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.     

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.     

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.     

Binomial Mixture Model Based Association Testing to Account for Genetic Heterogeneity for GWAS

Genome‐wide association studies (GWAS) have confirmed the ubiquitous existence of genetic heterogeneity for common disease: multiple common genetic variants have been identified to be associated, while many more are yet expected to be uncovered. However, the single SNP (single‐nucleotide polymorphism) based trend test (or its variants) that has been dominantly used in GWAS is based on contrasting the allele frequency difference between the case and control groups, completely ignoring possible genetic heterogeneity. In spite of the widely accepted notion of genetic heterogeneity, we are not aware of any previous attempt to apply genetic heterogeneity motivated methods in GWAS. Here, to explicitly account for unknown genetic heterogeneity, we applied a mixture model based single‐SNP test to the Wellcome Trust Case Control Consortium (WTCCC) GWAS data with traits of Crohn's disease, bipolar disease, coronary artery disease, and type 2 diabetes, identifying much larger numbers of significant SNPs and risk loci for each trait than those of the popular trend test, demonstrating potential power gain of the mixture model based test.     

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.     

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.     

Evaluating the Calibration and Power of Three Gene‐Based Association Tests of Rare Variants for the X Chromosome

Although genome‐wide association studies (GWAS) have identified thousands of trait‐associated genetic variants, there are relatively few findings on the X chromosome. For analysis of low‐frequency variants (minor allele frequency <5%), investigators can use region‐ or gene‐based tests where multiple variants are analyzed jointly to increase power. To date, there are no gene‐based tests designed for association testing of low‐frequency variants on the X chromosome. Here we propose three gene‐based tests for the X chromosome: burden, sequence kernel association test (SKAT), and optimal unified SKAT (SKAT‐O). Using simulated case‐control and quantitative trait (QT) data, we evaluate the calibration and power of these tests as a function of (1) male:female sample size ratio; and (2) coding of haploid male genotypes for variants under X‐inactivation. For case‐control studies, all three tests are reasonably well‐calibrated for all scenarios we evaluated. As expected, power for gene‐based tests depends on the underlying genetic architecture of the genomic region analyzed. Studies with more (haploid) males are generally less powerful due to decreased number of chromosomes. Power generally is slightly greater when the coding scheme for male genotypes matches the true underlying model, but the power loss for misspecifying the (generally unknown) model is small. For QT studies, type I error and power results largely mirror those for binary traits. We demonstrate the use of these three gene‐based tests for X‐chromosome association analysis in simulated data and sequencing data from the Genetics of Type 2 Diabetes (GoT2D) 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.     

Pleiotropy Analysis of Quantitative Traits at Gene Level by Multivariate Functional Linear Models

In genetics, pleiotropy describes the genetic effect of a single gene on multiple phenotypic traits. A common approach is to analyze the phenotypic traits separately using univariate analyses and combine the test results through multiple comparisons. This approach may lead to low power. Multivariate functional linear models are developed to connect genetic variant data to multiple quantitative traits adjusting for covariates for a unified analysis. Three types of approximate F‐distribution tests based on Pillai–Bartlett trace, Hotelling–Lawley trace, and Wilks's Lambda are introduced to test for association between multiple quantitative traits and multiple genetic variants in one genetic region. The approximate F‐distribution tests provide much more significant results than those of F‐tests of univariate analysis and optimal sequence kernel association test (SKAT‐O). Extensive simulations were performed to evaluate the false positive rates and power performance of the proposed models and tests. We show that the approximate F‐distribution tests control the type I error rates very well. Overall, simultaneous analysis of multiple traits can increase power performance compared to an individual test of each trait. The proposed methods were applied to analyze (1) four lipid traits in eight European cohorts, and (2) three biochemical traits in the Trinity Students Study. The approximate F‐distribution tests provide much more significant results than those of F‐tests of univariate analysis and SKAT‐O for the three biochemical traits. The approximate F‐distribution tests of the proposed functional linear models are more sensitive than those of the traditional multivariate linear models that in turn are more sensitive than SKAT‐O in the univariate case. The analysis of the four lipid traits and the three biochemical traits detects more association than SKAT‐O in the univariate case.     

Pathway‐Based Association Study of Multiple Candidate Genes and Multiple Traits Using Structural Equation Models

There is increasing interest in the joint analysis of multiple genetic variants from multiple genes and multiple correlated quantitative traits in association studies. The classical approach involves testing univariate associations between genotypes and phenotypes and correcting for multiple testing that results in loss of power to detect associations. In this paper, we propose modeling complex relationships between genetic variants in candidate genes and measured correlated traits using structural equation models (SEM), taking advantage of prior knowledge on clinical and genetic pathways. We adopt generalized structured component analysis (GSCA) as an approach to SEM and develop a single association test between multiple genetic variants in a gene and a set of correlated traits, taking into account all available data from other genes and other traits. The performance of this test is investigated by simulations. We apply the proposed method to the Quebec Child and Adolescent Health and Social Survey (1999) data to investigate genetic associations with cardiovascular disease‐related traits.     

A modified forward multiple regression in high‐density genome‐wide association studies for complex traits

Genome‐wide association studies (GWAS) have been widely used to identify genetic effects on complex diseases or traits. Most currently used methods are based on separate single‐nucleotide polymorphism (SNP) analyses. Because this approach requires correction for multiple testing to avoid excessive false‐positive results, it suffers from reduced power to detect weak genetic effects under limited sample size. To increase the power to detect multiple weak genetic factors and reduce false‐positive results caused by multiple tests and dependence among test statistics, a modified forward multiple regression (MFMR) approach is proposed. Simulation studies show that MFMR has higher power than the Bonferroni and false discovery rate procedures for detecting moderate and weak genetic effects, and MFMR retains an acceptable‐false positive rate even if causal SNPs are correlated with many SNPs due to population stratification or other unknown reasons. Genet. Epidemiol. 33:518–525, 2009. © 2009 Wiley‐Liss, Inc.     

