Methods for meta‐analysis of multiple traits using GWAS summary statistics

Genome‐wide association studies (GWAS) for complex diseases have focused primarily on single‐trait analyses for disease status and disease‐related quantitative traits. For example, GWAS on risk factors for coronary artery disease analyze genetic associations of plasma lipids such as total cholesterol, LDL‐cholesterol, HDL‐cholesterol, and triglycerides (TGs) separately. However, traits are often correlated and a joint analysis may yield increased statistical power for association over multiple univariate analyses. Recently several multivariate methods have been proposed that require individual‐level data. Here, we develop metaUSAT (where USAT is unified score‐based association test), a novel unified association test of a single genetic variant with multiple traits that uses only summary statistics from existing GWAS. Although the existing methods either perform well when most correlated traits are affected by the genetic variant in the same direction or are powerful when only a few of the correlated traits are associated, metaUSAT is designed to be robust to the association structure of correlated traits. metaUSAT does not require individual‐level data and can test genetic associations of categorical and/or continuous traits. One can also use metaUSAT to analyze a single trait over multiple studies, appropriately accounting for overlapping samples, if any. metaUSAT provides an approximate asymptotic P‐value for association and is computationally efficient for implementation at a genome‐wide level. Simulation experiments show that metaUSAT maintains proper type‐I error at low error levels. It has similar and sometimes greater power to detect association across a wide array of scenarios compared to existing methods, which are usually powerful for some specific association scenarios only. When applied to plasma lipids summary data from the METSIM and the T2D‐GENES studies, metaUSAT detected genome‐wide significant loci beyond the ones identified by univariate analyses. Evidence from larger studies suggest that the variants additionally detected by our test are, indeed, associated with lipid levels in humans. In summary, metaUSAT can provide novel insights into the genetic architecture of a common disease or traits.     

Conditional analysis of multiple quantitative traits based on marginal GWAS summary statistics

There has been an increasing interest in joint association testing of multiple traits for possible pleiotropic effects. However, even in the presence of pleiotropy, most of the existing methods cannot distinguish direct and indirect effects of a genetic variant, say single‐nucleotide polymorphism (SNP), on multiple traits, and a conditional analysis of a trait adjusting for other traits is perhaps the simplest and most common approach to addressing this question. However, without individual‐level genotypic and phenotypic data but with only genome‐wide association study (GWAS) summary statistics, as typical with most large‐scale GWAS consortium studies, we are not aware of any existing method for such a conditional analysis. We propose such a conditional analysis, offering formulas of necessary calculations to fit a joint linear regression model for multiple quantitative traits. Furthermore, our method can also accommodate conditional analysis on multiple SNPs in addition to on multiple quantitative traits, which is expected to be useful for fine mapping. We provide numerical examples based on both simulated and real GWAS data to demonstrate the effectiveness of our proposed approach, and illustrate possible usefulness of conditional analysis by contrasting its result differences from those of standard marginal analyses.     

Truncated tests for combining evidence of summary statistics

To date, thousands of genetic variants to be associated with numerous human traits and diseases have been identified by genome-wide association studies (GWASs). The GWASs focus on testing the association between single trait and genetic variants. However, the analysis of multiple traits and single nucleotide polymorphisms (SNPs) might reflect physiological process of complex diseases and the corresponding study is called pleiotropy association analysis. Modern day GWASs report only summary statistics instead of individual-level phenotype and genotype data to avoid logistical and privacy issues. Existing methods for combining multiple phenotypes GWAS summary statistics mainly focus on low-dimensional phenotypes while lose power in high-dimensional cases. To overcome this defect, we propose two kinds of truncated tests to combine multiple phenotypes summary statistics. Extensive simulations show that the proposed methods are robust and powerful when the dimension of the phenotypes is high and only part of the phenotypes are associated with the SNPs. We apply the proposed methods to blood cytokines data collected from Finnish population. Results show that the proposed tests can identify additional genetic markers that are missed by single trait analysis.     

