A Gaussian copula approach for the analysis of secondary phenotypes in case-control genetic association studies

In many case-control genetic association studies, a set of correlated secondary phenotypes that may share common genetic factors with disease status are collected. Examination of these secondary phenotypes can yield valuable insights about the disease etiology and supplement the main studies. However, due to unequal sampling probabilities between cases and controls, standard regression analysis that assesses the effect of SNPs (single nucleotide polymorphisms) on secondary phenotypes using cases only, controls only, or combined samples of cases and controls can yield inflated type I error rates when the test SNP is associated with the disease. To solve this issue, we propose a Gaussian copula-based approach that efficiently models the dependence between disease status and secondary phenotypes. Through simulations, we show that our method yields correct type I error rates for the analysis of secondary phenotypes under a wide range of situations. To illustrate the effectiveness of our method in the analysis of real data, we applied our method to a genome-wide association study on high-density lipoprotein cholesterol (HDL-C), where "cases" are defined as individuals with extremely high HDL-C level and "controls" are defined as those with low HDL-C level. We treated 4 quantitative traits with varying degrees of correlation with HDL-C as secondary phenotypes and tested for association with SNPs in LIPG, a gene that is well known to be associated with HDL-C. We show that when the correlation between the primary and secondary phenotypes is >0.2, the P values from case-control combined unadjusted analysis are much more significant than methods that aim to correct for ascertainment bias. Our results suggest that to avoid false-positive associations, it is important to appropriately model secondary phenotypes in case-control genetic association studies.     

Gene-based tests of association

Genome-wide association studies (GWAS) are now used routinely to identify SNPs associated with complex human phenotypes. In several cases, multiple variants within a gene contribute independently to disease risk. Here we introduce a novel Gene-Wide Significance (GWiS) test that uses greedy Bayesian model selection to identify the independent effects within a gene, which are combined to generate a stronger statistical signal. Permutation tests provide p-values that correct for the number of independent tests genome-wide and within each genetic locus. When applied to a dataset comprising 2.5 million SNPs in up to 8,000 individuals measured for various electrocardiography (ECG) parameters, this method identifies more validated associations than conventional GWAS approaches. The method also provides, for the first time, systematic assessments of the number of independent effects within a gene and the fraction of disease-associated genes housing multiple independent effects, observed at 35%-50% of loci in our study. This method can be generalized to other study designs, retains power for low-frequency alleles, and provides gene-based p-values that are directly compatible for pathway-based meta-analysis.     

Joint prediction of multiple quantitative traits using a Bayesian multivariate antedependence model

Predicting organismal phenotypes from genotype data is important for preventive and personalized medicine as well as plant and animal breeding. Although genome-wide association studies (GWAS) for complex traits have discovered a large number of trait- and disease-associated variants, phenotype prediction based on associated variants is usually in low accuracy even for a high-heritability trait because these variants can typically account for a limited fraction of total genetic variance. In comparison with GWAS, the whole-genome prediction (WGP) methods can increase prediction accuracy by making use of a huge number of variants simultaneously. Among various statistical methods for WGP, multiple-trait model and antedependence model show their respective advantages. To take advantage of both strategies within a unified framework, we proposed a novel multivariate antedependence-based method for joint prediction of multiple quantitative traits using a Bayesian algorithm via modeling a linear relationship of effect vector between each pair of adjacent markers. Through both simulation and real-data analyses, our studies demonstrated that the proposed antedependence-based multiple-trait WGP method is more accurate and robust than corresponding traditional counterparts (Bayes A and multi-trait Bayes A) under various scenarios. Our method can be readily extended to deal with missing phenotypes and resequence data with rare variants, offering a feasible way to jointly predict phenotypes for multiple complex traits in human genetic epidemiology as well as plant and livestock breeding.     

