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1.  Multivariate Phenotype Association Analysis by Marker-Set Kernel Machine Regression 
Genetic epidemiology  2012;36(7):686-695.
Genetic studies of complex diseases often collect multiple phenotypes relevant to the disorders. As these phenotypes can be correlated and share common genetic mechanisms, jointly analyzing these traits may bring more power to detect genes influencing individual or multiple phenotypes. Given the advancement brought by the multivariate phenotype approaches and the multimarker kernel machine regression, we construct a multivariate regression based on kernel machine to facilitate the joint evaluation of multimarker effects on multiple phenotypes. The kernel machine serves as a powerful dimension-reduction tool to capture complex effects among markers. The multivariate framework incorporates the potentially correlated multi-dimensional phenotypic information and accommodates common or different environmental covariates for each trait. We derive the multivariate kernel machine test based on a score-like statistic, and conduct simulations to evaluate the validity and efficacy of the method. We also study the performance of the commonly adapted strategies for kernel machine analysis on multiple phenotypes, including the multiple univariate kernel machine tests with original phenotypes or with their principal components. Our results suggest that none of these approaches has the uniformly best power, and the optimal test depends on the magnitude of the phenotype correlation and the effect patterns. However, the multivariate test retains to be a reasonable approach when the multiple phenotypes have none or mild correlations, and gives the best power once the correlation becomes stronger or when there exist genes that affect more than one phenotype. We illustrate the utility of the multivariate kernel machine method through the CATIE antibody study.
PMCID: PMC3703860  PMID: 22899176
Kernel machine regression; Multivariate regression; multivariate phenotypes; Score based test
2.  Statistical Estimation of Correlated Genome Associations to a Quantitative Trait Network 
PLoS Genetics  2009;5(8):e1000587.
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.
Author Summary
An association study examines a phenotype against genotypic variations over a large set of individuals in order to find the genetic variant that gives rise to the variation in the phenotype. Many complex disease syndromes consist of a large number of highly related clinical phenotypes, and the patient cohorts are routinely surveyed with a large number of traits, such as hundreds of clinical phenotypes and genome-wide profiling of thousands of gene expressions, many of which are correlated. However, most of the conventional approaches for association mapping or eQTL analysis consider a single phenotype at a time instead of taking advantage of the relatedness of traits by analyzing them jointly. Assuming that a group of tightly correlated traits may share a common genetic basis, in this paper, we present a new framework for association analysis that searches for genetic variations influencing a group of correlated traits. We explicitly represent the correlation information in multiple quantitative traits as a quantitative trait network and directly incorporate this network information to scan the genome for association. Our results on simulated and asthma data show that our approach has a significant advantage in detecting associations when a genetic marker perturbs synergistically a group of traits.
PMCID: PMC2719086  PMID: 19680538
3.  A multivariate regression approach to association analysis of a quantitative trait network 
Bioinformatics  2009;25(12):i204-i212.
Motivation: Many complex disease syndromes such as asthma consist of a large number of highly related, rather than independent, clinical phenotypes, raising a new technical challenge in identifying genetic variations associated simultaneously with correlated traits. Although a causal genetic variation may influence a group of highly correlated traits jointly, most of the previous association analyses considered each phenotype separately, or combined results from a set of single-phenotype analyses.
Results: We propose a new statistical framework called graph-guided fused lasso to address this issue in a principled way. Our approach represents the dependency structure among the quantitative traits explicitly as a network, and leverages this trait network to encode structured regularizations in a multivariate regression model over the genotypes and traits, so that the genetic markers that jointly influence subgroups of highly correlated traits can be detected with high sensitivity and specificity. While most of the traditional methods examined each phenotype independently, our approach analyzes all of the traits jointly in a single statistical method to discover the genetic markers that perturb a subset of correlated triats jointly rather than a single trait. Using simulated datasets based on the HapMap consortium data and an asthma dataset, we compare the performance of our method with the single-marker analysis, and other sparse regression methods that do not use any structural information in the traits. Our results show that there is a significant advantage in detecting the true causal single nucleotide polymorphisms when we incorporate the correlation pattern in traits using our proposed methods.
Availability: Software for GFlasso is available at
PMCID: PMC2687972  PMID: 19477989
4.  Projection Regression Models for Multivariate Imaging Phenotype 
Genetic epidemiology  2012;36(6):631-641.