JAM: A Scalable Bayesian Framework for Joint Analysis of Marginal SNP Effects

Recently, large scale genome‐wide association study (GWAS) meta‐analyses have boosted the number of known signals for some traits into the tens and hundreds. Typically, however, variants are only analysed one‐at‐a‐time. This complicates the ability of fine‐mapping to identify a small set of SNPs for further functional follow‐up. We describe a new and scalable algorithm, joint analysis of marginal summary statistics (JAM), for the re‐analysis of published marginal summary stactistics under joint multi‐SNP models. The correlation is accounted for according to estimates from a reference dataset, and models and SNPs that best explain the complete joint pattern of marginal effects are highlighted via an integrated Bayesian penalized regression framework. We provide both enumerated and Reversible Jump MCMC implementations of JAM and present some comparisons of performance. In a series of realistic simulation studies, JAM demonstrated identical performance to various alternatives designed for single region settings. In multi‐region settings, where the only multivariate alternative involves stepwise selection, JAM offered greater power and specificity. We also present an application to real published results from MAGIC (meta‐analysis of glucose and insulin related traits consortium) – a GWAS meta‐analysis of more than 15,000 people. We re‐analysed several genomic regions that produced multiple significant signals with glucose levels 2 hr after oral stimulation. Through joint multivariate modelling, JAM was able to formally rule out many SNPs, and for one gene, ADCY5, suggests that an additional SNP, which transpired to be more biologically plausible, should be followed up with equal priority to the reported index.     

Genetic Association Analysis and Meta‐Analysis of Imputed SNPs in Longitudinal Studies

In this paper we propose a new method to analyze time‐to‐event data in longitudinal genetic studies. This method address the fundamental problem of incorporating uncertainty when analyzing survival data and imputed single‐nucleotide polymorphisms (SNPs) from genome‐wide association studies (GWAS). Our method incorporates uncertainty in the likelihood function, the opposite of existing methods that incorporate the uncertainty in the design matrix. Through simulation studies and real data analyses, we show that our proposed method is unbiased and provides powerful results. We also show how combining results from different GWAS (meta‐analysis) may lead to wrong results when effects are not estimated using our approach. The model is implemented in an R package that is designed to analyze uncertainty not only arising from imputed SNPs, but also from copy number variants.     

PSEA: Phenotype Set Enrichment Analysis--a new method for analysis of multiple phenotypes

Most genome-wide association studies (GWAS) are restricted to one phenotype, even if multiple related or unrelated phenotypes are available. However, an integrated analysis of multiple phenotypes can provide insight into their shared genetic basis and may improve the power of association studies. We present a new method, called "phenotype set enrichment analysis" (PSEA), which uses ideas of gene set enrichment analysis for the investigation of phenotype sets. PSEA combines statistics of univariate phenotype analyses and tests by permutation. It does not only allow analyzing predefined phenotype sets, but also to identify new phenotype sets. Apart from the application to situations where phenotypes and genotypes are available for each person, the method was adjusted to the analysis of GWAS summary statistics. PSEA was applied to data from the population-based cohort KORA F4 (N = 1,814) using iron-related and blood count traits. By confirming associations previously found in large meta-analyses on these traits, PSEA was shown to be a reliable tool. Many of these associations were not detectable by GWAS on single phenotypes in KORA F4. Therefore, the results suggest that PSEA can be more powerful than a single phenotype GWAS for the identification of association with multiple phenotypes. PSEA is a valuable method for analysis of multiple phenotypes, which can help to understand phenotype networks. Its flexible design enables both the use of prior knowledge and the generation of new knowledge on connection of multiple phenotypes. A software program for PSEA based on GWAS results is available upon request.     

A hierarchical clustering method for dimension reduction in joint analysis of multiple phenotypes

Genome‐wide association studies (GWAS) have become a very effective research tool to identify genetic variants of underlying various complex diseases. In spite of the success of GWAS in identifying thousands of reproducible associations between genetic variants and complex disease, in general, the association between genetic variants and a single phenotype is usually weak. It is increasingly recognized that joint analysis of multiple phenotypes can be potentially more powerful than the univariate analysis, and can shed new light on underlying biological mechanisms of complex diseases. In this paper, we develop a novel variable reduction method using hierarchical clustering method (HCM) for joint analysis of multiple phenotypes in association studies. The proposed method involves two steps. The first step applies a dimension reduction technique by using a representative phenotype for each cluster of phenotypes. Then, existing methods are used in the second step to test the association between genetic variants and the representative phenotypes rather than the individual phenotypes. We perform extensive simulation studies to compare the powers of multivariate analysis of variance (MANOVA), joint model of multiple phenotypes (MultiPhen), and trait‐based association test that uses extended simes procedure (TATES) using HCM with those of without using HCM. Our simulation studies show that using HCM is more powerful than without using HCM in most scenarios. We also illustrate the usefulness of using HCM by analyzing a whole‐genome genotyping data from a lung function study.     

