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1.  An omnibus test for family-based association studies with multiple SNPs and multiple phenotypes 
We propose an omnibus family-based association test (MFBAT), that can be applied to multiple markers and multiple phenotypes and that has only 1 degree of freedom. The proposed test statistic extends current FBAT methodology to incorporate multiple markers as well as multiple phenotypes. Using simulation studies, power estimates for the proposed methodology are compared with the standard methodologies. Based on these simulations, we find that MFBAT substantially outperforms other methods including some haplotypic approaches and doing multiple tests with single SNPs and single phenotypes. The practical relevance of the approach is illustrated by an application to asthma where SNPs/phenotype combinations are identified and reach overall significance that would not have been identified using other approaches. This methodology is directly applicable to cases where there are multiple SNPs, such as candidate gene studies, cases where there are multiple phenotypes, such as expression data, and cases where there are multiple phenotypes and genotypes, such as genome-wide association studies that incorporate expression profiles as phenotypes. This program is available in the PBAT analysis package1.
PMCID: PMC2874662  PMID: 20087406
Family-based association testing (FBAT); genome-wide association studies; FBAT-PC; multiple marker; multiple phenotypes; multiple testing
2.  Screening and Replication using the Same Data Set: Testing Strategies for Family-Based Studies in which All Probands Are Affected 
PLoS Genetics  2008;4(9):e1000197.
For genome-wide association studies in family-based designs, we propose a powerful two-stage testing strategy that can be applied in situations in which parent-offspring trio data are available and all offspring are affected with the trait or disease under study. In the first step of the testing strategy, we construct estimators of genetic effect size in the completely ascertained sample of affected offspring and their parents that are statistically independent of the family-based association/transmission disequilibrium tests (FBATs/TDTs) that are calculated in the second step of the testing strategy. For each marker, the genetic effect is estimated (without requiring an estimate of the SNP allele frequency) and the conditional power of the corresponding FBAT/TDT is computed. Based on the power estimates, a weighted Bonferroni procedure assigns an individually adjusted significance level to each SNP. In the second stage, the SNPs are tested with the FBAT/TDT statistic at the individually adjusted significance levels. Using simulation studies for scenarios with up to 1,000,000 SNPs, varying allele frequencies and genetic effect sizes, the power of the strategy is compared with standard methodology (e.g., FBATs/TDTs with Bonferroni correction). In all considered situations, the proposed testing strategy demonstrates substantial power increases over the standard approach, even when the true genetic model is unknown and must be selected based on the conditional power estimates. The practical relevance of our methodology is illustrated by an application to a genome-wide association study for childhood asthma, in which we detect two markers meeting genome-wide significance that would not have been detected using standard methodology.
Author Summary
The current state of genotyping technology has enabled researchers to conduct genome-wide association studies of up to 1,000,000 SNPs, allowing for systematic scanning of the genome for variants that might influence the development and progression of complex diseases. One of the largest obstacles to the successful detection of such variants is the multiple comparisons/testing problem in the genetic association analysis. For family-based designs in which all offspring are affected with the disease/trait under study, we developed a methodology that addresses this problem by partitioning the family-based data into two statistically independent components. The first component is used to screen the data and determine the most promising SNPs. The second component is used to test the SNPs for association, where information from the screening is used to weight the SNPs during testing. This methodology is more powerful than standard procedures for multiple comparisons adjustment (i.e., Bonferroni correction). Additionally, as only one data set is required for screening and testing, our testing strategy is less susceptible to study heterogeneity. Finally, as many family-based studies collect data only from affected offspring, this method addresses a major limitation of previous methodologies for multiple comparisons in family-based designs, which require variation in the disease/trait among offspring.
PMCID: PMC2529406  PMID: 18802462
3.  GEE-based SNP Set Association Test for Continuous and Discrete Traits in Family Based Association Studies 
Genetic epidemiology  2013;37(8):778-786.
Family-based genetic association studies of related individuals provide opportunities to detect genetic variants that complement studies of unrelated individuals. Most statistical methods for family association studies for common variants are single-marker-based, which test one SNP a time. In this paper, we consider testing the effect of a SNP set, e.g., SNPs in a gene, in family studies, for both continuous and discrete traits. Specifically, we propose a Generalized Estimating Equations (GEE)-based kernel association test, a variance component-based testing method, to test for the association between a phenotype and multiple variants in a SNP set jointly using family samples. The proposed approach allows for both continuous and discrete traits, where the correlation among family members is taken into account through the use of an empirical covariance estimator. We derive the theoretical distribution of the proposed statistic under the null and develop analytical methods to calculate the p-values. We also propose an efficient resampling method for correcting for small sample size bias in family studies. The proposed method allows for easily incorporating covariates and SNP-SNP interactions. Simulation studies show that the proposed method properly controls for type-I error rates under both random and ascertained sampling schemes in family studies. We demonstrate through simulation studies that our approach has superior performance for association mapping compared to the single marker based minimum p-value GEE test for a SNP set effect over a range of scenarios. We illustrate the application of the proposed method using data from the Cleveland Family GWAS Study.
PMCID: PMC4007511  PMID: 24166731
Family-based association; Generalized estimation equations; Kernel machine regression; Marginal models; Score test; Variance component
4.  Genome-wide association study for subclinical atherosclerosis in major arterial territories in the NHLBI's Framingham Heart Study 
BMC Medical Genetics  2007;8(Suppl 1):S4.
Subclinical atherosclerosis (SCA) measures in multiple arterial beds are heritable phenotypes that are associated with increased incidence of cardiovascular disease. We conducted a genome-wide association study (GWAS) for SCA measurements in the community-based Framingham Heart Study.