This paper presents a projection regression model (PRM) to assess the relationship between a multivariate phenotype and a set of covariates, such as a genetic marker, age and gender. In the existing literature, a standard statistical approach to this problem is to fit a multivariate linear model to the multivariate phenotype and then use Hotelling’s T2 to test hypotheses of interest. An alternative approach is to fit a simple linear model and test hypotheses for each individual phenotype and then correct for multiplicity. However, even when the dimension of the multivariate phenotype is relatively small, say 5, such standard approaches can suffer from the issue of low statistical power in detecting the association between the multivariate phenotype and the covariates. The PRM generalizes a statistical method based on the principal component of heritability for association analysis in genetic studies of complex multivariate phenotypes. The key components of the PRM include an estimation procedure for extracting several principal directions of multivariate phenotypes relating to covariates and a test procedure based on wild-bootstrap method for testing for the association between the weighted multivariate phenotype and explanatory variables. Simulation studies and an imaging genetic dataset are used to examine the finite sample performance of the PRM.
PMCID: PMC3418398  PMID: 22807230
imaging genetics; multivariate phenotype; projection regression model; single nucleotide polymorphism; wild bootstrap
5.  Mapping complex traits using Random Forests 
BMC Genetics  2003;4(Suppl 1):S64.
Random Forest is a prediction technique based on growing trees on bootstrap samples of data, in conjunction with a random selection of explanatory variables to define the best split at each node. In the case of a quantitative outcome, the tree predictor takes on a numerical value. We applied Random Forest to the first replicate of the Genetic Analysis Workshop 13 simulated data set, with the sibling pairs as our units of analysis and identity by descent (IBD) at selected loci as our explanatory variables. With the knowledge of the true model, we performed two sets of analyses on three phenotypes: HDL, triglycerides, and glucose. The goal was to approach the mapping of complex traits from a multivariate perspective. The first set of analyses mimics a candidate gene approach with a high proportion of true genes among the predictors while the second set represents a genome scan analysis using microsatellite markers. Random Forest was able to identify a few of the major genes influencing the phenotypes, such as baseline HDL and triglycerides, but failed to identify the major genes regulating baseline glucose levels.
PMCID: PMC1866502  PMID: 14975132
6.  Random forests on Hadoop for genome-wide association studies of multivariate neuroimaging phenotypes 
BMC Bioinformatics  2013;14(Suppl 16):S6.
Multivariate quantitative traits arise naturally in recent neuroimaging genetics studies, in which both structural and functional variability of the human brain is measured non-invasively through techniques such as magnetic resonance imaging (MRI). There is growing interest in detecting genetic variants associated with such multivariate traits, especially in genome-wide studies. Random forests (RFs) classifiers, which are ensembles of decision trees, are amongst the best performing machine learning algorithms and have been successfully employed for the prioritisation of genetic variants in case-control studies. RFs can also be applied to produce gene rankings in association studies with multivariate quantitative traits, and to estimate genetic similarities measures that are predictive of the trait. However, in studies involving hundreds of thousands of SNPs and high-dimensional traits, a very large ensemble of trees must be inferred from the data in order to obtain reliable rankings, which makes the application of these algorithms computationally prohibitive.
We have developed a parallel version of the RF algorithm for regression and genetic similarity learning tasks in large-scale population genetic association studies involving multivariate traits, called PaRFR (Parallel Random Forest Regression). Our implementation takes advantage of the MapReduce programming model and is deployed on Hadoop, an open-source software framework that supports data-intensive distributed applications. Notable speed-ups are obtained by introducing a distance-based criterion for node splitting in the tree estimation process. PaRFR has been applied to a genome-wide association study on Alzheimer's disease (AD) in which the quantitative trait consists of a high-dimensional neuroimaging phenotype describing longitudinal changes in the human brain structure. PaRFR provides a ranking of SNPs associated to this trait, and produces pair-wise measures of genetic proximity that can be directly compared to pair-wise measures of phenotypic proximity. Several known AD-related variants have been identified, including APOE4 and TOMM40. We also present experimental evidence supporting the hypothesis of a linear relationship between the number of top-ranked mutated states, or frequent mutation patterns, and an indicator of disease severity.
The Java codes are freely available at
PMCID: PMC3853073  PMID: 24564704
7.  A Unified Framework for Association Analysis with Multiple Related Phenotypes 
PLoS ONE  2013;8(7):e65245.
We consider the problem of assessing associations between multiple related outcome variables, and a single explanatory variable of interest. This problem arises in many settings, including genetic association studies, where the explanatory variable is genotype at a genetic variant. We outline a framework for conducting this type of analysis, based on Bayesian model comparison and model averaging for multivariate regressions. This framework unifies several common approaches to this problem, and includes both standard univariate and standard multivariate association tests as special cases. The framework also unifies the problems of testing for associations and explaining associations – that is, identifying which outcome variables are associated with genotype. This provides an alternative to the usual, but conceptually unsatisfying, approach of resorting to univariate tests when explaining and interpreting significant multivariate findings. The method is computationally tractable genome-wide for modest numbers of phenotypes (e.g. 5–10), and can be applied to summary data, without access to raw genotype and phenotype data. We illustrate the methods on both simulated examples, and to a genome-wide association study of blood lipid traits where we identify 18 potential novel genetic associations that were not identified by univariate analyses of the same data.
