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.     

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.     

MF‐TOWmuT: Testing an optimally weighted combination of common and rare variants with multiple traits using family data

With rapid advancements of sequencing technologies and accumulations of electronic health records, a large number of genetic variants and multiple correlated human complex traits have become available in many genetic association studies. Thus, it becomes necessary and important to develop new methods that can jointly analyze the association between multiple genetic variants and multiple traits. Compared with methods that only use a single marker or trait, the joint analysis of multiple genetic variants and multiple traits is more powerful since such an analysis can fully incorporate the correlation structure of genetic variants and/or traits and their mutual dependence patterns. However, most of existing methods that simultaneously analyze multiple genetic variants and multiple traits are only applicable to unrelated samples. We develop a new method called MF‐TOWmuT to detect association of multiple phenotypes and multiple genetic variants in a genomic region with family samples. MF‐TOWmuT is based on an optimally weighted combination of variants. Our method can be applied to both rare and common variants and both qualitative and quantitative traits. Our simulation results show that (1) the type I error of MF‐TOWmuT is preserved; (2) MF‐TOWmuT outperforms two existing methods such as Multiple Family‐based Quasi‐Likelihood Score Test and Multivariate Family‐based Rare Variant Association Test in terms of power. We also illustrate the usefulness of MF‐TOWmuT by analyzing genotypic and phenotipic data from the Genetics of Kidneys in Diabetes study. R program is available at https://github.com/gaochengPRC/MF-TOWmuT .     

Kernel Approach for Modeling Interaction Effects in Genetic Association Studies of Complex Quantitative Traits

The etiology of complex traits likely involves the effects of genetic and environmental factors, along with complicated interaction effects between them. Consequently, there has been interest in applying genetic association tests of complex traits that account for potential modification of the genetic effect in the presence of an environmental factor. One can perform such an analysis using a joint test of gene and gene‐environment interaction. An optimal joint test would be one that remains powerful under a variety of models ranging from those of strong gene‐environment interaction effect to those of little or no gene‐environment interaction effect. To fill this demand, we have extended a kernel machine based approach for association mapping of multiple SNPs to consider joint tests of gene and gene‐environment interaction. The kernel‐based approach for joint testing is promising, because it incorporates linkage disequilibrium information from multiple SNPs simultaneously in analysis and permits flexible modeling of interaction effects. Using simulated data, we show that our kernel machine approach typically outperforms the traditional joint test under strong gene‐environment interaction models and further outperforms the traditional main‐effect association test under models of weak or no gene‐environment interaction effects. We illustrate our test using genome‐wide association data from the Grady Trauma Project, a cohort of highly traumatized, at‐risk individuals, which has previously been investigated for interaction effects.     

An Adaptive Association Test for Multiple Phenotypes with GWAS Summary Statistics

We study the problem of testing for single marker‐multiple phenotype associations based on genome‐wide association study (GWAS) summary statistics without access to individual‐level genotype and phenotype data. For most published GWASs, because obtaining summary data is substantially easier than accessing individual‐level phenotype and genotype data, while often multiple correlated traits have been collected, the problem studied here has become increasingly important. We propose a powerful adaptive test and compare its performance with some existing tests. We illustrate its applications to analyses of a meta‐analyzed GWAS dataset with three blood lipid traits and another with sex‐stratified anthropometric traits, and further demonstrate its potential power gain over some existing methods through realistic simulation studies. We start from the situation with only one set of (possibly meta‐analyzed) genome‐wide summary statistics, then extend the method to meta‐analysis of multiple sets of genome‐wide summary statistics, each from one GWAS. We expect the proposed test to be useful in practice as more powerful than or complementary to existing methods.     

A Fast Multiple‐Kernel Method With Applications to Detect Gene‐Environment Interaction

Kernel machine (KM) models are a powerful tool for exploring associations between sets of genetic variants and complex traits. Although most KM methods use a single kernel function to assess the marginal effect of a variable set, KM analyses involving multiple kernels have become increasingly popular. Multikernel analysis allows researchers to study more complex problems, such as assessing gene‐gene or gene‐environment interactions, incorporating variance‐component based methods for population substructure into rare‐variant association testing, and assessing the conditional effects of a variable set adjusting for other variable sets. The KM framework is robust, powerful, and provides efficient dimension reduction for multifactor analyses, but requires the estimation of high dimensional nuisance parameters. Traditional estimation techniques, including regularization and the “expectation‐maximization (EM)” algorithm, have a large computational cost and are not scalable to large sample sizes needed for rare variant analysis. Therefore, under the context of gene‐environment interaction, we propose a computationally efficient and statistically rigorous “fastKM” algorithm for multikernel analysis that is based on a low‐rank approximation to the nuisance effect kernel matrices. Our algorithm is applicable to various trait types (e.g., continuous, binary, and survival traits) and can be implemented using any existing single‐kernel analysis software. Through extensive simulation studies, we show that our algorithm has similar performance to an EM‐based KM approach for quantitative traits while running much faster. We also apply our method to the Vitamin Intervention for Stroke Prevention (VISP) clinical trial, examining gene‐by‐vitamin effects on recurrent stroke risk and gene‐by‐age effects on change in homocysteine level.     