Functional Regression Models for Epistasis Analysis of Multiple Quantitative Traits

To date, most genetic analyses of phenotypes have focused on analyzing single traits or analyzing each phenotype independently. However, joint epistasis analysis of multiple complementary traits will increase statistical power and improve our understanding of the complicated genetic structure of the complex diseases. Despite their importance in uncovering the genetic structure of complex traits, the statistical methods for identifying epistasis in multiple phenotypes remains fundamentally unexplored. To fill this gap, we formulate a test for interaction between two genes in multiple quantitative trait analysis as a multiple functional regression (MFRG) in which the genotype functions (genetic variant profiles) are defined as a function of the genomic position of the genetic variants. We use large-scale simulations to calculate Type I error rates for testing interaction between two genes with multiple phenotypes and to compare the power with multivariate pairwise interaction analysis and single trait interaction analysis by a single variate functional regression model. To further evaluate performance, the MFRG for epistasis analysis is applied to five phenotypes of exome sequence data from the NHLBI’s Exome Sequencing Project (ESP) to detect pleiotropic epistasis. A total of 267 pairs of genes that formed a genetic interaction network showed significant evidence of epistasis influencing five traits. The results demonstrate that the joint interaction analysis of multiple phenotypes has a much higher power to detect interaction than the interaction analysis of a single trait and may open a new direction to fully uncovering the genetic structure of multiple phenotypes.     

Two-stage designs in case-control association analysis

DNA pooling is a cost-effective approach for collecting information on marker allele frequency in genetic studies. It is often suggested as a screening tool to identify a subset of candidate markers from a very large number of markers to be followed up by more accurate and informative individual genotyping. In this article, we investigate several statistical properties and design issues related to this two-stage design, including the selection of the candidate markers for second-stage analysis, statistical power of this design, and the probability that truly disease-associated markers are ranked among the top after second-stage analysis. We have derived analytical results on the proportion of markers to be selected for second-stage analysis. For example, to detect disease-associated markers with an allele frequency difference of 0.05 between the cases and controls through an initial sample of 1000 cases and 1000 controls, our results suggest that when the measurement errors are small (0.005), approximately 3% of the markers should be selected. For the statistical power to identify disease-associated markers, we find that the measurement errors associated with DNA pooling have little effect on its power. This is in contrast to the one-stage pooling scheme where measurement errors may have large effect on statistical power. As for the probability that the disease-associated markers are ranked among the top in the second stage, we show that there is a high probability that at least one disease-associated marker is ranked among the top when the allele frequency differences between the cases and controls are not <0.05 for reasonably large sample sizes, even though the errors associated with DNA pooling in the first stage are not small. Therefore, the two-stage design with DNA pooling as a screening tool offers an efficient strategy in genomewide association studies, even when the measurement errors associated with DNA pooling are nonnegligible. For any disease model, we find that all the statistical results essentially depend on the population allele frequency and the allele frequency differences between the cases and controls at the disease-associated markers. The general conclusions hold whether the second stage uses an entirely independent sample or includes both the samples used in the first stage and an independent set of samples.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.     

Canonical Correlation Analysis for Gene-Based Pleiotropy Discovery

Genome-wide association studies have identified a wealth of genetic variants involved in complex traits and multifactorial diseases. There is now considerable interest in testing variants for association with multiple phenotypes (pleiotropy) and for testing multiple variants for association with a single phenotype (gene-based association tests). Such approaches can increase statistical power by combining evidence for association over multiple phenotypes or genetic variants respectively. Canonical Correlation Analysis (CCA) measures the correlation between two sets of multidimensional variables, and thus offers the potential to combine these two approaches. To apply CCA, we must restrict the number of attributes relative to the number of samples. Hence we consider modules of genetic variation that can comprise a gene, a pathway or another biologically relevant grouping, and/or a set of phenotypes. In order to do this, we use an attribute selection strategy based on a binary genetic algorithm. Applied to a UK-based prospective cohort study of 4286 women (the British Women''s Heart and Health Study), we find improved statistical power in the detection of previously reported genetic associations, and identify a number of novel pleiotropic associations between genetic variants and phenotypes. New discoveries include gene-based association of NSF with triglyceride levels and several genes (ACSM3, ERI2, IL18RAP, IL23RAP and NRG1) with left ventricular hypertrophy phenotypes. In multiple-phenotype analyses we find association of NRG1 with left ventricular hypertrophy phenotypes, fibrinogen and urea and pleiotropic relationships of F7 and F10 with Factor VII, Factor IX and cholesterol levels.     

