Joint Analysis of Multiple Traits in Rare Variant Association Studies

The joint analysis of multiple traits has recently become popular since it can increase statistical power to detect genetic variants and there is increasing evidence showing that pleiotropy is a widespread phenomenon in complex diseases. Currently, the majority of existing methods for the joint analysis of multiple traits test association between one common variant and multiple traits. However, the variant‐by‐variant methods for common variant association studies may not be optimal for rare variant association studies due to the allelic heterogeneity as well as the extreme rarity of individual variants. Current statistical methods for rare variant association studies are for one single trait only. In this paper, we propose an adaptive weighting reverse regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compare the performance of AWRR with canonical correlation analysis (CCA), Single‐TOW, and the weighted sum reverse regression (WSRR). Our results show that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most scenarios, AWRR is more powerful than Single‐TOW and WSRR.     

A Family‐Based Robust Multivariate Association Test Using Maximum Statistic

For characterizing the genetic mechanisms of complex diseases familial data with multiple correlated quantitative traits are usually collected in genetic studies. To analyze such data, various multivariate tests have been proposed to investigate the association between the underlying disease genes and the multiple traits. Although these multivariate association tests may have better power performance than the univariate association tests, they suffer from loss of testing power when the genetic models of the putative genes are misspecified. To address the problem, in this paper we aim to develop a family‐based robust multivariate association test. We will first establish the optimal multivariate score tests for the recessive, additive, and dominant genetic models. Based on these optimal tests, a maximum‐type robust multivariate association test is then obtained. Simulations are conducted to compare the power of our method with that of other existing multivariate methods. The results show that the robust multivariate test does manifest the robustness in power over all plausible genetic models. A practical data set is applied to demonstrate the applicability of our approach. The results suggest that the robust multivariate test is more powerful than the robust univariate test when dealing with multiple quantitative traits.     

Robust Quantitative Trait Association Tests in the Parent-Offspring Triad Design: Conditional Likelihood-Based Approaches

Association studies, based on either population data or familial data, have been widely applied to mapping of genes underlying complex diseases. In family-based association studies, using case-parent triad families, the popularly used transmission/disequilibrium test (TDT) was proposed for avoidance of spurious association results caused by other confounders such as population stratification. Originally, the TDT was developed for analysis of binary disease data. Extending it to allow for quantitative trait analysis of complex diseases and for robust analysis of binary diseases against the uncertainty of mode of inheritance has been thoroughly discussed. Nevertheless, studies on robust analysis of quantitative traits for complex diseases received relatively less attention. In this paper, we use parent-offspring triad families to demonstrate the feasibility of establishment of the robust candidate-gene association tests for quantitative traits. We first introduce the score statistics from the conditional likelihoods based on parent-offspring triad data under various genetic models. By applying two existing robust procedures we then construct the robust association tests for analysis of quantitative traits. Simulations are conducted to evaluate empirical type I error rates and powers of the proposed robust tests. The results show that these robust association tests do exhibit robustness against the effect of misspecification of the underlying genetic model on testing powers.     

Joint Identification of Multiple Genetic Variants via Elastic‐Net Variable Selection in a Genome‐Wide Association Analysis

Unraveling the genetic background of common complex traits is a major goal in modern genetics. In recent years, genome‐wide association (GWA) studies have been conducted with large‐scale data sets of genetic variants. Most of those studies have relied on single‐marker approaches that identify single genetic factors individually and can be limited in considering fully the joint effects of multiple genetic factors on complex traits. Joint identification of multiple genetic factors would be more powerful and would provide better prediction on complex traits since it utilizes combined information across variants. Here we propose a multi‐stage approach for GWA analysis: (1) prescreening, (2) joint identification of putative SNPs based on elastic‐net variable selection, and (3) empirical replication using bootstrap samples. Our approach enables an efficient joint search for genetic associations in GWA analysis. The suggested empirical replication method can be beneficial in GWA studies because one can avoid a costly, independent replication study while eliminating false‐positive associations and focusing on a smaller number of replicable variants. We applied the proposed approach to a GWA analysis, and jointly identified 129 genetic variants having an association with adult height in a Korean population.     