USAT: A Unified Score‐Based Association Test for Multiple Phenotype‐Genotype Analysis

Genome‐wide association studies (GWASs) for complex diseases often collect data on multiple correlated endo‐phenotypes. Multivariate analysis of these correlated phenotypes can improve the power to detect genetic variants. Multivariate analysis of variance (MANOVA) can perform such association analysis at a GWAS level, but the behavior of MANOVA under different trait models has not been carefully investigated. In this paper, we show that MANOVA is generally very powerful for detecting association but there are situations, such as when a genetic variant is associated with all the traits, where MANOVA may not have any detection power. In these situations, marginal model based methods, however, perform much better than multivariate methods. We investigate the behavior of MANOVA, both theoretically and using simulations, and derive the conditions where MANOVA loses power. Based on our findings, we propose a unified score‐based test statistic USAT that can perform better than MANOVA in such situations and nearly as well as MANOVA elsewhere. Our proposed test reports an approximate asymptotic P‐value for association and is computationally very efficient to implement at a GWAS level. We have studied through extensive simulations the performance of USAT, MANOVA, and other existing approaches and demonstrated the advantage of using the USAT approach to detect association between a genetic variant and multivariate phenotypes. We applied USAT to data from three correlated traits collected on 5, 816 Caucasian individuals from the Atherosclerosis Risk in Communities (ARIC, The ARIC Investigators [ 1989 ]) Study and detected some interesting associations.     

Multiple SNP Set Analysis for Genome‐Wide Association Studies Through Bayesian Latent Variable Selection

The power of genome‐wide association studies (GWAS) for mapping complex traits with single‐SNP analysis (where SNP is single‐nucleotide polymorphism) may be undermined by modest SNP effect sizes, unobserved causal SNPs, correlation among adjacent SNPs, and SNP‐SNP interactions. Alternative approaches for testing the association between a single SNP set and individual phenotypes have been shown to be promising for improving the power of GWAS. We propose a Bayesian latent variable selection (BLVS) method to simultaneously model the joint association mapping between a large number of SNP sets and complex traits. Compared with single SNP set analysis, such joint association mapping not only accounts for the correlation among SNP sets but also is capable of detecting causal SNP sets that are marginally uncorrelated with traits. The spike‐and‐slab prior assigned to the effects of SNP sets can greatly reduce the dimension of effective SNP sets, while speeding up computation. An efficient Markov chain Monte Carlo algorithm is developed. Simulations demonstrate that BLVS outperforms several competing variable selection methods in some important scenarios.     

General Framework for Meta‐Analysis of Haplotype Association Tests

For complex traits, most associated single nucleotide variants (SNV) discovered to date have a small effect, and detection of association is only possible with large sample sizes. Because of patient confidentiality concerns, it is often not possible to pool genetic data from multiple cohorts, and meta‐analysis has emerged as the method of choice to combine results from multiple studies. Many meta‐analysis methods are available for single SNV analyses. As new approaches allow the capture of low frequency and rare genetic variation, it is of interest to jointly consider multiple variants to improve power. However, for the analysis of haplotypes formed by multiple SNVs, meta‐analysis remains a challenge, because different haplotypes may be observed across studies. We propose a two‐stage meta‐analysis approach to combine haplotype analysis results. In the first stage, each cohort estimate haplotype effect sizes in a regression framework, accounting for relatedness among observations if appropriate. For the second stage, we use a multivariate generalized least square meta‐analysis approach to combine haplotype effect estimates from multiple cohorts. Haplotype‐specific association tests and a global test of independence between haplotypes and traits are obtained within our framework. We demonstrate through simulation studies that we control the type‐I error rate, and our approach is more powerful than inverse variance weighted meta‐analysis of single SNV analysis when haplotype effects are present. We replicate a published haplotype association between fasting glucose‐associated locus (G6PC2) and fasting glucose in seven studies from the Cohorts for Heart and Aging Research in Genomic Epidemiology Consortium and we provide more precise haplotype effect estimates.     