PMCID: PMC3702528  PMID: 23861737
8.  Genetic correlates of longevity and selected age-related phenotypes: a genome-wide association study in the Framingham Study 
BMC Medical Genetics  2007;8(Suppl 1):S13.
Family studies and heritability estimates provide evidence for a genetic contribution to variation in the human life span.
We conducted a genome wide association study (Affymetrix 100K SNP GeneChip) for longevity-related traits in a community-based sample. We report on 5 longevity and aging traits in up to 1345 Framingham Study participants from 330 families. Multivariable-adjusted residuals were computed using appropriate models (Cox proportional hazards, logistic, or linear regression) and the residuals from these models were used to test for association with qualifying SNPs (70, 987 autosomal SNPs with genotypic call rate ≥80%, minor allele frequency ≥10%, Hardy-Weinberg test p ≥ 0.001).
In family-based association test (FBAT) models, 8 SNPs in two regions approximately 500 kb apart on chromosome 1 (physical positions 73,091,610 and 73, 527,652) were associated with age at death (p-value < 10-5). The two sets of SNPs were in high linkage disequilibrium (minimum r2 = 0.58). The top 30 SNPs for generalized estimating equation (GEE) tests of association with age at death included rs10507486 (p = 0.0001) and rs4943794 (p = 0.0002), SNPs intronic to FOXO1A, a gene implicated in lifespan extension in animal models. FBAT models identified 7 SNPs and GEE models identified 9 SNPs associated with both age at death and morbidity-free survival at age 65 including rs2374983 near PON1. In the analysis of selected candidate genes, SNP associations (FBAT or GEE p-value < 0.01) were identified for age at death in or near the following genes: FOXO1A, GAPDH, KL, LEPR, PON1, PSEN1, SOD2, and WRN. Top ranked SNP associations in the GEE model for age at natural menopause included rs6910534 (p = 0.00003) near FOXO3a and rs3751591 (p = 0.00006) in CYP19A1. Results of all longevity phenotype-genotype associations for all autosomal SNPs are web posted at .
Longevity and aging traits are associated with SNPs on the Affymetrix 100K GeneChip. None of the associations achieved genome-wide significance. These data generate hypotheses and serve as a resource for replication as more genes and biologic pathways are proposed as contributing to longevity and healthy aging.
PMCID: PMC1995604  PMID: 17903295
9.  Impacts of Population Structure and Analytical Models in Genome-Wide Association Studies of Complex Traits in Forest Trees: A Case Study in Eucalyptus globulus 
PLoS ONE  2013;8(11):e81267.
The promise of association genetics to identify genes or genomic regions controlling complex traits has generated a flurry of interest. Such phenotype-genotype associations could be useful to accelerate tree breeding cycles, increase precision and selection intensity for late expressing, low heritability traits. However, the prospects of association genetics in highly heterozygous undomesticated forest trees can be severely impacted by the presence of cryptic population and pedigree structure. To investigate how to better account for this, we compared the GLM and five combinations of the Unified Mixed Model (UMM) on data of a low-density genome-wide association study for growth and wood property traits carried out in a Eucalyptus globulus population (n = 303) with 7,680 Diversity Array Technology (DArT) markers. Model comparisons were based on the degree of deviation from the uniform distribution and estimates of the mean square differences between the observed and expected p-values of all significant marker-trait associations detected. Our analysis revealed the presence of population and family structure. There was not a single best model for all traits. Striking differences in detection power and accuracy were observed among the different models especially when population structure was not accounted for. The UMM method was the best and produced superior results when compared to GLM for all traits. Following stringent correction for false discoveries, 18 marker-trait associations were detected, 16 for tree diameter growth and two for lignin monomer composition (S∶G ratio), a key wood property trait. The two DArT markers associated with S∶G ratio on chromosome 10, physically map within 1 Mbp of the ferulate 5-hydroxylase (F5H) gene, providing a putative independent validation of this marker-trait association. This study details the merit of collectively integrate population structure and relatedness in association analyses in undomesticated, highly heterozygous forest trees, and provides additional insights into the nature of complex quantitative traits in Eucalyptus.
PMCID: PMC3839935  PMID: 24282578
10.  A genome-wide scan using tree-based association analysis for candidate loci related to fasting plasma glucose levels 
BMC Genetics  2003;4(Suppl 1):S65.