Novel EDGE encoding method enhances ability to identify genetic interactions

Assumptions are made about the genetic model of single nucleotide polymorphisms (SNPs) when choosing a traditional genetic encoding: additive, dominant, and recessive. Furthermore, SNPs across the genome are unlikely to demonstrate identical genetic models. However, running SNP-SNP interaction analyses with every combination of encodings raises the multiple testing burden. Here, we present a novel and flexible encoding for genetic interactions, the elastic data-driven genetic encoding (EDGE), in which SNPs are assigned a heterozygous value based on the genetic model they demonstrate in a dataset prior to interaction testing. We assessed the power of EDGE to detect genetic interactions using 29 combinations of simulated genetic models and found it outperformed the traditional encoding methods across 10%, 30%, and 50% minor allele frequencies (MAFs). Further, EDGE maintained a low false-positive rate, while additive and dominant encodings demonstrated inflation. We evaluated EDGE and the traditional encodings with genetic data from the Electronic Medical Records and Genomics (eMERGE) Network for five phenotypes: age-related macular degeneration (AMD), age-related cataract, glaucoma, type 2 diabetes (T2D), and resistant hypertension. A multi-encoding genome-wide association study (GWAS) for each phenotype was performed using the traditional encodings, and the top results of the multi-encoding GWAS were considered for SNP-SNP interaction using the traditional encodings and EDGE. EDGE identified a novel SNP-SNP interaction for age-related cataract that no other method identified: rs7787286 (MAF: 0.041; intergenic region of chromosome 7)–rs4695885 (MAF: 0.34; intergenic region of chromosome 4) with a Bonferroni LRT p of 0.018. A SNP-SNP interaction was found in data from the UK Biobank within 25 kb of these SNPs using the recessive encoding: rs60374751 (MAF: 0.030) and rs6843594 (MAF: 0.34) (Bonferroni LRT p: 0.026). We recommend using EDGE to flexibly detect interactions between SNPs exhibiting diverse action.     

Using the noninformative families in family-based association tests: a powerful new testing strategy

For genetic association studies with multiple phenotypes, we propose a new strategy for multiple testing with family-based association tests (FBATs). The strategy increases the power by both using all available family data and reducing the number of hypotheses tested while being robust against population admixture and stratification. By use of conditional power calculations, the approach screens all possible null hypotheses without biasing the nominal significance level, and it identifies the subset of phenotypes that has optimal power when tested for association by either univariate or multivariate FBATs. An application of our strategy to an asthma study shows the practical relevance of the proposed methodology. In simulation studies, we compare our testing strategy with standard methodology for family studies. Furthermore, the proposed principle of using all data without biasing the nominal significance in an analysis prior to the computation of the test statistic has broad and powerful applications in many areas of family-based association studies.     

A Groupwise Association Test for Rare Mutations Using a Weighted Sum Statistic

Resequencing is an emerging tool for identification of rare disease-associated mutations. Rare mutations are difficult to tag with SNP genotyping, as genotyping studies are designed to detect common variants. However, studies have shown that genetic heterogeneity is a probable scenario for common diseases, in which multiple rare mutations together explain a large proportion of the genetic basis for the disease. Thus, we propose a weighted-sum method to jointly analyse a group of mutations in order to test for groupwise association with disease status. For example, such a group of mutations may result from resequencing a gene. We compare the proposed weighted-sum method to alternative methods and show that it is powerful for identifying disease-associated genes, both on simulated and Encode data. Using the weighted-sum method, a resequencing study can identify a disease-associated gene with an overall population attributable risk (PAR) of 2%, even when each individual mutation has much lower PAR, using 1,000 to 7,000 affected and unaffected individuals, depending on the underlying genetic model. This study thus demonstrates that resequencing studies can identify important genetic associations, provided that specialised analysis methods, such as the weighted-sum method, are used.     