Fine‐Mapping Additive and Dominant SNP Effects Using Group‐LASSO and Fractional Resample Model Averaging

Genomewide association studies (GWAS) sometimes identify loci at which both the number and identities of the underlying causal variants are ambiguous. In such cases, statistical methods that model effects of multiple single‐nucleotide polymorphisms (SNPs) simultaneously can help disentangle the observed patterns of association and provide information about how those SNPs could be prioritized for follow‐up studies. Current multi‐SNP methods, however, tend to assume that SNP effects are well captured by additive genetics; yet when genetic dominance is present, this assumption translates to reduced power and faulty prioritizations. We describe a statistical procedure for prioritizing SNPs at GWAS loci that efficiently models both additive and dominance effects. Our method, LLARRMA‐dawg, combines a group LASSO procedure for sparse modeling of multiple SNP effects with a resampling procedure based on fractional observation weights. It estimates for each SNP the robustness of association with the phenotype both to sampling variation and to competing explanations from other SNPs. In producing an SNP prioritization that best identifies underlying true signals, we show the following: our method easily outperforms a single‐marker analysis; when additive‐only signals are present, our joint model for additive and dominance is equivalent to or only slightly less powerful than modeling additive‐only effects; and when dominance signals are present, even in combination with substantial additive effects, our joint model is unequivocally more powerful than a model assuming additivity. We also describe how performance can be improved through calibrated randomized penalization, and discuss how dominance in ungenotyped SNPs can be incorporated through either heterozygote dosage or multiple imputation.     

SNP Set Association Analysis for Familial Data

Genome‐wide association studies (GWAS) are a popular approach for identifying common genetic variants and epistatic effects associated with a disease phenotype. The traditional statistical analysis of such GWAS attempts to assess the association between each individual single‐nucleotide polymorphism (SNP) and the observed phenotype. Recently, kernel machine‐based tests for association between a SNP set (e.g., SNPs in a gene) and the disease phenotype have been proposed as a useful alternative to the traditional individual‐SNP approach, and allow for flexible modeling of the potentially complicated joint SNP effects in a SNP set while adjusting for covariates. We extend the kernel machine framework to accommodate related subjects from multiple independent families, and provide a score‐based variance component test for assessing the association of a given SNP set with a continuous phenotype, while adjusting for additional covariates and accounting for within‐family correlation. We illustrate the proposed method using simulation studies and an application to genetic data from the Genetic Epidemiology Network of Arteriopathy (GENOA) study.     

Ordered multinomial regression for genetic association analysis of ordinal phenotypes at Biobank scale

Logistic regression is the primary analysis tool for binary traits in genome-wide association studies (GWAS). Multinomial regression extends logistic regression to multiple categories. However, many phenotypes more naturally take ordered, discrete values. Examples include (a) subtypes defined from multiple sources of clinical information and (b) derived phenotypes generated by specific phenotyping algorithms for electronic health records (EHR). GWAS of ordinal traits have been problematic. Dichotomizing can lead to a range of arbitrary cutoff values, generating inconsistent, hard to interpret results. Using multinomial regression ignores trait value hierarchy and potentially loses power. Treating ordinal data as quantitative can lead to misleading inference. To address these issues, we analyze ordinal traits with an ordered, multinomial model. This approach increases power and leads to more interpretable results. We derive efficient algorithms for computing test statistics, making ordinal trait GWAS computationally practical for Biobank scale data. Our method is available as a Julia package OrdinalGWAS.jl. Application to a COPDGene study confirms previously found signals based on binary case–control status, but with more significance. Additionally, we demonstrate the capability of our package to run on UK Biobank data by analyzing hypertension as an ordinal trait.     

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.     