Over 100,000 single nucleotide polymorphisms (SNPs) were genotyped (Human 100K GeneChip, Affymetrix) in 1345 subjects from 310 families. We calculated sex-specific age-adjusted and multivariable-adjusted residuals in subjects tested for quantitative SCA phenotypes, including ankle-brachial index, coronary artery calcification and abdominal aortic calcification using multi-detector computed tomography, and carotid intimal medial thickness (IMT) using carotid ultrasonography. We evaluated associations of these phenotypes with 70,987 autosomal SNPs with minor allele frequency ≥ 0.10, call rate ≥ 80%, and Hardy-Weinberg p-value ≥ 0.001 in samples ranging from 673 to 984 subjects, using linear regression with generalized estimating equations (GEE) methodology and family-based association testing (FBAT). Variance components LOD scores were also calculated.
There was no association result meeting criteria for genome-wide significance, but our methods identified 11 SNPs with p < 10-5 by GEE and five SNPs with p < 10-5 by FBAT for multivariable-adjusted phenotypes. Among the associated variants were SNPs in or near genes that may be considered candidates for further study, such as rs1376877 (GEE p < 0.000001, located in ABI2) for maximum internal carotid artery IMT and rs4814615 (FBAT p = 0.000003, located in PCSK2) for maximum common carotid artery IMT. Modest significant associations were noted with various SCA phenotypes for variants in previously reported atherosclerosis candidate genes, including NOS3 and ESR1. Associations were also noted of a region on chromosome 9p21 with CAC phenotypes that confirm associations with coronary heart disease and CAC in two recently reported genome-wide association studies. In linkage analyses, several regions of genome-wide linkage were noted, confirming previously reported linkage of internal carotid artery IMT on chromosome 12. All GEE, FBAT and linkage results are provided as an open-access results resource at .
The results from this GWAS generate hypotheses regarding several SNPs that may be associated with SCA phenotypes in multiple arterial beds. Given the number of tests conducted, subsequent independent replication in a staged approach is essential to identify genetic variants that may be implicated in atherosclerosis.
PMCID: PMC1995605  PMID: 17903303
5.  Testing for direct genetic effects using a screening step in family-based association studies 
Frontiers in Genetics  2013;4:243.
In genome wide association studies (GWAS), family-based studies tend to have less power to detect genetic associations than population-based studies, such as case-control studies. This can be an issue when testing if genes in a family-based GWAS have a direct effect on the phenotype of interest over and above their possible indirect effect through a secondary phenotype. When multiple SNPs are tested for a direct effect in the family-based study, a screening step can be used to minimize the burden of multiple comparisons in the causal analysis. We propose a 2-stage screening step that can be incorporated into the family-based association test (FBAT) approach similar to the conditional mean model approach in the Van Steen-algorithm (Van Steen et al., 2005). Simulations demonstrate that the type 1 error is preserved and this method is advantageous when multiple markers are tested. This method is illustrated by an application to the Framingham Heart Study.
PMCID: PMC3836057  PMID: 24312120
family-based association analysis; causal inference; genetic pathway; mediation; pleiotropy
6.  Combining an Evolution-guided Clustering Algorithm and Haplotype-based LRT in Family Association Studies 
BMC Genetics  2011;12:48.
With the completion of the international HapMap project, many studies have been conducted to investigate the association between complex diseases and haplotype variants. Such haplotype-based association studies, however, often face two difficulties; one is the large number of haplotype configurations in the chromosome region under study, and the other is the ambiguity in haplotype phase when only genotype data are observed. The latter complexity may be handled based on an EM algorithm with family data incorporated, whereas the former can be more problematic, especially when haplotypes of rare frequencies are involved. Here based on family data we propose to cluster long haplotypes of linked SNPs in a biological sense, so that the number of haplotypes can be reduced and the power of statistical tests of association can be increased.
In this paper we employ family genotype data and combine a clustering scheme with a likelihood ratio statistic to test the association between quantitative phenotypes and haplotype variants. Haplotypes are first grouped based on their evolutionary closeness to establish a set containing core haplotypes. Then, we construct for each family the transmission and non-transmission phase in terms of these core haplotypes, taking into account simultaneously the phase ambiguity as weights. The likelihood ratio test (LRT) is next conducted with these weighted and clustered haplotypes to test for association with disease. This combination of evolution-guided haplotype clustering and weighted assignment in LRT is able, via its core-coding system, to incorporate into analysis both haplotype phase ambiguity and transmission uncertainty. Simulation studies show that this proposed procedure is more informative and powerful than three family-based association tests, FAMHAP, FBAT, and an LRT with a group consisting exclusively of rare haplotypes.
The proposed procedure takes into account the uncertainty in phase determination and in transmission, utilizes the evolutionary information contained in haplotypes, reduces the dimension in haplotype space and the degrees of freedom in tests, and performs better in association studies. This evolution-guided clustering procedure is particularly useful for long haplotypes containing linked SNPs, and is applicable to other haplotype-based association tests. This procedure is now implemented in R and is free for download.
PMCID: PMC3118131  PMID: 21592403
7.  Is a gene important for bone resorption a candidate for obesity? An association and linkage study on the RANK (receptor activator of nuclear factor-κB) gene in a large Caucasian sample 
Human genetics  2006;120(4):561-570.