In the analysis of complex traits such as fasting plasma glucose levels, researchers often adjust the trait for some important covariates before assessing gene susceptibility, and may at times encounter confounding among the covariates and the susceptible genes. Previously, the tree-based method has been employed to accommodate the heterogeneity in complex traits. In this study, we performed a genome-wide screen on fasting glucose levels in the offspring generation of the Framingham Heart Study provided by the Genetic Analysis Workshop 13. We defined one quantitative trait and converted it to a dichotomous trait based on a predetermined cut-off value, and performed association analyses using regression and classification trees for the two traits, respectively. A marker was interpreted as positive if at least one of its alleles exhibited association in both analyses. Our purpose was to identify candidate genes susceptible to fasting glucose levels in the presence of other covariates. The covariates entered in the analysis including sex, body mass index, and lipids (total plasma cholesterol, high density lipoprotein cholesterol, and triglycerides) of the subjects, and those of their parents.
Four out of seven positive regions in chromosomes 1, 2, 6, 11, 16, 18, and 19 from our analyses harbored or were very close to previously reported diabetes related genes or potential candidate genes.
This screen method that employed tree-based association showed promise for identifying candidate loci in the presence of covariates in genome scans for complex traits.
PMCID: PMC1866503  PMID: 14975133
11.  Bivariate Association Analyses for the Mixture of Continuous and Binary Traits with the Use of Extended Generalized Estimating Equations 
Genetic epidemiology  2009;33(3):217-227.
Genome-wide association (GWA) study is becoming a powerful tool in deciphering genetic basis of complex human diseases/traits. Currently, the univariate analysis is the most commonly used method to identify genes associated with a certain disease/phenotype under study. A major limitation with the univariate analysis is that it may not make use of the information of multiple correlated phenotypes, which are usually measured and collected in practical studies. The multivariate analysis has proven to be a powerful approach in linkage studies of complex diseases/traits, but it has received little attention in GWA. In this study, we aim to develop a bivariate analytical method for GWAS, which can be used for a complex situation that a continuous trait and a binary trait measured are under study. Based on the modified extended generalized estimating equation (EGEE) method we proposed herein, we assessed the performance of our bivariate analyses through extensive simulations as well as real data analyses. In the study, to develop an EGEE approach for bivariate genetic analyses, we combined two different generalized linear models corresponding to phenotypic variables using a Seemingly Unrelated Regression (SUR) model. The simulation results demonstrated that our EGEE-based bivariate analytical method outperforms univariate analyses in increasing statistical power under a variety of simulation scenarios. Notably, EGEE-based bivariate analyses have consistent advantages over univariate analyses whether or not there exits a phenotypic correlation between the two traits. Our study has practical importance, as one can always use multivariate analyses as a screening tool when multiple phenotypes are available, without extra costs of statistical power and false positive rate. Analyses on empirical GWA data further affirm the advantages of our bivariate analytical method.
PMCID: PMC2745071  PMID: 18924135
12.  A Functional Variant of NEDD4L Is Associated with Obesity and Related Phenotypes in a Han Population of Southern China 
NEDD4L is a candidate gene for hypertension, both functionally and genetically. Recently, studies showed evidence for the association of NEDD4L with obesity, a key intermediate phenotype in hypertension. To further investigate the relationship between NEDD4L and body mass-related phenotypes, we genotyped three common variants (rs2288774, rs3865418 and rs4149601) in a population-based study of 892 unrelated Han Cantonese using the Sequenom MALDI-TOF-MS platform. Allele frequencies and genotype distribution were calculated in lean controls and overweight/obese cases and analyzed for association by the Chi-squared test and Logistic regression. Linear regression analysis was used to analyze the effect of individual genotypes on quantitative traits. Multivariate analyses demonstrated that the minor allele of rs4149601(A = 20.9%) was associated with a 2.60 kg, 2.78 cm and 0.97 kg/m2 decrease per allele copy in weight, waist and BMI, respectively. Carriers of this allele also had a significant lower risk of overweight/obesity (p < 0.0001, OR = 0.52, 95% CI: 0.37–0.74) as compared to non-carriers. However, no significant association between genotypes at rs2288774 and rs3865418 and covariate-adjusted overweight/obesity or any related phenotypes was observed. These results suggested that the functional variant of NEDD4L, rs4149601, may be associated with obesity and related phenotypes, and further genetic and functional studies are required to understand its role in the manifestation of obesity.
PMCID: PMC3645694  PMID: 23549273
NEDD4L; genetic diversity; obesity
13.  Principal-component-based multivariate regression for genetic association studies of metabolic syndrome components 
BMC Genetics  2010;11:100.
Quantitative traits often underlie risk for complex diseases. For example, weight and body mass index (BMI) underlie the human abdominal obesity-metabolic syndrome. Many attempts have been made to identify quantitative trait loci (QTL) over the past decade, including association studies. However, a single QTL is often capable of affecting multiple traits, a quality known as gene pleiotropy. Gene pleiotropy may therefore cause a loss of power in association studies focused only on a single trait, whether based on single or multiple markers.