Association Tests of Multiple Phenotypes: ATeMP

Joint analysis of multiple phenotypes has gained growing attention in genome-wide association studies (GWASs), especially for the analysis of multiple intermediate phenotypes which measure the same underlying complex human disorder. One of the multivariate methods, MultiPhen (O’ Reilly et al. 2012), employs the proportional odds model to regress a genotype on multiple phenotypes, hence ignoring the phenotypic distributions. Despite the flexibilities of MultiPhen, the properties and performance of MultiPhen are not well understood, especially when the phenotypic distributions are non-normal. In fact, it is well known in the statistical literature that the estimation is attenuated when the explanatory variables contain measurement errors. In this study, we first established an equivalence relationship between MultiPhen and the generalized Kendall tau association test, shedding light on why MultiPhen can perform well for joint association analysis of multiple phenotypes. Through the equivalence, we show that MultiPhen may lose power when the phenotypes are non-normal. To maintain the power, we propose two solutions (ATeMP-rn and ATeMP-or) to improve MultiPhen, and demonstrate their effectiveness through extensive simulation studies and a real case study from the Guangzhou Twin Eye Study.     

Meta-analysis of Correlated Traits via Summary Statistics from GWASs with an Application in Hypertension

Genome-wide association studies (GWASs) have identified many genetic variants underlying complex traits. Many detected genetic loci harbor variants that associate with multiple—even distinct—traits. Most current analysis approaches focus on single traits, even though the final results from multiple traits are evaluated together. Such approaches miss the opportunity to systemically integrate the phenome-wide data available for genetic association analysis. In this study, we propose a general approach that can integrate association evidence from summary statistics of multiple traits, either correlated, independent, continuous, or binary traits, which might come from the same or different studies. We allow for trait heterogeneity effects. Population structure and cryptic relatedness can also be controlled. Our simulations suggest that the proposed method has improved statistical power over single-trait analysis in most of the cases we studied. We applied our method to the Continental Origins and Genetic Epidemiology Network (COGENT) African ancestry samples for three blood pressure traits and identified four loci (CHIC2, HOXA-EVX1, IGFBP1/IGFBP3, and CDH17; p < 5.0 × 10⁻⁸) associated with hypertension-related traits that were missed by a single-trait analysis in the original report. Six additional loci with suggestive association evidence (p < 5.0 × 10⁻⁷) were also observed, including CACNA1D and WNT3. Our study strongly suggests that analyzing multiple phenotypes can improve statistical power and that such analysis can be executed with the summary statistics from GWASs. Our method also provides a way to study a cross phenotype (CP) association by using summary statistics from GWASs of multiple phenotypes.     

Replication of genome-wide association studies on asthma and allergic diseases in Korean adult population

Allergic diseases such as asthma, allergic rhinitis, and atopic dermatitis are heterogeneous diseases characterized by multiple symptoms and phenotypes. Recent advancements in genetic study enabled us to identify disease associated genetic factors. Numerous genome-wide association studies (GWAS) have revealed multiple associated loci for allergic diseases. However, the majority of previous studies have been conducted in populations of European ancestry. Moreover, the associations of single nucleotide polymorphisms (SNPs) with allergic diseases have not been studied amongst the large-scale general Korean population. Herein, we performed the replication study to validate the previous variants, known to be associated with allergic diseases, in the Korean population. In this study, we categorized three allergic related phenotypes, one allergy and two asthma related phenotypes, based on self-reports of physician diagnosis and their symptoms from 8,842 samples. As a result, we found nominally significant associations of 6 SNPs with at least one allergic related phenotype in the Korean population.     