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.     

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.     

Pathway‐Based Approaches for Sequencing‐Based Genome‐Wide Association Studies

For analyzing complex trait association with sequencing data, most current studies test aggregated effects of variants in a gene or genomic region. Although gene‐based tests have insufficient power even for moderately sized samples, pathway‐based analyses combine information across multiple genes in biological pathways and may offer additional insight. However, most existing pathway association methods are originally designed for genome‐wide association studies, and are not comprehensively evaluated for sequencing data. Moreover, region‐based rare variant association methods, although potentially applicable to pathway‐based analysis by extending their region definition to gene sets, have never been rigorously tested. In the context of exome‐based studies, we use simulated and real datasets to evaluate pathway‐based association tests. Our simulation strategy adopts a genome‐wide genetic model that distributes total genetic effects hierarchically into pathways, genes, and individual variants, allowing the evaluation of pathway‐based methods with realistic quantifiable assumptions on the underlying genetic architectures. The results show that, although no single pathway‐based association method offers superior performance in all simulated scenarios, a modification of Gene Set Enrichment Analysis approach using statistics from single‐marker tests without gene‐level collapsing (weighted Kolmogrov‐Smirnov [WKS]‐Variant method) is consistently powerful. Interestingly, directly applying rare variant association tests (e.g., sequence kernel association test) to pathway analysis offers a similar power, but its results are sensitive to assumptions of genetic architecture. We applied pathway association analysis to an exome‐sequencing data of the chronic obstructive pulmonary disease, and found that the WKS‐Variant method confirms associated genes previously published.     

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.     

Detecting rare variants for complex traits using family and unrelated data

Large genome‐wide association studies (GWAS) have been performed to detect common genetic variants involved in common diseases, but most of the variants found this way account for only a small portion of the trait variance. Furthermore, candidate gene‐based resequencing suggests that many rare genetic variants contribute to the trait variance of common diseases. Here we propose two designs, sibpair and unrelated‐case designs, to detect rare genetic variants in either a candidate gene‐based or genome‐wide association analysis. First we show that we can detect and classify together rare risk haplotypes using a relatively small sample with either of these designs, and then have increased power to test association in a larger case‐control sample. This method can also be applied to resequencing data. Next we apply the method to the Wellcome Trust Case Control Consortium (WTCCC) coronary artery disease (CAD) and hypertension (HT) data, the latter being the only trait for which no genome‐wide association evidence was reported in the original WTCCC study, and identify one interesting gene associated with HT and four associated with CAD at a genome‐wide significance level of 5%. These results suggest that searching for rare genetic variants is feasible and can be fruitful in current GWAS, candidate gene studies or resequencing studies. Genet. Epidemiol. 34: 171–187, 2010. © 2009 Wiley‐Liss, Inc.     

Genome‐wide association scans for secondary traits using case‐control samples

Genome‐wide association studies (GWAS) require considerable investment, so researchers often study multiple traits collected on the same set of subjects to maximize return. However, many GWAS have adopted a case‐control design; improperly accounting for case‐control ascertainment can lead to biased estimates of association between markers and secondary traits. We show that under the null hypothesis of no marker‐secondary trait association, naïve analyses that ignore ascertainment or stratify on case‐control status have proper Type I error rates except when both the marker and secondary trait are independently associated with disease risk. Under the alternative hypothesis, these methods are unbiased when the secondary trait is not associated with disease risk. We also show that inverse‐probability‐of‐sampling‐weighted (IPW) regression provides unbiased estimates of marker‐secondary trait association. We use simulation to quantify the Type I error, power and bias of naïve and IPW methods. IPW regression has appropriate Type I error in all situations we consider, but has lower power than naïve analyses. The bias for naïve analyses is small provided the marker is independent of disease risk. Considering the majority of tested markers in a GWAS are not associated with disease risk, naïve analyses provide valid tests of and nearly unbiased estimates of marker‐secondary trait association. Care must be taken when there is evidence that both the secondary trait and tested marker are associated with the primary disease, a situation we illustrate using an analysis of the relationship between a marker in FGFR2 and mammographic density in a breast cancer case‐control sample. Genet. Epidemiol. 33:717–728, 2009. © 2009 Wiley‐Liss, Inc.     

A Robust Method for Genome‐Wide Association Meta‐Analysis With the Application to Circulating Insulin‐Like Growth Factor I Concentrations

Genome‐wide association studies (GWAS) offer an excellent opportunity to identify the genetic variants underlying complex human diseases. Successful utilization of this approach requires a large sample size to identify single nucleotide polymorphisms (SNPs) with subtle effects. Meta‐analysis is a cost‐efficient means to achieve large sample size by combining data from multiple independent GWAS; however, results from studies performed on different populations can be variable due to various reasons, including varied linkage equilibrium structures as well as gene‐gene and gene‐environment interactions. Nevertheless, one should expect effects of the SNP are more similar between similar populations than those between populations with quite different genetic and environmental backgrounds. Prior information on populations of GWAS is often not considered in current meta‐analysis methods, rendering such analyses less optimal for the detecting association. This article describes a test that improves meta‐analysis to incorporate variable heterogeneity among populations. The proposed method is remarkably simple in computation and hence can be performed in a rapid fashion in the setting of GWAS. Simulation results demonstrate the validity and higher power of the proposed method over conventional methods in the presence of heterogeneity. As a demonstration, we applied the test to real GWAS data to identify SNPs associated with circulating insulin‐like growth factor I concentrations.