We propose using principal-component-based multivariate regression (PCBMR) to test for gene pleiotropy with comprehensive evaluation. This method generates one or more independent canonical variables based on the principal components of original traits and conducts a multivariate regression to test for association with these new variables. Systematic simulation studies have shown that PCBMR has great power. PCBMR-based pleiotropic association studies of abdominal obesity-metabolic syndrome and its possible linkage to chromosomal band 3q27 identified 11 susceptibility genes with significant associations. Whereas some of these genes had been previously reported to be associated with metabolic traits, others had never been identified as metabolism-associated genes.
PCBMR is a computationally efficient and powerful test for gene pleiotropy. Application of PCBMR to abdominal obesity-metabolic syndrome indicated the existence of gene pleiotropy affecting this syndrome.
PMCID: PMC2991276  PMID: 21062472
14.  Predicting complex quantitative traits with Bayesian neural networks: a case study with Jersey cows and wheat 
BMC Genetics  2011;12:87.
In the study of associations between genomic data and complex phenotypes there may be relationships that are not amenable to parametric statistical modeling. Such associations have been investigated mainly using single-marker and Bayesian linear regression models that differ in their distributions, but that assume additive inheritance while ignoring interactions and non-linearity. When interactions have been included in the model, their effects have entered linearly. There is a growing interest in non-parametric methods for predicting quantitative traits based on reproducing kernel Hilbert spaces regressions on markers and radial basis functions. Artificial neural networks (ANN) provide an alternative, because these act as universal approximators of complex functions and can capture non-linear relationships between predictors and responses, with the interplay among variables learned adaptively. ANNs are interesting candidates for analysis of traits affected by cryptic forms of gene action.
We investigated various Bayesian ANN architectures using for predicting phenotypes in two data sets consisting of milk production in Jersey cows and yield of inbred lines of wheat. For the Jerseys, predictor variables were derived from pedigree and molecular marker (35,798 single nucleotide polymorphisms, SNPS) information on 297 individually cows. The wheat data represented 599 lines, each genotyped with 1,279 markers. The ability of predicting fat, milk and protein yield was low when using pedigrees, but it was better when SNPs were employed, irrespective of the ANN trained. Predictive ability was even better in wheat because the trait was a mean, as opposed to an individual phenotype in cows. Non-linear neural networks outperformed a linear model in predictive ability in both data sets, but more clearly in wheat.
Results suggest that neural networks may be useful for predicting complex traits using high-dimensional genomic information, a situation where the number of unknowns exceeds sample size. ANNs can capture nonlinearities, adaptively. This may be useful when prediction of phenotypes is crucial.
PMCID: PMC3474182  PMID: 21981731
15.  Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall’s Tau* 
Identifying the risk factors for comorbidity is important in psychiatric research. Empirically, studies have shown that testing multiple, correlated traits simultaneously is more powerful than testing a single trait at a time in association analysis. Furthermore, for complex diseases, especially mental illnesses and behavioral disorders, the traits are often recorded in different scales such as dichotomous, ordinal and quantitative. In the absence of covariates, nonparametric association tests have been developed for multiple complex traits to study comorbidity. However, genetic studies generally contain measurements of some covariates that may affect the relationship between the risk factors of major interest (such as genes) and the outcomes. While it is relatively easy to adjust these covariates in a parametric model for quantitative traits, it is challenging for multiple complex traits with possibly different scales. In this article, we propose a nonparametric test for multiple complex traits that can adjust for covariate effects. The test aims to achieve an optimal scheme of adjustment by using a maximum statistic calculated from multiple adjusted test statistics. We derive the asymptotic null distribution of the maximum test statistic, and also propose a resampling approach, both of which can be used to assess the significance of our test. Simulations are conducted to compare the type I error and power of the nonparametric adjusted test to the unadjusted test and other existing adjusted tests. The empirical results suggest that our proposed test increases the power through adjustment for covariates when there exist environmental effects, and is more robust to model misspecifications than some existing parametric adjusted tests. We further demonstrate the advantage of our test by analyzing a data set on genetics of alcoholism.
PMCID: PMC3381868  PMID: 22745516
Comorbidity; Environmental factor; Family-based association test; Maximum test statistic; Multiple traits; Ordinal traits
16.  MultiPhen: Joint Model of Multiple Phenotypes Can Increase Discovery in GWAS 
PLoS ONE  2012;7(5):e34861.