Tests of Association Between Quantitative Traits and Haplotypes In A Reduced-Dimensional Space

Candidate gene association tests are currently performed using several intragenic SNPs simultaneously, by testing SNP haplotype or genotype effects in multifactorial diseases or traits. The number of haplotypes drastically increases with an increase in the number of typed SNPs. As a result, large numbers of haplotypes will introduce large degrees of freedom in haplotype‐based tests, and thus limit the power of the tests. In this study we propose using the principal component method to reduce the dimension, and then construct association tests on the lower‐dimensional space to test the association between haplotypes and a quantitative trait using population‐based samples. The proposed method allows ambiguous haplotypes. We use simulation studies to evaluate the type I error rate of the tests, and compare the power of the proposed tests with that of the tests without dimension reduction, and the tests with dimension reduction by merging rare haplotypes. The simulation results show that the proposed tests have correct type I error rates and are more powerful than other tests in most cases considered in our simulation studies.     

EMK: A Novel Program for Family-Based Allelic and Genotypic Association Tests on Quantitative Traits

The QTDT program is a widely‐used program for analyzing quantitative trait data, but the methods mainly test allelic association. Since the genotype of a marker is a direct observation for an individual, it is of interest to assess association at the genotypic level. In this study, we extended the allele‐based association method developed by Monks and Kaplan (MK method) to genotype‐based association tests for quantitative traits. We implemented a novel extended MK (EMK) program that can perform both allele‐ and genotype‐ based association tests in any pedigree structure. To evaluate the performance of EMK, we utilized simulated pedigree data and real data from our previous report of GSTO1 and GSTO2 genes in Alzheimer disease (AD). Both allele‐ and genotype‐based EMK methods (allele‐EMK and geno‐EMK) showed correct type I error for various pedigree structures and admixture populations. The geno‐EMK method showed comparable power to the allele‐EMK test. By treating age‐at‐onset (AAO) as a quantitative trait, the EMK program was able to detect significant associations for rs4925 in GSTO1 (P= 0.006 for allele‐EMK and P= 0.009 for geno‐EMK), and rs2297235 in GSTO2 (P= 0.005 for allele‐EMK and P= 0.009 for geno‐EMK), which are consistent with our previous findings.     

Using Tree-Based Recursive Partitioning Methods to Group Haplotypes for Increased Power in Association Studies

Motivated by the increasing availability of high‐density single nucleotide polymorphism (SNP) markers across the genome, various haplotype‐based methods have been developed for candidate gene association studies, and even for genome‐wide association studies. Although haplotype approaches dramatically reduce the multiple comparisons problem (as compared to single SNP analysis), even the number of existing haplotypes is relatively large, which increases the degrees of freedom and decreases the power for the corresponding test statistic. Grouping haplotypes is a way to reduce the degrees of freedom. We propose a procedure that uses a tree‐based recursive partitioning algorithm to group haplotypes into a small number of clusters, and conducts the association test based on groups of haplotypes instead of individual haplotypes. The method can be used for both population‐based and family‐based association studies, with known or ambiguous phase information. Simulation studies suggest that the proposed method has the right type I error rate, and is more powerful than some existing haplotype‐based tests.     

U‐Statistics‐based Tests for Multiple Genes in Genetic Association Studies

As our understanding of biological pathways and the genes that regulate these pathways increases, consideration of these biological pathways has become an increasingly important part of genetic and molecular epidemiology. Pathway‐based genetic association studies often involve genotyping of variants in genes acting in certain biological pathways. Such pathway‐based genetic association studies can potentially capture the highly heterogeneous nature of many complex traits, with multiple causative loci and multiple alleles at some of the causative loci. In this paper, we develop two nonparametric test statistics that consider simultaneously the effects of multiple markers. Our approach, which is based on data‐adaptive U‐statistics, can handle both qualitative data such as case‐control data and quantitative continuous phenotype data. Simulations demonstrate that our proposed methods are more powerful than standard methods, especially when there are multiple risk loci each with small genetic effects. When the number of disease‐predisposing genes is small, the data‐adaptive weighting of the U‐statistics over all the markers produces similar power to commonly used single marker tests. We further illustrate the potential merits of our proposed tests in the analysis of a data set from a pathway‐based candidate gene association study of breast cancer and hormone metabolism pathways. Finally, potential applications of the proposed tests to genome‐wide association studies are also discussed.     

Multivariate Association Test Using Haplotype Trend Regression

Genetic association analyses with haplotypes may be more powerful than analyses with single markers, under certain conditions. Furthermore, simultaneously considering multiple correlated traits may make use of additional information that would not be considered when analyzing individual traits. In this study, we propose a haplotype based test of association for multivariate quantitative traits in unrelated samples. Specifically, we extend a population based haplotype trend regression (HTR) approach to multivariate scenarios. We mainly focused on bivariate HTR, and the simulation results showed that the proposed method had correct pre-specified type-I error rates. The power of the proposed method was largely influenced by the size and source of correlation between variables, being greatest when correlation of a specific gene was opposite in sign to the residual correlation.     