In light of findings that osteoporosis and obesity may share some common genetic determination and previous reports that RANK (receptor activator of nuclear factor-κB) is expressed in skeletal muscles which are important for energy metabolism, we hypothesize that RANK, a gene essential for osteoclastogenesis, is also important for obesity. In order to test the hypothesis with solid data we first performed a linkage analysis around the RANK gene in 4,102 Caucasian subjects from 434 pedigrees, then we genotyped 19 SNPs in or around the RANK gene. A family-based association test (FBAT) was performed with both a quantitative measure of obesity [fat mass, lean mass, body mass index (BMI), and percentage fat mass (PFM)] and a dichotomously defined obesity phenotype–OB (OB if BMI ≥ 30 kg/m2). In the linkage analysis, an empirical P = 0.004 was achieved at the location of the RANK gene for BMI. Family-based association analysis revealed significant associations of eight SNPs with at least one obesity-related phenotype (P < 0.05). Evidence of association was obtained at SNP10 (P = 0.002) and SNP16 (P = 0.001) with OB; SNP1 with fat mass (P = 0.003); SNP1 (P = 0.003) and SNP7 (P = 0.003) with lean mass; SNP1 (P = 0.002) and SNP7 (P = 0.002) with BMI; SNP1 (P = 0.003), SNP4 (P = 0.007), and SNP7 (P = 0.002) with PFM. In order to deal with the complex multiple testing issues, we performed FBAT multi-marker test (FBAT-MM) to evaluate the association between all the 18 SNPs and each obesity phenotype. The P value is 0.126 for OB, 0.033 for fat mass, 0.021 for lean mass, 0.016 for BMI, and 0.006 for PFM. The haplotype data analyses provide further association evidence. In conclusion, for the first time, our results suggest that RANK is a novel candidate for determination of obesity.
PMCID: PMC1829481  PMID: 16960694
8.  Family-based association analysis: a fast and efficient method of multivariate association analysis with multiple variants 
BMC Bioinformatics  2015;16(1):46.
Many disease phenotypes are outcomes of the complicated interplay between multiple genes, and multiple phenotypes are affected by a single or multiple genotypes. Therefore, joint analysis of multiple phenotypes and multiple markers has been considered as an efficient strategy for genome-wide association analysis, and in this work we propose an omnibus family-based association test for the joint analysis of multiple genotypes and multiple phenotypes.
The proposed test can be applied for both quantitative and dichotomous phenotypes, and it is robust under the presence of population substructure, as long as large-scale genomic data is available. Using simulated data, we showed that our method is statistically more efficient than the existing methods, and the practical relevance is illustrated by application of the approach to obesity-related phenotypes.
The proposed method may be more statistically efficient than the existing methods. The application was developed in C++ and is available at the following URL:
PMCID: PMC4339744  PMID: 25887481
Family-based association analysis; Multiple variants; Multiple phenotypes
9.  Imputation-Based Analysis of Association Studies: Candidate Regions and Quantitative Traits 
PLoS Genetics  2007;3(7):e114.
We introduce a new framework for the analysis of association studies, designed to allow untyped variants to be more effectively and directly tested for association with a phenotype. The idea is to combine knowledge on patterns of correlation among SNPs (e.g., from the International HapMap project or resequencing data in a candidate region of interest) with genotype data at tag SNPs collected on a phenotyped study sample, to estimate (“impute”) unmeasured genotypes, and then assess association between the phenotype and these estimated genotypes. Compared with standard single-SNP tests, this approach results in increased power to detect association, even in cases in which the causal variant is typed, with the greatest gain occurring when multiple causal variants are present. It also provides more interpretable explanations for observed associations, including assessing, for each SNP, the strength of the evidence that it (rather than another correlated SNP) is causal. Although we focus on association studies with quantitative phenotype and a relatively restricted region (e.g., a candidate gene), the framework is applicable and computationally practical for whole genome association studies. Methods described here are implemented in a software package, Bim-Bam, available from the Stephens Lab website
Author Summary
Ongoing association studies are evaluating the influence of genetic variation on phenotypes of interest (hereditary traits and susceptibility to disease) in large patient samples. However, although genotyping is relatively cheap, most association studies genotype only a small proportion of SNPs in the region of study, with many SNPs remaining untyped. Here, we present methods for assessing whether these untyped SNPs are associated with the phenotype of interest. The methods exploit information on patterns of multi-marker correlation (“linkage disequilibrium”) from publically available databases, such as the International HapMap project or the SeattleSNPs resequencing studies, to estimate (“impute”) patient genotypes at untyped SNPs, and assess the estimated genotypes for association with phenotype. We show that, particularly for common causal variants, these methods are highly effective. Compared with standard methods, they provide both greater power to detect associations between genetic variation and phenotypes, and also better explanations of detected associations, in many cases closely approximating results that would have been obtained by genotyping all SNPs.
PMCID: PMC1934390  PMID: 17676998
10.  Detecting purely epistatic multi-locus interactions by an omnibus permutation test on ensembles of two-locus analyses 
BMC Bioinformatics  2009;10:294.
Purely epistatic multi-locus interactions cannot generally be detected via single-locus analysis in case-control studies of complex diseases. Recently, many two-locus and multi-locus analysis techniques have been shown to be promising for the epistasis detection. However, exhaustive multi-locus analysis requires prohibitively large computational efforts when problems involve large-scale or genome-wide data. Furthermore, there is no explicit proof that a combination of multiple two-locus analyses can lead to the correct identification of multi-locus interactions.
The proposed 2LOmb algorithm performs an omnibus permutation test on ensembles of two-locus analyses. The algorithm consists of four main steps: two-locus analysis, a permutation test, global p-value determination and a progressive search for the best ensemble. 2LOmb is benchmarked against an exhaustive two-locus analysis technique, a set association approach, a correlation-based feature selection (CFS) technique and a tuned ReliefF (TuRF) technique. The simulation results indicate that 2LOmb produces a low false-positive error. Moreover, 2LOmb has the best performance in terms of an ability to identify all causative single nucleotide polymorphisms (SNPs) and a low number of output SNPs in purely epistatic two-, three- and four-locus interaction problems. The interaction models constructed from the 2LOmb outputs via a multifactor dimensionality reduction (MDR) method are also included for the confirmation of epistasis detection. 2LOmb is subsequently applied to a type 2 diabetes mellitus (T2D) data set, which is obtained as a part of the UK genome-wide genetic epidemiology study by the Wellcome Trust Case Control Consortium (WTCCC). After primarily screening for SNPs that locate within or near 372 candidate genes and exhibit no marginal single-locus effects, the T2D data set is reduced to 7,065 SNPs from 370 genes. The 2LOmb search in the reduced T2D data reveals that four intronic SNPs in PGM1 (phosphoglucomutase 1), two intronic SNPs in LMX1A (LIM homeobox transcription factor 1, alpha), two intronic SNPs in PARK2 (Parkinson disease (autosomal recessive, juvenile) 2, parkin) and three intronic SNPs in GYS2 (glycogen synthase 2 (liver)) are associated with the disease. The 2LOmb result suggests that there is no interaction between each pair of the identified genes that can be described by purely epistatic two-locus interaction models. Moreover, there are no interactions between these four genes that can be described by purely epistatic multi-locus interaction models with marginal two-locus effects. The findings provide an alternative explanation for the aetiology of T2D in a UK population.