The genome-wide association study (GWAS) approach has discovered hundreds of genetic variants associated with diseases and quantitative traits. However, despite clinical overlap and statistical correlation between many phenotypes, GWAS are generally performed one-phenotype-at-a-time. Here we compare the performance of modelling multiple phenotypes jointly with that of the standard univariate approach. We introduce a new method and software, MultiPhen, that models multiple phenotypes simultaneously in a fast and interpretable way. By performing ordinal regression, MultiPhen tests the linear combination of phenotypes most associated with the genotypes at each SNP, and thus potentially captures effects hidden to single phenotype GWAS. We demonstrate via simulation that this approach provides a dramatic increase in power in many scenarios. There is a boost in power for variants that affect multiple phenotypes and for those that affect only one phenotype. While other multivariate methods have similar power gains, we describe several benefits of MultiPhen over these. In particular, we demonstrate that other multivariate methods that assume the genotypes are normally distributed, such as canonical correlation analysis (CCA) and MANOVA, can have highly inflated type-1 error rates when testing case-control or non-normal continuous phenotypes, while MultiPhen produces no such inflation. To test the performance of MultiPhen on real data we applied it to lipid traits in the Northern Finland Birth Cohort 1966 (NFBC1966). In these data MultiPhen discovers 21% more independent SNPs with known associations than the standard univariate GWAS approach, while applying MultiPhen in addition to the standard approach provides 37% increased discovery. The most associated linear combinations of the lipids estimated by MultiPhen at the leading SNPs accurately reflect the Friedewald Formula, suggesting that MultiPhen could be used to refine the definition of existing phenotypes or uncover novel heritable phenotypes.
PMCID: PMC3342314  PMID: 22567092
17.  Moving toward System Genetics through Multiple Trait Analysis in Genome-Wide Association Studies 
Association studies are a staple of genotype–phenotype mapping studies, whether they are based on single markers, haplotypes, candidate genes, genome-wide genotypes, or whole genome sequences. Although genetic epidemiological studies typically contain data collected on multiple traits which themselves are often correlated, most analyses have been performed on single traits. Here, I review several methods that have been developed to perform multiple trait analysis. These methods range from traditional multivariate models for systems of equations to recently developed graphical approaches based on network theory. The application of network theory to genetics is termed systems genetics and has the potential to address long-standing questions in genetics about complex processes such as coordinate regulation, homeostasis, and pleiotropy.
PMCID: PMC3266611  PMID: 22303408
multivariate analysis; pleiotropy; systems genetics
18.  Joint association analysis of bivariate quantitative and qualitative traits 
BMC Proceedings  2011;5(Suppl 9):S74.
Univariate genome-wide association analysis of quantitative and qualitative traits has been investigated extensively in the literature. In the presence of correlated phenotypes, it is more intuitive to analyze all phenotypes simultaneously. We describe an efficient likelihood-based approach for the joint association analysis of quantitative and qualitative traits in unrelated individuals. We assume a probit model for the qualitative trait, under which an unobserved latent variable and a prespecified threshold determine the value of the qualitative trait. To jointly model the quantitative and qualitative traits, we assume that the quantitative trait and the latent variable follow a bivariate normal distribution. The latent variable is allowed to be correlated with the quantitative phenotype. Simultaneous modeling of the quantitative and qualitative traits allows us to make more precise inference on the pleiotropic genetic effects. We derive likelihood ratio tests for the testing of genetic effects. An application to the Genetic Analysis Workshop 17 data is provided. The new method yields reasonable power and meaningful results for the joint association analysis of the quantitative trait Q1 and the qualitative trait disease status at SNPs with not too small MAF.
PMCID: PMC3287914  PMID: 22373162
19.  A Predictive Framework for Integrating Disparate Genomic Data Types Using Sample-Specific Gene Set Enrichment Analysis and Multi-Task Learning 
PLoS ONE  2012;7(9):e44635.
Understanding the root molecular and genetic causes driving complex traits is a fundamental challenge in genomics and genetics. Numerous studies have used variation in gene expression to understand complex traits, but the underlying genomic variation that contributes to these expression changes is not well understood. In this study, we developed a framework to integrate gene expression and genotype data to identify biological differences between samples from opposing complex trait classes that are driven by expression changes and genotypic variation. This framework utilizes pathway analysis and multi-task learning to build a predictive model and discover pathways relevant to the complex trait of interest. We simulated expression and genotype data to test the predictive ability of our framework and to measure how well it uncovered pathways with genes both differentially expressed and genetically associated with a complex trait. We found that the predictive performance of the multi-task model was comparable to other similar methods. Also, methods like multi-task learning that considered enrichment analysis scores from both data sets found pathways with both genetic and expression differences related to the phenotype. We used our framework to analyze differences between estrogen receptor (ER) positive and negative breast cancer samples. An analysis of the top 15 gene sets from the multi-task model showed they were all related to estrogen, steroids, cell signaling, or the cell cycle. Although our study suggests that multi-task learning does not enhance predictive accuracy, the models generated by our framework do provide valuable biological pathway knowledge for complex traits.