A General Framework for Association Tests With Multivariate Traits in Large‐Scale Genomics Studies

Genetic association studies often collect data on multiple traits that are correlated. Discovery of genetic variants influencing multiple traits can lead to better understanding of the etiology of complex human diseases. Conventional univariate association tests may miss variants that have weak or moderate effects on individual traits. We propose several multivariate test statistics to complement univariate tests. Our framework covers both studies of unrelated individuals and family studies and allows any type/mixture of traits. We relate the marginal distributions of multivariate traits to genetic variants and covariates through generalized linear models without modeling the dependence among the traits or family members. We construct score‐type statistics, which are computationally fast and numerically stable even in the presence of covariates and which can be combined efficiently across studies with different designs and arbitrary patterns of missing data. We compare the power of the test statistics both theoretically and empirically. We provide a strategy to determine genome‐wide significance that properly accounts for the linkage disequilibrium (LD) of genetic variants. The application of the new methods to the meta‐analysis of five major cardiovascular cohort studies identifies a new locus (HSCB) that is pleiotropic for the four traits analyzed.     

Bayesian meta-analysis across genome-wide association studies of diverse phenotypes

Genome-wide association studies (GWAS) are a powerful tool for understanding the genetic basis of diseases and traits, but most studies have been conducted in isolation, with a focus on either a single or a set of closely related phenotypes. We describe MetABF, a simple Bayesian framework for performing integrative meta-analysis across multiple GWAS using summary statistics. The approach is applicable across a wide range of study designs and can increase the power by 50% compared with standard frequentist tests when only a subset of studies have a true effect. We demonstrate its utility in a meta-analysis of 20 diverse GWAS which were part of the Wellcome Trust Case Control Consortium 2. The novelty of the approach is its ability to explore, and assess the evidence for a range of possible true patterns of association across studies in a computationally efficient framework.     

Rare variant association test with multiple phenotypes

Although genome‐wide association studies (GWAS) have now discovered thousands of genetic variants associated with common traits, such variants cannot explain the large degree of “missing heritability,” likely due to rare variants. The advent of next generation sequencing technology has allowed rare variant detection and association with common traits, often by investigating specific genomic regions for rare variant effects on a trait. Although multiple correlated phenotypes are often concurrently observed in GWAS, most studies analyze only single phenotypes, which may lessen statistical power. To increase power, multivariate analyses, which consider correlations between multiple phenotypes, can be used. However, few existing multivariant analyses can identify rare variants for assessing multiple phenotypes. Here, we propose Multivariate Association Analysis using Score Statistics (MAAUSS), to identify rare variants associated with multiple phenotypes, based on the widely used sequence kernel association test (SKAT) for a single phenotype. We applied MAAUSS to whole exome sequencing (WES) data from a Korean population of 1,058 subjects to discover genes associated with multiple traits of liver function. We then assessed validation of those genes by a replication study, using an independent dataset of 3,445 individuals. Notably, we detected the gene ZNF620 among five significant genes. We then performed a simulation study to compare MAAUSS's performance with existing methods. Overall, MAAUSS successfully conserved type 1 error rates and in many cases had a higher power than the existing methods. This study illustrates a feasible and straightforward approach for identifying rare variants correlated with multiple phenotypes, with likely relevance to missing heritability.     

Resetting the bar: Statistical significance in whole‐genome sequencing‐based association studies of global populations

Genome‐wide association studies (GWAS) of common disease have been hugely successful in implicating loci that modify disease risk. The bulk of these associations have proven robust and reproducible, in part due to community adoption of statistical criteria for claiming significant genotype‐phenotype associations. As the cost of sequencing continues to drop, assembling large samples in global populations is becoming increasingly feasible. Sequencing studies interrogate not only common variants, as was true for genotyping‐based GWAS, but variation across the full allele frequency spectrum, yielding many more (independent) statistical tests. We sought to empirically determine genome‐wide significance thresholds for various analysis scenarios. Using whole‐genome sequence data, we simulated sequencing‐based disease studies of varying sample size and ancestry. We determined that future sequencing efforts in >2,000 samples of European, Asian, or admixed ancestry should set genome‐wide significance at approximately P = 5 × 10^?9, and studies of African samples should apply a more stringent genome‐wide significance threshold of P = 1 × 10^?9. Adoption of a revised multiple test correction will be crucial in avoiding irreproducible claims of association.     