An omnibus permutation test on ensembles of two-locus analyses can detect purely epistatic multi-locus interactions with marginal two-locus effects. The study also reveals that SNPs from large-scale or genome-wide case-control data which are discarded after single-locus analysis detects no association can still be useful for genetic epidemiology studies.
PMCID: PMC2759961  PMID: 19761607
11.  Association Study of SNAP25 and Schizophrenia in Irish Family and Case–Control Samples 
SNAP25 occurs on chromosome 20p12.2, which has been linked to schizophrenia in some samples, and recently linked to latent classes of psychotic illness in our sample. SNAP25 is crucial to synaptic functioning, may be involved in axonal growth and dendritic sprouting, and its expression may be decreased in schizophrenia. We genotyped 18 haplotype-tagging SNPs in SNAP25 in a sample of 270 Irish high-density families. Single marker and haplotype analyses were performed in FBAT and PDT. We adjusted for multiple testing by computing q values. Association was followed up in an independent sample of 657 cases and 411 controls. We tested for allelic effects on the clinical phenotype by using the method of sequential addition and 5 factor-derived scores of the OPCRIT. Nine of 18 SNPs had P values <0.05 in either FBAT or PDT for one or more definitions of illness. Several two-marker haplotypes were also associated. Subjects inheriting the risk alleles of the most significantly associated two-marker haplotype were likely to have higher levels of hallucinations and delusions. The most significantly associated marker, rs6039820, was observed to perturb 12 transcription-factor binding sites in in silico analyses. An attempt to replicate association findings in the case–control sample resulted in no SNPs being significantly associated. We observed robust association in both single marker and haplotype-based analyses between SNAP25 and schizophrenia in an Irish family sample. Although we failed to replicate this in an independent sample, this gene should be further tested in other samples.
PMCID: PMC2859301  PMID: 19806613
schizophrenia; SNAP25; polymorphism; association; clinical features
12.  A Dimension Reduction Approach for Modeling Multi-Locus Interaction in Case-Control Studies 
Human Heredity  2011;71(4):234-245.
Studying one locus or one single nucleotide polymorphism (SNP) at a time may not be sufficient to understand complex diseases because they are unlikely to result from the effect of only one SNP. Each SNP alone may have little or no effect on the risk of the disease, but together they may increase the risk substantially. Analyses focusing on individual SNPs ignore the possibility of interaction among SNPs. In this paper, we propose a parsimonious model to assess the joint effect of a group of SNPs in a case-control study. The model implements a data reduction strategy within a likelihood framework and uses a test to assess the statistical significance of the effect of the group of SNPs on the binary trait. The primary advantage of the proposed approach is that the dimension reduction technique produces a test statistic with degrees of freedom significantly lower than a multiple logistic regression with only main effects of the SNPs, and our parsimonious model can incorporate the possibility of interaction among the SNPs. Moreover, the proposed approach estimates the direction of association of each SNP with the disease and provides an estimate of the average effect of the group of SNPs positively and negatively associated with the disease in the given SNP set. We illustrate the proposed model on simulated and real data, and compare its performance with a few other existing approaches. Our proposed approach appeared to outperform the other approaches for independent SNPs in our simulation studies.
PMCID: PMC3136376  PMID: 21734407
Case-control study; Gene-gene interaction; Dimension reduction
13.  Identifying genetic marker sets associated with phenotypes via an efficient adaptive score test 
Biostatistics (Oxford, England)  2012;13(4):776-790.
In recent years, genome-wide association studies (GWAS) and gene-expression profiling have generated a large number of valuable datasets for assessing how genetic variations are related to disease outcomes. With such datasets, it is often of interest to assess the overall effect of a set of genetic markers, assembled based on biological knowledge. Genetic marker-set analyses have been advocated as more reliable and powerful approaches compared with the traditional marginal approaches (Curtis and others, 2005. Pathways to the analysis of microarray data. TRENDS in Biotechnology 23, 429–435; Efroni and others, 2007. Identification of key processes underlying cancer phenotypes using biologic pathway analysis. PLoS One 2, 425). Procedures for testing the overall effect of a marker-set have been actively studied in recent years. For example, score tests derived under an Empirical Bayes (EB) framework (Liu and others, 2007. Semiparametric regression of multidimensional genetic pathway data: least-squares kernel machines and linear mixed models. Biometrics 63, 1079–1088; Liu and others, 2008. Estimation and testing for the effect of a genetic pathway on a disease outcome using logistic kernel machine regression via logistic mixed models. BMC bioinformatics 9, 292–2; Wu and others, 2010. Powerful SNP-set analysis for case-control genome-wide association studies. American Journal of Human Genetics 86, 929) have been proposed as powerful alternatives to the standard Rao score test (Rao, 1948. Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 50–57). The advantages of these EB-based tests are most apparent when the markers are correlated, due to the reduction in the degrees of freedom. In this paper, we propose an adaptive score test which up- or down-weights the contributions from each member of the marker-set based on the Z-scores of their effects. Such an adaptive procedure gains power over the existing procedures when the signal is sparse and the correlation among the markers is weak. By combining evidence from both the EB-based score test and the adaptive test, we further construct an omnibus test that attains good power in most settings. The null distributions of the proposed test statistics can be approximated well either via simple perturbation procedures or via distributional approximations. Through extensive simulation studies, we demonstrate that the proposed procedures perform well in finite samples. We apply the tests to a breast cancer genetic study to assess the overall effect of the FGFR2 gene on breast cancer risk.