Statistical Estimation of Correlated Genome Associations to a Quantitative Trait Network

Many complex disease syndromes, such as asthma, consist of a large number of highly related, rather than independent, clinical or molecular phenotypes. This raises a new technical challenge in identifying genetic variations associated simultaneously with correlated traits. In this study, we propose a new statistical framework called graph-guided fused lasso (GFlasso) to directly and effectively incorporate the correlation structure of multiple quantitative traits such as clinical metrics and gene expressions in association analysis. Our approach represents correlation information explicitly among the quantitative traits as a quantitative trait network (QTN) and then leverages this network to encode structured regularization functions in a multivariate regression model over the genotypes and traits. The result is that the genetic markers that jointly influence subgroups of highly correlated traits can be detected jointly with high sensitivity and specificity. While most of the traditional methods examined each phenotype independently and combined the results afterwards, our approach analyzes all of the traits jointly in a single statistical framework. This allows our method to borrow information across correlated phenotypes to discover the genetic markers that perturb a subset of the correlated traits synergistically. Using simulated datasets based on the HapMap consortium and an asthma dataset, we compared the performance of our method with other methods based on single-marker analysis and regression-based methods that do not use any of the relational information in the traits. We found that our method showed an increased power in detecting causal variants affecting correlated traits. Our results showed that, when correlation patterns among traits in a QTN are considered explicitly and directly during a structured multivariate genome association analysis using our proposed methods, the power of detecting true causal SNPs with possibly pleiotropic effects increased significantly without compromising performance on non-pleiotropic SNPs.     

Mixed Model with Correction for Case-Control Ascertainment Increases Association Power

We introduce a liability-threshold mixed linear model (LTMLM) association statistic for case-control studies and show that it has a well-controlled false-positive rate and more power than existing mixed-model methods for diseases with low prevalence. Existing mixed-model methods suffer a loss in power under case-control ascertainment, but no solution has been proposed. Here, we solve this problem by using a χ² score statistic computed from posterior mean liabilities (PMLs) under the liability-threshold model. Each individual’s PML is conditional not only on that individual’s case-control status but also on every individual’s case-control status and the genetic relationship matrix (GRM) obtained from the data. The PMLs are estimated with a multivariate Gibbs sampler; the liability-scale phenotypic covariance matrix is based on the GRM, and a heritability parameter is estimated via Haseman-Elston regression on case-control phenotypes and then transformed to the liability scale. In simulations of unrelated individuals, the LTMLM statistic was correctly calibrated and achieved higher power than existing mixed-model methods for diseases with low prevalence, and the magnitude of the improvement depended on sample size and severity of case-control ascertainment. In a Wellcome Trust Case Control Consortium 2 multiple sclerosis dataset with >10,000 samples, LTMLM was correctly calibrated and attained a 4.3% improvement (p = 0.005) in χ² statistics over existing mixed-model methods at 75 known associated SNPs, consistent with simulations. Larger increases in power are expected at larger sample sizes. In conclusion, case-control studies of diseases with low prevalence can achieve power higher than that in existing mixed-model methods.     

Selecting tagging SNPs for association studies using power calculations from genotype data

Recent studies have indicated that linkage disequilibrium (LD) between single nucleotide polymorphism (SNP) markers can be used to derive a reduced set of tagging SNPs (tSNPs) for genetic association studies. Previous strategies for identifying tSNPs have focused on LD measures or haplotype diversity, but the statistical power to detect disease-associated variants using tSNPs in genetic studies has not been fully characterized. We propose a new approach of selecting tSNPs based on determining the set of SNPs with the highest power to detect association. Two-locus genotype frequencies are used in the power calculations. To show utility, we applied this power method to a large number of SNPs that had been genotyped in Caucasian samples. We demonstrate that a significant reduction in genotyping efforts can be achieved although the reduction depends on genotypic relative risk, inheritance mode and the prevalence of disease in the human population. The tSNP sets identified by our method are remarkably robust to changes in the disease model when small relative risk and additive mode of inheritance are employed. We have also evaluated the ability of the method to detect unidentified SNPs. Our findings have important implications in applying tSNPs from different data sources in association studies.     