Post‐Genome‐Wide Association Study Challenges for Lipid Traits: Describing Age as a Modifier of Gene‐Lipid Associations in the Population Architecture Using Genomics and Epidemiology (PAGE) Study

Numerous common genetic variants that influence plasma high‐density lipoprotein cholesterol, low‐density lipoprotein cholesterol (LDL‐C), and triglyceride distributions have been identified via genome‐wide association studies (GWAS). However, whether or not these associations are age‐dependent has largely been overlooked. We conducted an association study and meta‐analysis in more than 22,000 European Americans between 49 previously identified GWAS variants and the three lipid traits, stratified by age (males: <50 or ≥50 years of age; females: pre‐ or postmenopausal). For each variant, a test of heterogeneity was performed between the two age strata and significant P_het values were used as evidence of age‐specific genetic effects. We identified seven associations in females and eight in males that displayed suggestive heterogeneity by age (P_het < 0.05). The association between rs174547 (FADS1) and LDL‐C in males displayed the most evidence for heterogeneity between age groups (P_het = 1.74E‐03, I² = 89.8), with a significant association in older males (P = 1.39E‐06) but not younger males (P = 0.99). However, none of the suggestive modifying effects survived adjustment for multiple testing, highlighting the challenges of identifying modifiers of modest SNP‐trait associations despite large sample sizes.     

A Family‐Based Joint Test for Mean and Variance Heterogeneity for Quantitative Traits

Traditional quantitative trait locus (QTL) analysis focuses on identifying loci associated with mean heterogeneity. Recent research has discovered loci associated with phenotype variance heterogeneity (vQTL), which is important in studying genetic association with complex traits, especially for identifying gene–gene and gene–environment interactions. While several tests have been proposed to detect vQTL for unrelated individuals, there are no tests for related individuals, commonly seen in family‐based genetic studies. Here we introduce a likelihood ratio test (LRT) for identifying mean and variance heterogeneity simultaneously or for either effect alone, adjusting for covariates and family relatedness using a linear mixed effect model approach. The LRT test statistic for normally distributed quantitative traits approximately follows χ²‐distributions. To correct for inflated Type I error for non‐normally distributed quantitative traits, we propose a parametric bootstrap‐based LRT that removes the best linear unbiased prediction (BLUP) of family random effect. Simulation studies show that our family‐based test controls Type I error and has good power, while Type I error inflation is observed when family relatedness is ignored. We demonstrate the utility and efficiency gains of the proposed method using data from the Framingham Heart Study to detect loci associated with body mass index (BMI) variability.     

A fast multilocus test with adaptive SNP selection for large-scale genetic-association studies

As increasing evidence suggests that multiple correlated genetic variants could jointly influence the outcome, a multilocus test that aggregates association evidence across multiple genetic markers in a considered gene or a genomic region may be more powerful than a single-marker test for detecting susceptibility loci. We propose a multilocus test, AdaJoint, which adopts a variable selection procedure to identify a subset of genetic markers that jointly show the strongest association signal, and defines the test statistic based on the selected genetic markers. The P-value from the AdaJoint test is evaluated by a computationally efficient algorithm that effectively adjusts for multiple-comparison, and is hundreds of times faster than the standard permutation method. Simulation studies demonstrate that AdaJoint has the most robust performance among several commonly used multilocus tests. We perform multilocus analysis of over 26 000 genes/regions on two genome-wide association studies of pancreatic cancer. Compared with its competitors, AdaJoint identifies a much stronger association between the gene CLPTM1L and pancreatic cancer risk (6.0 × 10⁻⁸), with the signal optimally captured by two correlated single-nucleotide polymorphisms (SNPs). Finally, we show AdaJoint as a powerful tool for mapping cis-regulating methylation quantitative trait loci on normal breast tissues, and find many CpG sites whose methylation levels are jointly regulated by multiple SNPs nearby.     