PMCID: PMC3440238  PMID: 22734045
Adaptive procedures; Empirical Bayes; GWAS; Pathway analysis; Score test; SNP sets
14.  PBAT: A comprehensive software package for genome-wide association analysis of complex family-based studies 
Human Genomics  2005;2(1):67-69.
The PBAT software package (v2.5) provides a unique set of tools for complex family-based association analysis at a genome-wide level. PBAT can handle nuclear families with missing parental genotypes, extended pedigrees with missing genotypic information, analysis of single nucleotide polymorphisms (SNPs), haplotype analysis, quantitative traits, multivariate/longitudinal data and time to onset phenotypes. The data analysis can be adjusted for covariates and gene/environment interactions. Haplotype-based features include sliding windows and the reconstruction of the haplotypes of the probands. PBAT's screening tools allow the user successfully to handle the multiple comparisons problem at a genome-wide level, even for 100,000 SNPs and more. Moreover, PBAT is computationally fast. A genome scan of 300,000 SNPs in 2,000 trios takes 4 central processing unit (CPU)-days. PBAT is available for Linux, Sun Solaris and Windows XP.
PMCID: PMC3525120  PMID: 15814068
association analysis; extended pedigrees; genome-wide screening; quantitative and qualitative traits; haplotypes
15.  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
16.  A Joint Association Test for Multiple SNPs in Genetic Case-Control Studies 
Genetic epidemiology  2009;33(2):151-163.
For a dense set of genetic markers such as single nucleotide polymorphisms (SNPs) on high linkage disequilibrium within a small candidate region, a haplotype-based approach for testing association between a disease phenotype and the set of markers is attractive in reducing the data complexity and increasing the statistical power. However, due to unknown status of the underlying disease variant, a comprehensive association test may require consideration of various combinations of the SNPs, which often leads to severe multiple testing problems. In this paper, we propose a latent variable approach to test for association of multiple tightly linked SNPs in case-control studies. First, we introduce a latent variable into the penetrance model to characterize a putative disease susceptible locus (DSL) that may consist of a marker allele, a haplotype from a subset of the markers, or an allele at a putative locus between the markers. Next, through using of a retrospective likelihood to adjust for the case-control sampling ascertainment and appropriately handle the Hardy-Weinberg equilibrium constraint, we develop an expectation-maximization (EM)-based algorithm to fit the penetrance model and estimate the joint haplotype frequencies of the DSL and markers simultaneously. With the latent variable to describe a flexible role of the DSL, the likelihood ratio statistic can then provide a joint association test for the set of markers without requiring an adjustment for testing of multiple haplotypes. Our simulation results also reveal that the latent variable approach may have improved power under certain scenarios comparing with classical haplotype association methods.
PMCID: PMC2719721  PMID: 18770519
haplotype association; retrospective likelihood; latent variable; logistic mixture model; EM algorithm
The annals of applied statistics  2014;8(1):352-376.
Genetic association studies have been a popular approach for assessing the association between common Single Nucleotide Polymorphisms (SNPs) and complex diseases. However, other genomic data involved in the mechanism from SNPs to disease, e.g., gene expressions, are usually neglected in these association studies. In this paper, we propose to exploit gene expression information to more powerfully test the association between SNPs and diseases by jointly modeling the relations among SNPs, gene expressions and diseases. We propose a variance component test for the total effect of SNPs and a gene expression on disease risk. We cast the test within the causal mediation analysis framework with the gene expression as a potential mediator. For eQTL SNPs, the use of gene expression information can enhance power to test for the total effect of a SNP-set, which are the combined direct and indirect effects of the SNPs mediated through the gene expression, on disease risk. We show that the test statistic under the null hypothesis follows a mixture of χ2 distributions, which can be evaluated analytically or empirically using the resampling-based perturbation method. We construct tests for each of three disease models that is determined by SNPs only, SNPs and gene expression, or includes also their interactions. As the true disease model is unknown in practice, we further propose an omnibus test to accommodate different underlying disease models. We evaluate the finite sample performance of the proposed methods using simulation studies, and show that our proposed test performs well and the omnibus test can almost reach the optimal power where the disease model is known and correctly specified. We apply our method to re-analyze the overall effect of the SNP-set and expression of the ORMDL3 gene on the risk of asthma.
PMCID: PMC3981558  PMID: 24729824
Causal Inference; Data Integration; Mediation Analysis; Mixed Models; Score Test; SNP Set Analysis; Variance Component Test
18.  GUESS-ing Polygenic Associations with Multiple Phenotypes Using a GPU-Based Evolutionary Stochastic Search Algorithm 
PLoS Genetics  2013;9(8):e1003657.