Statistical Power of Model Selection Strategies for Genome-Wide Association Studies

Genome-wide association studies (GWAS) aim to identify genetic variants related to diseases by examining the associations between phenotypes and hundreds of thousands of genotyped markers. Because many genes are potentially involved in common diseases and a large number of markers are analyzed, it is crucial to devise an effective strategy to identify truly associated variants that have individual and/or interactive effects, while controlling false positives at the desired level. Although a number of model selection methods have been proposed in the literature, including marginal search, exhaustive search, and forward search, their relative performance has only been evaluated through limited simulations due to the lack of an analytical approach to calculating the power of these methods. This article develops a novel statistical approach for power calculation, derives accurate formulas for the power of different model selection strategies, and then uses the formulas to evaluate and compare these strategies in genetic model spaces. In contrast to previous studies, our theoretical framework allows for random genotypes, correlations among test statistics, and a false-positive control based on GWAS practice. After the accuracy of our analytical results is validated through simulations, they are utilized to systematically evaluate and compare the performance of these strategies in a wide class of genetic models. For a specific genetic model, our results clearly reveal how different factors, such as effect size, allele frequency, and interaction, jointly affect the statistical power of each strategy. An example is provided for the application of our approach to empirical research. The statistical approach used in our derivations is general and can be employed to address the model selection problems in other random predictor settings. We have developed an R package markerSearchPower to implement our formulas, which can be downloaded from the Comprehensive R Archive Network (CRAN) or http://bioinformatics.med.yale.edu/group/.     

Statistical equivalent of the classical TDT for quantitative traits and multivariate phenotypes

Clinical end-point traits are usually governed by quantitative precursors. Hence, there is active research interest in developing statistical methods for association mapping of quantitative traits. Unlike population-based tests for association, family-based tests for transmission disequilibrium are protected against population stratification. In this study, we propose a logistic regression model to test the association for quantitative traits based on a trio design. We show that the method can be viewed as a direct extension of the classical transmission diequilibrium test for binary traits to quantitative traits. We evaluate the performance of our method using extensive simulations and compare it with an existing method, family-based association test. We found that the two methods yield comparable powers if all families are considered. However, unlike FBAT, which yields an inflated rate of false positives when noninformative trios with all three individuals’ heterozygous are removed, our method maintains the correct size without compromising too much on power. We show that our method can be easily modified to incorporate multivariate phenotypes. Here, we applied this method to analyse a quantitative endophenotype associated with alcoholism.     

A Statistical Approach for Testing Cross-Phenotype Effects of Rare Variants

Increasing empirical evidence suggests that many genetic variants influence multiple distinct phenotypes. When cross-phenotype effects exist, multivariate association methods that consider pleiotropy are often more powerful than univariate methods that model each phenotype separately. Although several statistical approaches exist for testing cross-phenotype effects for common variants, there is a lack of similar tests for gene-based analysis of rare variants. In order to fill this important gap, we introduce a statistical method for cross-phenotype analysis of rare variants using a nonparametric distance-covariance approach that compares similarity in multivariate phenotypes to similarity in rare-variant genotypes across a gene. The approach can accommodate both binary and continuous phenotypes and further can adjust for covariates. Our approach yields a closed-form test whose significance can be evaluated analytically, thereby improving computational efficiency and permitting application on a genome-wide scale. We use simulated data to demonstrate that our method, which we refer to as the Gene Association with Multiple Traits (GAMuT) test, provides increased power over competing approaches. We also illustrate our approach using exome-chip data from the Genetic Epidemiology Network of Arteriopathy.