PMCID: PMC3441565  PMID: 23028573
20.  Retrospective analysis of main and interaction effects in genetic association studies of human complex traits 
BMC Genetics  2007;8:70.
The etiology of multifactorial human diseases involves complex interactions between numerous environmental factors and alleles of many genes. Efficient statistical tools are demanded in identifying the genetic and environmental variants that affect the risk of disease development. This paper introduces a retrospective polytomous logistic regression model to measure both the main and interaction effects in genetic association studies of human discrete and continuous complex traits. In this model, combinations of genotypes at two interacting loci or of environmental exposure and genotypes at one locus are treated as nominal outcomes of which the proportions are modeled as a function of the disease trait assigning both main and interaction effects and with no assumption of normality in the trait distribution. Performance of our method in detecting interaction effect is compared with that of the case-only model.
Results from our simulation study indicate that our retrospective model exhibits high power in capturing even relatively small effect with reasonable sample sizes. Application of our method to data from an association study on the catalase -262C/T promoter polymorphism and aging phenotypes detected significant main and interaction effects for age-group and allele T on individual's cognitive functioning and produced consistent results in estimating the interaction effect as compared with the popular case-only model.
The retrospective polytomous logistic regression model can be used as a convenient tool for assessing both main and interaction effects in genetic association studies of human multifactorial diseases involving genetic and non-genetic factors as well as categorical or continuous traits.
PMCID: PMC2099440  PMID: 17937824
21.  Use of Longitudinal Data in Genetic Studies in the Genome-wide Association Studies Era: Summary of Group 14 
Genetic epidemiology  2009;33(Suppl 1):S93-S98.
Participants analyzed actual and simulated longitudinal data from the Framingham Heart Study for various metabolic and cardiovascular traits. The genetic information incorporated into these investigations ranged from selected single-nucleotide polymorphisms to genome-wide association arrays. Genotypes were incorporated using a broad range of methodological approaches including conditional logistic regression, linear mixed models, generalized estimating equations, linear growth curve estimation, growth modeling, growth mixture modeling, population attributable risk fraction based on survival functions under the proportional hazards models, and multivariate adaptive splines for the analysis of longitudinal data. The specific scientific questions addressed by these different approaches also varied, ranging from a more precise definition of the phenotype, bias reduction in control selection, estimation of effect sizes and genotype associated risk, to direct incorporation of genetic data into longitudinal modeling approaches and the exploration of population heterogeneity with regard to longitudinal trajectories. The group reached several overall conclusions: 1) The additional information provided by longitudinal data may be useful in genetic analyses. 2) The precision of the phenotype definition as well as control selection in nested designs may be improved, especially if traits demonstrate a trend over time or have strong age-of-onset effects. 3) Analyzing genetic data stratified for high-risk subgroups defined by a unique development over time could be useful for the detection of rare mutations in common multi-factorial diseases. 4) Estimation of the population impact of genomic risk variants could be more precise. The challenges and computational complexity demanded by genome-wide single-nucleotide polymorphism data were also discussed.
PMCID: PMC2913696  PMID: 19924713
phenotype definition; trends; risk estimation; growth modeling; sampling of controls
22.  Exploiting SNP Correlations within Random Forest for Genome-Wide Association Studies 
PLoS ONE  2014;9(4):e93379.
The primary goal of genome-wide association studies (GWAS) is to discover variants that could lead, in isolation or in combination, to a particular trait or disease. Standard approaches to GWAS, however, are usually based on univariate hypothesis tests and therefore can account neither for correlations due to linkage disequilibrium nor for combinations of several markers. To discover and leverage such potential multivariate interactions, we propose in this work an extension of the Random Forest algorithm tailored for structured GWAS data. In terms of risk prediction, we show empirically on several GWAS datasets that the proposed T-Trees method significantly outperforms both the original Random Forest algorithm and standard linear models, thereby suggesting the actual existence of multivariate non-linear effects due to the combinations of several SNPs. We also demonstrate that variable importances as derived from our method can help identify relevant loci. Finally, we highlight the strong impact that quality control procedures may have, both in terms of predictive power and loci identification. Variable importance results and T-Trees source code are all available at and respectively.
PMCID: PMC3973686  PMID: 24695491
23.  TATES: Efficient Multivariate Genotype-Phenotype Analysis for Genome-Wide Association Studies 
PLoS Genetics  2013;9(1):e1003235.