Genome-wide association studies (GWAS) yielded significant advances in defining the genetic architecture of complex traits and disease. Still, a major hurdle of GWAS is narrowing down multiple genetic associations to a few causal variants for functional studies. This becomes critical in multi-phenotype GWAS where detection and interpretability of complex SNP(s)-trait(s) associations are complicated by complex Linkage Disequilibrium patterns between SNPs and correlation between traits. Here we propose a computationally efficient algorithm (GUESS) to explore complex genetic-association models and maximize genetic variant detection. We integrated our algorithm with a new Bayesian strategy for multi-phenotype analysis to identify the specific contribution of each SNP to different trait combinations and study genetic regulation of lipid metabolism in the Gutenberg Health Study (GHS). Despite the relatively small size of GHS (n = 3,175), when compared with the largest published meta-GWAS (n>100,000), GUESS recovered most of the major associations and was better at refining multi-trait associations than alternative methods. Amongst the new findings provided by GUESS, we revealed a strong association of SORT1 with TG-APOB and LIPC with TG-HDL phenotypic groups, which were overlooked in the larger meta-GWAS and not revealed by competing approaches, associations that we replicated in two independent cohorts. Moreover, we demonstrated the increased power of GUESS over alternative multi-phenotype approaches, both Bayesian and non-Bayesian, in a simulation study that mimics real-case scenarios. We showed that our parallel implementation based on Graphics Processing Units outperforms alternative multi-phenotype methods. Beyond multivariate modelling of multi-phenotypes, our Bayesian model employs a flexible hierarchical prior structure for genetic effects that adapts to any correlation structure of the predictors and increases the power to identify associated variants. This provides a powerful tool for the analysis of diverse genomic features, for instance including gene expression and exome sequencing data, where complex dependencies are present in the predictor space.
Author Summary
Nowadays, the availability of cheaper and accurate assays to quantify multiple (endo)phenotypes in large population cohorts allows multi-trait studies. However, these studies are limited by the lack of flexible models integrated with efficient computational tools for genome-wide multi SNPs-traits analyses. To overcome this problem, we propose a novel Bayesian analysis strategy and a new algorithmic implementation which exploits parallel processing architecture for fully multivariate modeling of groups of correlated phenotypes at the genome-wide scale. In addition to increased power of our algorithm over alternative Bayesian and well-established non-Bayesian multi-phenotype methods, we provide an application to a real case study of several blood lipid traits, and show how our method recovered most of the major associations and is better at refining multi-trait polygenic associations than alternative methods. We reveal and replicate in independent cohorts new associations with two phenotypic groups that were not detected by competing multivariate approaches and not noticed by a large meta-GWAS. We also discuss the applicability of the proposed method to large meta-analyses involving hundreds of thousands of individuals and to diverse genomic datasets where complex dependencies in the predictor space are present.
PMCID: PMC3738451  PMID: 23950726
19.  Simultaneous Discovery, Estimation and Prediction Analysis of Complex Traits Using a Bayesian Mixture Model 
PLoS Genetics  2015;11(4):e1004969.
Gene discovery, estimation of heritability captured by SNP arrays, inference on genetic architecture and prediction analyses of complex traits are usually performed using different statistical models and methods, leading to inefficiency and loss of power. Here we use a Bayesian mixture model that simultaneously allows variant discovery, estimation of genetic variance explained by all variants and prediction of unobserved phenotypes in new samples. We apply the method to simulated data of quantitative traits and Welcome Trust Case Control Consortium (WTCCC) data on disease and show that it provides accurate estimates of SNP-based heritability, produces unbiased estimators of risk in new samples, and that it can estimate genetic architecture by partitioning variation across hundreds to thousands of SNPs. We estimated that, depending on the trait, 2,633 to 9,411 SNPs explain all of the SNP-based heritability in the WTCCC diseases. The majority of those SNPs (>96%) had small effects, confirming a substantial polygenic component to common diseases. The proportion of the SNP-based variance explained by large effects (each SNP explaining 1% of the variance) varied markedly between diseases, ranging from almost zero for bipolar disorder to 72% for type 1 diabetes. Prediction analyses demonstrate that for diseases with major loci, such as type 1 diabetes and rheumatoid arthritis, Bayesian methods outperform profile scoring or mixed model approaches.
Author Summary
Most genome-wide association studies performed to date have focused on testing individual genetic markers for associations with phenotype. Recently, methods that analyse the joint effects of multiple markers on genetic variation have provided further insights into the genetic basis of complex human traits. In addition, there is increasing interest in using genotype data for genetic risk prediction of disease. Often disparate analytical methods are used for each of these tasks. We propose a flexible novel approach that simultaneously performs identification of susceptibility loci, inference on the genetic architecture and provides polygenic risk prediction in the same statistical model. We illustrate the broad applicability of the approach by considering both simulated and real data. In the analysis of seven common diseases we show large differences in the proportion of genetic variation due to loci with different effect sizes and differences in prediction accuracy between complex traits. These findings are important for future studies and the understanding of the complex genetic architecture of common diseases.
PMCID: PMC4388571  PMID: 25849665
20.  Capturing the Spectrum of Interaction Effects in Genetic Association Studies by Simulated Evaporative Cooling Network Analysis 
PLoS Genetics  2009;5(3):e1000432.
Evidence from human genetic studies of several disorders suggests that interactions between alleles at multiple genes play an important role in influencing phenotypic expression. Analytical methods for identifying Mendelian disease genes are not appropriate when applied to common multigenic diseases, because such methods investigate association with the phenotype only one genetic locus at a time. New strategies are needed that can capture the spectrum of genetic effects, from Mendelian to multifactorial epistasis. Random Forests (RF) and Relief-F are two powerful machine-learning methods that have been studied as filters for genetic case-control data due to their ability to account for the context of alleles at multiple genes when scoring the relevance of individual genetic variants to the phenotype. However, when variants interact strongly, the independence assumption of RF in the tree node-splitting criterion leads to diminished importance scores for relevant variants. Relief-F, on the other hand, was designed to detect strong interactions but is sensitive to large backgrounds of variants that are irrelevant to classification of the phenotype, which is an acute problem in genome-wide association studies. To overcome the weaknesses of these data mining approaches, we develop Evaporative Cooling (EC) feature selection, a flexible machine learning method that can integrate multiple importance scores while removing irrelevant genetic variants. To characterize detailed interactions, we construct a genetic-association interaction network (GAIN), whose edges quantify the synergy between variants with respect to the phenotype. We use simulation analysis to show that EC is able to identify a wide range of interaction effects in genetic association data. We apply the EC filter to a smallpox vaccine cohort study of single nucleotide polymorphisms (SNPs) and infer a GAIN for a collection of SNPs associated with adverse events. Our results suggest an important role for hubs in SNP disease susceptibility networks. The software is available at
Author Summary
Susceptibility to many diseases and disorders is caused by breakdown at multiple points in the genetic network. Each of these points of breakdown by itself may have a very modest effect on disease risk but the points may have a much stronger effect through statistical interactions with each other. Genome-wide association studies provide the opportunity to identify alleles at multiple loci that interact to influence phenotypic variation in common diseases and disorders. However, if each SNP is tested for association as though it were independent of the rest of the genome, then the full advantage of the variation from markers across the genome will be unfulfilled. In this study, we illustrate the utility of a new approach to high-dimensional genetic association analysis that treats the collection of SNPs as interacting on a system level. This approach uses a machine-learning filter followed by an information theoretic and graph theoretic approach to infer a phenotype-specific network of interacting SNPs.
