genome-wide SNP and mRNA expression data are available performing all pair wise comparisons is computationally burdensome and may not provide optimal power to detect associations. Consideration of different approaches to account for the high dimensionality and multiple testing issues may provide increased efficiency and statistical power. Here we present a novel approach to model and test the association between genetic variation and mRNA gene expression levels in the context of gene sets (GSs) and pathways, referred to as gene set - expression quantitative trait loci analysis (GS-eQTL). The method uses GSs to initially group SNPs and mRNA expression, followed by the application of principal components analysis (PCA) to collapse the variation and reduce the dimensionality within the GSs. We applied GS-eQTL to assess the association between SNP and mRNA expression level data collected from a cell-based model system using PharmGKB and KEGG defined GSs. We observed a large number of significant GS-eQTL associations, in which the most significant associations arose between genetic variation and mRNA expression from the same GS. However, a number of associations involving genetic variation and mRNA expression from different GSs were also identified. Our proposed GS-eQTL method effectively addresses the multiple testing limitations in eQTL studies and provides biological context for SNP-expression associations.     

GATES: a rapid and powerful gene-based association test using extended Simes procedure

The gene has been proposed as an attractive unit of analysis for association studies, but a simple yet valid, powerful, and sufficiently fast method of evaluating the statistical significance of all genes in large, genome-wide datasets has been lacking. Here we propose the use of an extended Simes test that integrates functional information and association evidence to combine the p values of the single nucleotide polymorphisms within a gene to obtain an overall p value for the association of the entire gene. Our computer simulations demonstrate that this test is more powerful than the SNP-based test, offers effective control of the type 1 error rate regardless of gene size and linkage-disequilibrium pattern among markers, and does not need permutation or simulation to evaluate empirical significance. Its statistical power in simulated data is at least comparable, and often superior, to that of several alternative gene-based tests. When applied to real genome-wide association study (GWAS) datasets on Crohn disease, the test detected more significant genes than SNP-based tests and alternative gene-based tests. The proposed test, implemented in an open-source package, has the potential to identify additional novel disease-susceptibility genes for complex diseases from large GWAS datasets.     

Robustness of group testing in the estimation of proportions

In binomial group testing, unlike one-at-a-time testing, the test unit consists of a group of individuals, and each group is declared to be defective or nondefective. A defective group is one that is presumed to include one or more defective (e.g., infected, positive) individuals and a nondefective group to contain only nondefective individuals. The usual binomial model considers the individuals being grouped as independent and identically distributed Bernoulli random variables. Under the binomial model and presuming that groups are tested and classified without error, it has been shown that, when the proportion of defective individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives. We discuss the robustness of group testing for estimating proportions when the underlying assumptions of (i) no testing errors and (ii) independent individuals are violated. To evaluate the effect of these model violations, two dilution-effect models and a serial correlation model are considered. Group testing proved to be quite robust to serial correlation. In the presence of a dilution effect, smaller group sizes should be used, but most of the benefits of group testing can still be realized.