A System‐Level Pathway‐Phenotype Association Analysis Using Synthetic Feature Random Forest

As the cost of genome‐wide genotyping decreases, the number of genome‐wide association studies (GWAS) has increased considerably. However, the transition from GWAS findings to the underlying biology of various phenotypes remains challenging. As a result, due to its system‐level interpretability, pathway analysis has become a popular tool for gaining insights on the underlying biology from high‐throughput genetic association data. In pathway analyses, gene sets representing particular biological processes are tested for significant associations with a given phenotype. Most existing pathway analysis approaches rely on single‐marker statistics and assume that pathways are independent of each other. As biological systems are driven by complex biomolecular interactions, embracing the complex relationships between single‐nucleotide polymorphisms (SNPs) and pathways needs to be addressed. To incorporate the complexity of gene‐gene interactions and pathway‐pathway relationships, we propose a system‐level pathway analysis approach, synthetic feature random forest (SF‐RF), which is designed to detect pathway‐phenotype associations without making assumptions about the relationships among SNPs or pathways. In our approach, the genotypes of SNPs in a particular pathway are aggregated into a synthetic feature representing that pathway via Random Forest (RF). Multiple synthetic features are analyzed using RF simultaneously and the significance of a synthetic feature indicates the significance of the corresponding pathway. We further complement SF‐RF with pathway‐based Statistical Epistasis Network (SEN) analysis that evaluates interactions among pathways. By investigating the pathway SEN, we hope to gain additional insights into the genetic mechanisms contributing to the pathway‐phenotype association. We apply SF‐RF to a population‐based genetic study of bladder cancer and further investigate the mechanisms that help explain the pathway‐phenotype associations using SEN. The bladder cancer associated pathways we found are both consistent with existing biological knowledge and reveal novel and plausible hypotheses for future biological validations.     

Meta‐analysis of genome‐wide association studies: no efficiency gain in using individual participant data

To identify genetic variants with modest effects on complex human diseases, a growing number of networks or consortia are created for sharing data from multiple genome‐wide association studies on the same disease or related disorders. A central question in this enterprise is whether to obtain summary results or individual participant data from relevant studies. We show theoretically and numerically that meta‐analysis of summary results is statistically as efficient as joint analysis of individual participant data (provided that both analyses are performed properly under the same modeling assumptions). We illustrate this equivalence with case‐control data from the Finland‐United States Investigation of NIDDM Genetics (FUSION) study. Collating only summary results will increase the number and representativeness of available studies, simplify data collection and analysis, reduce resource utilization, and accelerate discovery. Genet. Epidemiol. 34:60–66, 2010. © 2009 Wiley‐Liss, Inc.     

Meta‐analysis approaches to combine multiple gene set enrichment studies

In the field of gene set enrichment analysis (GSEA), meta‐analysis has been used to integrate information from multiple studies to present a reliable summarization of the expanding volume of individual biomedical research, as well as improve the power of detecting essential gene sets involved in complex human diseases. However, existing methods, Meta‐Analysis for Pathway Enrichment (MAPE), may be subject to power loss because of (1) using gross summary statistics for combining end results from component studies and (2) using enrichment scores whose distributions depend on the set sizes. In this paper, we adapt meta‐analysis approaches recently developed for genome‐wide association studies, which are based on fixed effect and random effects (RE) models, to integrate multiple GSEA studies. We further develop a mixed strategy via adaptive testing for choosing RE versus FE models to achieve greater statistical efficiency as well as flexibility. In addition, a size‐adjusted enrichment score based on a one‐sided Kolmogorov‐Smirnov statistic is proposed to formally account for varying set sizes when testing multiple gene sets. Our methods tend to have much better performance than the MAPE methods and can be applied to both discrete and continuous phenotypes. Specifically, the performance of the adaptive testing method seems to be the most stable in general situations.     