PMCID: PMC2653647  PMID: 19300503
21.  A three-stage approach for genome-wide association studies with family data for quantitative traits 
BMC Genetics  2010;11:40.
Genome-wide association (GWA) studies that use population-based association approaches may identify spurious associations in the presence of population admixture. In this paper, we propose a novel three-stage approach that is computationally efficient and robust to population admixture and more powerful than the family-based association test (FBAT) for GWA studies with family data.
We propose a three-stage approach for GWA studies with family data. The first stage is to perform linear regression ignoring phenotypic correlations among family members. SNPs with a first stage p-value below a liberal cut-off (e.g. 0.1) are then analyzed in the second stage that employs a linear mixed effects (LME) model that accounts for within family correlations. Next, SNPs that reach genome-wide significance (e.g. 10-6 for 34,625 genotyped SNPs in this paper) are analyzed in the third stage using FBAT, with correction of multiple testing only for SNPs that enter the third stage. Simulations are performed to evaluate type I error and power of the proposed method compared to LME adjusting for 10 principal components (PC) of the genotype data. We also apply the three-stage approach to the GWA analyses of uric acid in Framingham Heart Study's SNP Health Association Resource (SHARe) project.
Our simulations show that whether or not population admixture is present, the three-stage approach has no inflated type I error. In terms of power, using LME adjusting PC is only slightly more powerful than the three-stage approach. When applied to the GWA analyses of uric acid in the SHARe project of FHS, the three-stage approach successfully identified and confirmed three SNPs previously reported as genome-wide significant signals.
For GWA analyses of quantitative traits with family data, our three-stage approach provides another appealing solution to population admixture, in addition to LME adjusting for genetic PC.
PMCID: PMC2892427  PMID: 20470424
22.  Linkage and association of myocilin (MYOC) polymorphisms with high myopia in a Chinese population 
Molecular Vision  2007;13:534-544.
To test the association between myocilin gene (MYOC) polymorphisms and high myopia in Hong Kong Chinese by using family-based association study.
A total of 162 Chinese nuclear families, consisting of 557 members, were recruited from an optometry clinic. Each family had two parents and at least one offspring with high myopia (defined as -6.00D or less for both eyes). All offspring were healthy with no clinical evidence of syndromic disease and other ocular abnormality. Genotyping was performed for two MYOC microsatellites (NGA17 and NGA19) and five tag single nucleotide polymorphisms (SNPs) spreading across the gene. The genotype data were analyzed with Family-Based Association Test (FBAT) software to check linkage and association between the genetic markers and myopia, and with GenAssoc to generate case and pseudocontrol subjects for investigating main effects of genetic markers and calculating the genotype relative risks (GRR).
FBAT analysis showed linkage and association with high myopia for two microsatellites and two SNPs under one to three genetic models after correction for multiple comparisons by false discovery rate. NGA17 at the promoter was significant under an additive model (p=0.0084), while NGA19 at the 3' flanking region showed significant results under both additive (p=0.0172) and dominant (p=0.0053) models. SNP rs2421853 (C>T) exhibited both linkage and association under additive (p=0.0009) and dominant/recessive (p=0.0041) models. SNP rs235858 (T>C) was also significant under additive (p=4.0E-6) and dominant/recessive (p=2.5E-5) models. Both SNPs were downstream of NGA19 at the 3' flanking region. Positive results for these SNPs were novel findings. A stepwise conditional logistic regression analysis of the case-pseudocontrol dataset generated by GenAssoc from the families showed that both SNPs could separately account for the association of NGA17 or NGA19, and that both SNPs contributed separate main effects to high myopia. For rs2421853 and with C/C as the reference genotype, the GRR increased from 1.678 for G/A to 2.738 for A/A (p=9.0E-4, global Wald test). For rs235858 and with G/G as the reference, the GRR increased 2.083 for G/A to 3.931 for A/A (p=2.0E-2, global Wald test). GRR estimates thus suggested an additive model for both SNPs, which was consistent with the finding that, of the three models tested, the additive model gave the lowest p values in FBAT analysis.
Linkage and association was shown between the MYOC polymorphisms and high myopia in our family-based association study. The SNP rs235858 at the 3' flanking region showed the highest degree of confidence for association.
PMCID: PMC2652017  PMID: 17438518
23.  Statistical Power of Model Selection Strategies for Genome-Wide Association Studies 
PLoS Genetics  2009;5(7):e1000582.
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
Author Summary
Almost all published genome-wide association studies are based on single-marker analysis. Intuitively, joint consideration of multiple markers should be more informative when multiple genes and their interactions are involved in disease etiology. For example, an exhaustive search among models involving multiple markers and their interactions can identify certain gene–gene interactions that will be missed by single-marker analysis. However, an exhaustive search is difficult, or even impossible, to perform because of the computational requirements. Moreover, searching more models does not necessarily increase statistical power, because there may be an increased chance of finding false positive results when more models are explored. For power comparisons of different model selection methods, the published studies have relied on limited simulations due to the highly computationally intensive nature of such simulation studies. To enable researchers to compare different model search strategies without resorting to extensive simulations, we develop a novel analytical approach to evaluating the statistical power of these methods. Our results offer insights into how different parameters in a genetic model affect the statistical power of a given model selection strategy. We developed an R package to implement our results. This package can be used by researchers to compare and select an effective approach to detecting SNPs.