Bivariate association analysis in selected samples: application to a GWAS of two bone mineral density phenotypes in males with high or low BMD

Our specific aims were to evaluate the power of bivariate analysis and to compare its performance with traditional univariate analysis in samples of unrelated subjects under varying sampling selection designs. Bivariate association analysis was based on the seemingly unrelated regression (SUR) model that allows different genetic models for different traits. We conducted extensive simulations for the case of two correlated quantitative phenotypes, with the quantitative trait locus making equal or unequal contributions to each phenotype. Our simulation results confirmed that the power of bivariate analysis is affected by the size, direction and source of the phenotypic correlations between traits. They also showed that the optimal sampling scheme depends on the size and direction of the induced genetic correlation. In addition, we demonstrated the efficacy of SUR-based bivariate test by applying it to a real Genome-Wide Association Study (GWAS) of Bone Mineral Density (BMD) values measured at the lumbar spine (LS) and at the femoral neck (FN) in a sample of unrelated males with low BMD (LS Z-scores ≤ -2) and with high BMD (LS and FN Z-scores >0.5). A substantial amount of top hits in bivariate analysis did not reach nominal significance in any of the two single-trait analyses. Altogether, our studies suggest that bivariate analysis is of practical significance for GWAS of correlated phenotypes.     

Impact on Modes of Inheritance and Relative Risks of Using Extreme Sampling When Designing Genetic Association Studies

Using extreme phenotypes for association studies can improve statistical power . We study the impact of using samples with extremely high or low traits on the alternative model space, the genotype relative risks, and the genetic models in association studies. We prove the following results: when the risk allele causes high‐trait values, the more extreme the high traits, the larger the genotype relative risks, which is not always true for using extreme low traits; we also prove that a genetic model theoretically changes with more extreme trait except for the recessive or dominant models. Practically, however, the impact of deviations from the true genetic model at a functional locus due to selective sampling is virtually negligible. The implications of our findings are discussed. Numerical values are reported for illustrations.     

Sequential Sentinel SNP Regional Association Plots (SSS‐RAP): An Approach for Testing Independence of SNP Association Signals Using Meta‐Analysis Data

Genome‐Wide Association Studies (GWAS) frequently incorporate meta‐analysis within their framework. However, conditional analysis of individual‐level data, which is an established approach for fine mapping of causal sites, is often precluded where only group‐level summary data are available for analysis. Here, we present a numerical and graphical approach, “sequential sentinel SNP regional association plot” (SSS‐RAP), which estimates regression coefficients (beta) with their standard errors using the meta‐analysis summary results directly. Under an additive model, typical for genes with small effect, the effect for a sentinel SNP can be transformed to the predicted effect for a possibly dependent SNP through a 2×2 2‐SNP haplotypes table. The approach assumes Hardy–Weinberg equilibrium for test SNPs. SSS‐RAP is available as a Web‐tool ( http://apps.biocompute.org.uk/sssrap/sssrap.cgi ). To develop and illustrate SSS‐RAP we analyzed lipid and ECG traits data from the British Women's Heart and Health Study (BWHHS), evaluated a meta‐analysis for ECG trait and presented several simulations. We compared results with existing approaches such as model selection methods and conditional analysis. Generally findings were consistent. SSS‐RAP represents a tool for testing independence of SNP association signals using meta‐analysis data, and is also a convenient approach based on biological principles for fine mapping in group level summary data.     

Gene finding strategies

Both linkage and association methods have been used to localise and identify genes related to behaviour and other complex traits. The linkage approach (parametric or non-parametric) can be used for whole genome screens to localise genes of unknown function. The parametric linkage approach is very effective for locating single-gene disorders and is usually based on large family pedigrees. The non-parametric method is useful to detect quantitative trait loci (QTLs) for complex traits and was originally developed for sib pair analyses. Genetic association studies are most often used to test the association of alleles at a candidate gene with a disease or with levels of a quantitative trait. Allelic association between a trait and a marker can be studied in a case-control design, but because of possible problems due to population stratification, within-family designs have been proposed as the optimal test for association.     

Association analysis for quantitative traits by data mining: QHPM

Previously, we have presented a data mining-based algorithmic approach to genetic association analysis, Haplotype Pattern Mining. We have now extended the approach with the possibility of analysing quantitative traits and utilising covariates. This is accomplished by using a linear model for measuring association. We present results with the extended version, QHPM, with simulated quantitative trait data. One data set was simulated with the population simulator package Populus, and another was obtained from GAW12. In the former, there were 2–3 underlying susceptibility genes for a trait, each with several ancestral disease mutations, and 1 or 2 environmental components. We show that QHPM is capable of finding the susceptibility loci, even when there is strong allelic heterogeneity and environmental effects in the disease models. The power of finding quantitative trait loci is dependent on the ascertainment scheme of the data: collecting the study subjects from both ends of the quantitative trait distribution is more effective than using unselected individuals or individuals ascertained based on disease status, but QHPM has good power to localize the genes even with unselected individuals. Comparison with quantitative trait TDT (QTDT) showed that QHPM has better localization accuracy when the gene effect is weak.     