To date, the genome-wide association study (GWAS) is the primary tool to identify genetic variants that cause phenotypic variation. As GWAS analyses are generally univariate in nature, multivariate phenotypic information is usually reduced to a single composite score. This practice often results in loss of statistical power to detect causal variants. Multivariate genotype–phenotype methods do exist but attain maximal power only in special circumstances. Here, we present a new multivariate method that we refer to as TATES (Trait-based Association Test that uses Extended Simes procedure), inspired by the GATES procedure proposed by Li et al (2011). For each component of a multivariate trait, TATES combines p-values obtained in standard univariate GWAS to acquire one trait-based p-value, while correcting for correlations between components. Extensive simulations, probing a wide variety of genotype–phenotype models, show that TATES's false positive rate is correct, and that TATES's statistical power to detect causal variants explaining 0.5% of the variance can be 2.5–9 times higher than the power of univariate tests based on composite scores and 1.5–2 times higher than the power of the standard MANOVA. Unlike other multivariate methods, TATES detects both genetic variants that are common to multiple phenotypes and genetic variants that are specific to a single phenotype, i.e. TATES provides a more complete view of the genetic architecture of complex traits. As the actual causal genotype–phenotype model is usually unknown and probably phenotypically and genetically complex, TATES, available as an open source program, constitutes a powerful new multivariate strategy that allows researchers to identify novel causal variants, while the complexity of traits is no longer a limiting factor.
Author Summary
The genome-wide association study (GWAS) is the primary tool to identify genetic variants that cause phenotypic variation. As GWAS methods are generally univariate in nature, multivariate phenotypic information is usually reduced to a single composite score, which frequently results in a considerable loss of statistical power to detect causal variants. Multivariate genotype–phenotype methods do exist but attain maximal power only in special circumstances. We present a new multivariate method called TATES (Trait-based Association Test that uses Extended Simes procedure). Extensive simulations show that TATES's false positive rate is correct, and that TATES's statistical power to detect causal variants explaining 0.5% of the variance can be 2.5–9 times higher than the power of univariate tests of composite scores and 1.5–2 times higher than the power of the standard MANOVA. Unlike other multivariate methods, TATES uncovers both genetic variants that are common to multiple phenotypes as well as phenotype specific variants. TATES thus provides a more complete view of the genetic architecture of complex traits and constitutes a powerful new multivariate strategy that allows researchers to identify novel causal variants.
PMCID: PMC3554627  PMID: 23359524
24.  Recommendations for using standardised phenotypes in genetic association studies 
Human Genomics  2009;3(4):308-319.
Genetic association studies of complex traits often rely on standardised quantitative phenotypes, such as percentage of predicted forced expiratory volume and body mass index to measure an underlying trait of interest (eg lung function, obesity). These phenotypes are appealing because they provide an easy mechanism for comparing subjects, although such standardisations may not be the best way to control for confounders and other covariates. We recommend adjusting raw or standardised phenotypes within the study population via regression. We illustrate through simulation that optimal power in both population- and family-based association tests is attained by using the residuals from within-study adjustment as the complex trait phenotype. An application of family-based association analysis of forced expiratory volume in one second, and obesity in the Childhood Asthma Management Program data, illustrates that power is maintained or increased when adjusted phenotype residuals are used instead of typical standardised quantitative phenotypes.
PMCID: PMC3525193  PMID: 19706362
body mass index; confounding factors; covariate adjustment; forced expiratory volume; heritable quantitative traits
25.  A powerful latent variable method for detecting and characterizing gene-based gene-gene interaction on multiple quantitative traits 
BMC Genetics  2013;14:89.
On thinking quantitatively of complex diseases, there are at least three statistical strategies for analyzing the gene-gene interaction: SNP by SNP interaction on single trait, gene-gene (each can involve multiple SNPs) interaction on single trait and gene-gene interaction on multiple traits. The third one is the most general in dissecting the genetic mechanism underlying complex diseases underpinning multiple quantitative traits. In this paper, we developed a novel statistic for this strategy through modifying the Partial Least Squares Path Modeling (PLSPM), called mPLSPM statistic.
Simulation studies indicated that mPLSPM statistic was powerful and outperformed the principal component analysis (PCA) based linear regression method. Application to real data in the EPIC-Norfolk GWAS sub-cohort showed suggestive interaction (γ) between TMEM18 gene and BDNF gene on two composite body shape scores (γ = 0.047 and γ = 0.058, with P = 0.021, P = 0.005), and BMI (γ = 0.043, P = 0.034). This suggested these scores (synthetically latent traits) were more suitable to capture the obesity related genetic interaction effect between genes compared to single trait.
The proposed novel mPLSPM statistic is a valid and powerful gene-based method for detecting gene-gene interaction on multiple quantitative phenotypes.
PMCID: PMC3848962  PMID: 24059907
Thinking quantitatively for complex diseases; Gene-based gene-gene interaction; Quantitative traits; mPLSPM statistic

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