PMCID: PMC2712761  PMID: 19649321
24.  Genome-wide association and linkage analyses of hemostatic factors and hematological phenotypes in the Framingham Heart Study 
BMC Medical Genetics  2007;8(Suppl 1):S12.
Increased circulating levels of hemostatic factors as well as anemia have been associated with increased risk of cardiovascular disease (CVD). Known associations between hemostatic factors and sequence variants at genes encoding these factors explain only a small proportion of total phenotypic variation. We sought to confirm known putative loci and identify novel loci that may influence either trait in genome-wide association and linkage analyses using the Affymetrix GeneChip 100K single nucleotide polymorphism (SNP) set.
Plasma levels of circulating hemostatic factors (fibrinogen, factor VII, plasminogen activator inhibitor-1, von Willebrand factor, tissue plasminogen activator, D-dimer) and hematological phenotypes (platelet aggregation, viscosity, hemoglobin, red blood cell count, mean corpuscular volume, mean corpuscular hemoglobin concentration) were obtained in approximately 1000 Framingham Heart Study (FHS) participants from 310 families. Population-based association analyses using the generalized estimating equations (GEE), family-based association test (FBAT), and multipoint variance components linkage analyses were performed on the multivariable adjusted residuals of hemostatic and hematological phenotypes.
In association analysis, the lowest GEE p-value for hemostatic factors was p = 4.5*10-16 for factor VII at SNP rs561241, a variant located near the F7 gene and in complete linkage disequilibrium (LD) (r2 = 1) with the Arg353Gln F7 SNP previously shown to account for 9% of total phenotypic variance. The lowest GEE p-value for hematological phenotypes was 7*10-8 at SNP rs2412522 on chromosome 4 for mean corpuscular hemoglobin concentration. We presented top 25 most significant GEE results with p-values in the range of 10-6 to 10-5 for hemostatic or hematological phenotypes. In relating 100K SNPs to known candidate genes, we identified two SNPs (rs1582055, rs4897475) in erythrocyte membrane protein band 4.1-like 2 (EPB41L2) associated with hematological phenotypes (GEE p < 10-3). In linkage analyses, the highest linkage LOD score for hemostatic factors was 3.3 for factor VII on chromosome 10 around 15 Mb, and for hematological phenotypes, LOD 3.4 for hemoglobin on chromosome 4 around 55 Mb. All GEE and FBAT association and variance components linkage results can be found at
Using genome-wide association methodology, we have successfully identified a SNP in complete LD with a sequence variant previously shown to be strongly associated with factor VII, providing proof of principle for this approach. Further study of additional strongly associated SNPs and linked regions may identify novel variants that influence the inter-individual variability in hemostatic factors and hematological phenotypes.
PMCID: PMC1995619  PMID: 17903294
25.  Posterior Association Networks and Functional Modules Inferred from Rich Phenotypes of Gene Perturbations 
PLoS Computational Biology  2012;8(6):e1002566.
Combinatorial gene perturbations provide rich information for a systematic exploration of genetic interactions. Despite successful applications to bacteria and yeast, the scalability of this approach remains a major challenge for higher organisms such as humans. Here, we report a novel experimental and computational framework to efficiently address this challenge by limiting the ‘search space’ for important genetic interactions. We propose to integrate rich phenotypes of multiple single gene perturbations to robustly predict functional modules, which can subsequently be subjected to further experimental investigations such as combinatorial gene silencing. We present posterior association networks (PANs) to predict functional interactions between genes estimated using a Bayesian mixture modelling approach. The major advantage of this approach over conventional hypothesis tests is that prior knowledge can be incorporated to enhance predictive power. We demonstrate in a simulation study and on biological data, that integrating complementary information greatly improves prediction accuracy. To search for significant modules, we perform hierarchical clustering with multiscale bootstrap resampling. We demonstrate the power of the proposed methodologies in applications to Ewing's sarcoma and human adult stem cells using publicly available and custom generated data, respectively. In the former application, we identify a gene module including many confirmed and highly promising therapeutic targets. Genes in the module are also significantly overrepresented in signalling pathways that are known to be critical for proliferation of Ewing's sarcoma cells. In the latter application, we predict a functional network of chromatin factors controlling epidermal stem cell fate. Further examinations using ChIP-seq, ChIP-qPCR and RT-qPCR reveal that the basis of their genetic interactions may arise from transcriptional cross regulation. A Bioconductor package implementing PAN is freely available online at
Author Summary
Synthetic genetic interactions estimated from combinatorial gene perturbation screens provide systematic insights into synergistic interactions of genes in a biological process. However, this approach lacks scalability for large-scale genetic interaction profiling in metazoan organisms such as humans. We contribute to this field by proposing a more scalable and affordable approach, which takes the advantage of multiple single gene perturbation data to predict coherent functional modules followed by genetic interaction investigation using combinatorial perturbations. We developed a versatile computational framework (PAN) to robustly predict functional interactions and search for significant functional modules from rich phenotyping screens of single gene perturbations under different conditions or from multiple cell lines. PAN features a Bayesian mixture model to assess statistical significance of functional associations, the capability to incorporate prior knowledge as well as a generalized approach to search for significant functional modules by multiscale bootstrap resampling. In applications to Ewing's sarcoma and human adult stem cells, we demonstrate the general applicability and prediction power of PAN to both public and custom generated screening data.
PMCID: PMC3386165  PMID: 22761558

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