Association analysis for quantitative traits by data mining: QHPM

Previously, we have presented a data mining-based algorithmic approach to genetic association analysis, Haplotype Pattern Mining. We have now extended the approach with the possibility of analysing quantitative traits and utilising covariates. This is accomplished by using a linear model for measuring association. We present results with the extended version, QHPM, with simulated quantitative trait data. One data set was simulated with the population simulator package Populus, and another was obtained from GAW12. In the former, there were 2-3 underlying susceptibility genes for a trait, each with several ancestral disease mutations, and 1 or 2 environmental components. We show that QHPM is capable of finding the susceptibility loci, even when there is strong allelic heterogeneity and environmental effects in the disease models. The power of finding quantitative trait loci is dependent on the ascertainment scheme of the data: collecting the study subjects from both ends of the quantitative trait distribution is more effective than using unselected individuals or individuals ascertained based on disease status, but QHPM has good power to localize the genes even with unselected individuals. Comparison with quantitative trait TDT (QTDT) showed that QHPM has better localization accuracy when the gene effect is weak.     

Effectiveness of Shrinkage and Variable Selection Methods for the Prediction of Complex Human Traits using Data from Distantly Related Individuals

Genome‐wide association studies (GWAS) have detected large numbers of variants associated with complex human traits and diseases. However, the proportion of variance explained by GWAS‐significant single nucleotide polymorphisms has been usually small. This brought interest in the use of whole‐genome regression (WGR) methods. However, there has been limited research on the factors that affect prediction accuracy (PA) of WGRs when applied to human data of distantly related individuals. Here, we examine, using real human genotypes and simulated phenotypes, how trait complexity, marker‐quantitative trait loci (QTL) linkage disequilibrium (LD), and the model used affect the performance of WGRs. Our results indicated that the estimated rate of missing heritability is dependent on the extent of marker‐QTL LD. However, this parameter was not greatly affected by trait complexity. Regarding PA our results indicated that: (a) under perfect marker‐QTL LD WGR can achieve moderately high prediction accuracy, and with simple genetic architectures variable selection methods outperform shrinkage procedures and (b) under imperfect marker‐QTL LD, variable selection methods can achieved reasonably good PA with simple or moderately complex genetic architectures; however, the PA of these methods deteriorated as trait complexity increases and with highly complex traits variable selection and shrinkage methods both performed poorly. This was confirmed with an analysis of human height.     

Association of CHRNA4 polymorphisms with smoking behavior in two populations

CHRNA4, the gene that encodes the nicotinic acetylcholine receptor α₄ subunit, is a potential candidate gene for nicotine dependence (ND). However, studies of the association of CHNRA4 with smoking behavior have shown inconsistent results. Our meta‐analysis of linkage studies of smoking behavior identified a genome‐wide significant linkage of the phenotype maximum number of cigarettes smoked in a 24‐hour period to a region (20q13.12‐q13.32) harboring CHRNA4. This motivated us to examine the association of CHRNA4 with smoking behavior in two independent samples. In this study, we examined five single nucleotide polymorphisms (SNPs) within CHRNA4 and three smoking‐related behaviors: one quantitative trait [cigarettes smoked per day (CPD)], and two binary traits [DSM‐IV diagnosis of ND and dichotomized Fagerstrom test of ND (FTND)], in 1,249 unrelated European‐Americans (EAs) and 1,790 unrelated African‐Americans (AAs). Using the combined sample with sex, age, and race as covariates, the synonymous SNP rs1044394 was significantly associated with ND (P = 0.001) and FTND (P = 0.01). Rs2236196, which has a low correlation with rs1044394, was also significantly associated with CPD (P = 0.003). The pattern of association for these SNPs was similar in AAs and EAs. After correction for multiple testing, the association between rs1044394 and ND in the combined sample remained significant (P = 0.033). In summary, our study supports association between CHRNA4 common variation and ND in AA and EA samples. Additional studies will be necessary to evaluate the role of rare variants at CHRNA4 for ND. © 2011 Wiley‐Liss, Inc.