X chromosome association testing in genome wide association studies

Genome wide association studies (GWAS) have revealed many fascinating insights into complex diseases even from simple, single-marker statistical tests. Most of these tests are designed for testing of associations between a phenotype and an autosomal genotype and are therefore not applicable to X chromosome data. Testing for association on the X chromosome raises unique challenges that have motivated the development of X-specific statistical tests in the literature. However, to date there has been no study of these methods under a wide range of realistic study designs, allele frequencies and disease models to assess the size and power of each test. To address this, we have performed an extensive simulation study to investigate the effects of the sex ratios in the case and control cohorts, as well as the allele frequencies, on the size and power of eight test statistics under three different disease models that each account for X-inactivation. We show that existing, but under-used, methods that make use of both male and female data are uniformly more powerful than popular methods that make use of only female data. In particular, we show that Clayton's one degree of freedom statistic [Clayton, 2008] is robust and powerful across a wide range of realistic simulation parameters. Our results provide guidance on selecting the most appropriate test statistic to analyse X chromosome data from GWAS and show that much power can be gained by a more careful analysis of X chromosome GWAS data.     

Improved Evidence for Linkage on 6p and 5p with Retrospective Pooling of Data from Three Asthma Genome Screens

To improve our ability to identify genes for complex diseases, evaluation of new methods that retrospectively pool genotype and phenotype data collected by multiple centers is important. Availability of three whole‐genome screens enabled us to compare two methods, pooling raw data and meta‐analysis. Multipoint linkage analyses were performed on two outcomes, total serum IgE levels and asthma affection status, using an improved Haseman‐Elston algorithm. Two regions showed stronger evidence for linkage using covariate‐adjusted pooled data, compared with any individual sample. Both methods for pooling data identified strong linkage to Z‐transformed log_eIgE levels at a location between D6S1019 and D6S426, and to the asthma trait at D5S268. In conclusion, retrospective analysis of pooled genome scan data is a potentially powerful and useful method to examine both positive and negative evidence for linkage of quantitative and categorical phenotypes across populations. © 2001 Wiley‐Liss, Inc.     

Meta‐Analysis of Sequencing Studies With Heterogeneous Genetic Associations

Recent advances in sequencing technologies have made it possible to explore the influence of rare variants on complex diseases and traits. Meta‐analysis is essential to this exploration because large sample sizes are required to detect rare variants. Several methods are available to conduct meta‐analysis for rare variants under fixed‐effects models, which assume that the genetic effects are the same across all studies. In practice, genetic associations are likely to be heterogeneous among studies because of differences in population composition, environmental factors, phenotype and genotype measurements, or analysis method. We propose random‐effects models which allow the genetic effects to vary among studies and develop the corresponding meta‐analysis methods for gene‐level association tests. Our methods take score statistics, rather than individual participant data, as input and thus can accommodate any study designs and any phenotypes. We produce the random‐effects versions of all commonly used gene‐level association tests, including burden, variable threshold, and variance‐component tests. We demonstrate through extensive simulation studies that our random‐effects tests are substantially more powerful than the fixed‐effects tests in the presence of moderate and high between‐study heterogeneity and achieve similar power to the latter when the heterogeneity is low. The usefulness of the proposed methods is further illustrated with data from National Heart, Lung, and Blood Institute Exome Sequencing Project (NHLBI ESP). The relevant software is freely available.     

Statistics for X‐chromosome associations

In a genome‐wide association study (GWAS), association between genotype and phenotype at autosomal loci is generally tested by regression models. However, X‐chromosome data are often excluded from published analyses of autosomes because of the difference between males and females in number of X chromosomes. Failure to analyze X‐chromosome data at all is obviously less than ideal, and can lead to missed discoveries. Even when X‐chromosome data are included, they are often analyzed with suboptimal statistics. Several mathematically sensible statistics for X‐chromosome association have been proposed. The optimality of these statistics, however, is based on very specific simple genetic models. In addition, while previous simulation studies of these statistics have been informative, they have focused on single‐marker tests and have not considered the types of error that occur even under the null hypothesis when the entire X chromosome is scanned. In this study, we comprehensively tested several X‐chromosome association statistics using simulation studies that include the entire chromosome. We also considered a wide range of trait models for sex differences and phenotypic effects of X inactivation. We found that models that do not incorporate a sex effect can have large type I error in some cases. We also found that many of the best statistics perform well even when there are modest deviations, such as trait variance differences between the sexes or small sex differences in allele frequencies, from assumptions.