Powerful statistical method to detect disease-associated genes using publicly available genome-wide association studies summary data

Genome-wide association studies (GWAS) have thus far achieved substantial success. In the last decade, a large number of common variants underlying complex diseases have been identified through GWAS. In most existing GWAS, the identified common variants are obtained by single marker-based tests, that is, testing one single-nucleotide polymorphism (SNP) at a time. Generally, the basic functional unit of inheritance is a gene, rather than a SNP. Thus, results from gene-level association test can be more readily integrated with downstream functional and pathogenic investigation. In this paper, we propose a general gene-based p-value adaptive combination approach (GPA) which can integrate association evidence of multiple genetic variants using only GWAS summary statistics (either p-value or other test statistics). The proposed method could be used to test genetic association for both continuous and binary traits through not only one study but also multiple studies, which would be helpful to overcome the limitation of existing methods that can only be applied to a specific type of data. We conducted thorough simulation studies to verify that the proposed method controls type I errors well, and performs favorably compared to single-marker analysis and other existing methods. We demonstrated the utility of our proposed method through analysis of GWAS meta-analysis results for fasting glucose and lipids from the international MAGIC consortium and Global Lipids Consortium, respectively. The proposed method identified some novel trait associated genes which can improve our understanding of the mechanisms involved in -cell function, glucose homeostasis, and lipids traits.     

A Whole‐Genome Simulator Capable of Modeling High‐Order Epistasis for Complex Disease

Genome‐wide association studies (GWAS) have been successful in finding numerous new risk variants for complex diseases, but the results almost exclusively rely on single‐marker scans. Methods that can analyze joint effects of many variants in GWAS data are still being developed and trialed. To evaluate the performance of such methods it is essential to have a GWAS data simulator that can rapidly simulate a large number of samples, and capture key features of real GWAS data such as linkage disequilibrium (LD) among single‐nucleotide polymorphisms (SNPs) and joint effects of multiple loci (multilocus epistasis). In the current study, we combine techniques for specifying high‐order epistasis among risk SNPs with an existing program GWAsimulator [Li and Li, 2008] to achieve rapid whole‐genome simulation with accurate modeling of complex interactions. We considered various approaches to specifying interaction models including the following: departure from product of marginal effects for pairwise interactions, product terms in logistic regression models for low‐order interactions, and penetrance tables conforming to marginal effect constraints for high‐order interactions or prescribing known biological interactions. Methods for conversion among different model specifications are developed using penetrance table as the fundamental characterization of disease models. The new program, called simGWA, is capable of efficiently generating large samples of GWAS data with high precision. We show that data simulated by simGWA are faithful to template LD structures, and conform to prespecified diseases models with (or without) interactions.     

Estimating and Testing Pleiotropy of Single Genetic Variant for Two Quantitative Traits

Along with the accumulated data of genetic variants and biomedical phenotypes in the genome era, statistical identification of pleiotropy is of growing interest for dissecting and understanding genetic correlations between complex traits. We proposed a novel method for estimating and testing pleiotropic effect of a genetic variant on two quantitative traits. Based on a covariance decomposition and estimation, our method quantifies pleiotropy as the portion of between‐trait correlation explained by the same genetic variant. Unlike most multiple‐trait methods that assess potential pleiotropy (i.e., whether a variant contributes to at least one trait), our method formulates a statistic that tests exact pleiotropy (i.e., whether a variant contributes to both of two traits). We developed two approaches (a regression approach and a bootstrapping approach) for such test and investigated their statistical properties, in comparison with other potential pleiotropy test methods. Our simulation shows that the regression approach produces correct P‐values under both the complete null (i.e., a variant has no effect on both two traits) and the incomplete null (i.e., a variant has effect on only one of two traits), but requires large sample sizes to achieve a good power, when the bootstrapping approach has a better power and produces conservative P‐values under the complete null. We demonstrate our method for detecting exact pleiotropy using a real GWAS dataset. Our method provides an easy‐to‐implement tool for measuring, testing, and understanding the pleiotropic effect of a single variant on the correlation architecture of two complex traits.     

Analyzing Association Mapping in Pedigree‐Based GWAS Using a Penalized Multitrait Mixed Model

Genome‐wide association studies (GWAS) have led to the identification of many genetic variants associated with complex diseases in the past 10 years. Penalization methods, with significant numerical and statistical advantages, have been extensively adopted in analyzing GWAS. This study has been partly motivated by the analysis of Genetic Analysis Workshop (GAW) 18 data, which have two notable characteristics. First, the subjects are from a small number of pedigrees and hence related. Second, for each subject, multiple correlated traits have been measured. Most of the existing penalization methods assume independence between subjects and traits and can be suboptimal. There are a few methods in the literature based on mixed modeling that can accommodate correlations. However, they cannot fully accommodate the two types of correlations while conducting effective marker selection. In this study, we develop a penalized multitrait mixed modeling approach. It accommodates the two different types of correlations and includes several existing methods as special cases. Effective penalization is adopted for marker selection. Simulation demonstrates its satisfactory performance. The GAW 18 data are analyzed using the proposed method.