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1.  Genetic Analysis Workshop 17 mini-exome simulation 
BMC Proceedings  2011;5(Suppl 9):S2.
The data set simulated for Genetic Analysis Workshop 17 was designed to mimic a subset of data that might be produced in a full exome screen for a complex disorder and related risk factors in order to permit workshop participants to investigate issues of study design and statistical genetic analysis. Real sequence data from the 1000 Genomes Project formed the basis for simulating a common disease trait with a prevalence of 30% and three related quantitative risk factors in a sample of 697 unrelated individuals and a second sample of 697 individuals in large, extended pedigrees. Called genotypes for 24,487 autosomal markers assigned to 3,205 genes and simulated affection status, quantitative traits, age, sex, pedigree relationships, and cigarette smoking were provided to workshop participants. The simulating model included both common and rare variants with minor allele frequencies ranging from 0.07% to 25.8% and a wide range of effect sizes for these variants. Genotype-smoking interaction effects were included for variants in one gene. Functional variants were concentrated in genes selected from specific biological pathways and were selected on the basis of the predicted deleteriousness of the coding change. For each sample, unrelated individuals and family, 200 replicates of the phenotypes were simulated.
PMCID: PMC3287854  PMID: 22373155
2.  Evaluation of a LASSO regression approach on the unrelated samples of Genetic Analysis Workshop 17 
BMC Proceedings  2011;5(Suppl 9):S12.
The Genetic Analysis Workshop 17 data we used comprise 697 unrelated individuals genotyped at 24,487 single-nucleotide polymorphisms (SNPs) from a mini-exome scan, using real sequence data for 3,205 genes annotated by the 1000 Genomes Project and simulated phenotypes. We studied 200 sets of simulated phenotypes of trait Q2. An important feature of this data set is that most SNPs are rare, with 87% of the SNPs having a minor allele frequency less than 0.05. For rare SNP detection, in this study we performed a least absolute shrinkage and selection operator (LASSO) regression and F tests at the gene level and calculated the generalized degrees of freedom to avoid any selection bias. For comparison, we also carried out linear regression and the collapsing method, which sums the rare SNPs, modified for a quantitative trait and with two different allele frequency thresholds. The aim of this paper is to evaluate these four approaches in this mini-exome data and compare their performance in terms of power and false positive rates. In most situations the LASSO approach is more powerful than linear regression and collapsing methods. We also note the difficulty in determining the optimal threshold for the collapsing method and the significant role that linkage disequilibrium plays in detecting rare causal SNPs. If a rare causal SNP is in strong linkage disequilibrium with a common marker in the same gene, power will be much improved.
PMCID: PMC3287844  PMID: 22373385
3.  A Flexible Approach for the Analysis of Rare Variants Allowing for a Mixture of Effects on Binary or Quantitative Traits 
PLoS Genetics  2013;9(8):e1003694.
Multiple rare variants either within or across genes have been hypothesised to collectively influence complex human traits. The increasing availability of high throughput sequencing technologies offers the opportunity to study the effect of rare variants on these traits. However, appropriate and computationally efficient analytical methods are required to account for collections of rare variants that display a combination of protective, deleterious and null effects on the trait. We have developed a novel method for the analysis of rare genetic variation in a gene, region or pathway that, by simply aggregating summary statistics at each variant, can: (i) test for the presence of a mixture of effects on a trait; (ii) be applied to both binary and quantitative traits in population-based and family-based data; (iii) adjust for covariates to allow for non-genetic risk factors and; (iv) incorporate imputed genetic variation. In addition, for preliminary identification of promising genes, the method can be applied to association summary statistics, available from meta-analysis of published data, for example, without the need for individual level genotype data. Through simulation, we show that our method is immune to the presence of bi-directional effects, with no apparent loss in power across a range of different mixtures, and can achieve greater power than existing approaches as long as summary statistics at each variant are robust. We apply our method to investigate association of type-1 diabetes with imputed rare variants within genes in the major histocompatibility complex using genotype data from the Wellcome Trust Case Control Consortium.
Author Summary
Rapid advances in sequencing technology mean that it is now possible to directly assay rare genetic variation. In addition, the availability of almost fully sequenced human genomes by the 1000 Genomes Project allows genotyping at rare variants that are not present on arrays commonly used in genome-wide association studies. Rare variants within a gene or region may act to collectively influence a complex trait. Methods for testing these rare variants should be able to account for a combination of those that serve to either increase, decrease or have no effect on the trait of interest. Here, we introduce a method for the analysis of a collection of rare genetic variants, within a gene or region, which assesses evidence for a mixture of effects. Our method simply aggregates summary statistics at each variant and, as such, can be applied to both population and family-based data, to binary or quantitative traits and to either directly genotyped or imputed data. In addition, it does not require individual level genotype or phenotype data, and can be adjusted for non-genetic risk factors. We illustrate our approach by examining imputed rare variants in the major histocompatibility complex for association with type-1 diabetes using genotype data from the Wellcome Trust case Control Consortium.
PMCID: PMC3744430  PMID: 23966874
4.  Collapsing-based and kernel-based single-gene analyses applied to Genetic Analysis Workshop 17 mini-exome data 
BMC Proceedings  2011;5(Suppl 9):S117.
Recently there has been great interest in identifying rare variants associated with common diseases. We apply several collapsing-based and kernel-based single-gene association tests to Genetic Analysis Workshop 17 (GAW17) rare variant association data with unrelated individuals without knowledge of the simulation model. We also implement modified versions of these methods using additional information, such as minor allele frequency (MAF) and functional annotation. For each of four given traits provided in GAW17, we use the Bayesian mixed-effects model to estimate the phenotypic variance explained by the given environmental and genotypic data and to infer an individual-specific genetic effect to use directly in single-gene association tests. After obtaining information on the GAW17 simulation model, we compare the performance of all methods and examine the top genes identified by those methods. We find that collapsing-based methods with weights based on MAFs are sensitive to the “lower MAF, larger effect size” assumption, whereas kernel-based methods are more robust when this assumption is violated. In addition, many false-positive genes identified by multiple methods often contain variants with exactly the same genotype distribution as the causal variants used in the simulation model. When the sample size is much smaller than the number of rare variants, it is more likely that causal and noncausal variants will share the same or similar genotype distribution. This likely contributes to the low power and large number of false-positive results of all methods in detecting causal variants associated with disease in the GAW17 data set.
PMCID: PMC3287841  PMID: 22373309
5.  Testing Genetic Association with Rare and Common Variants in Family Data 
Genetic epidemiology  2014;38(0 1):S37-S43.
With the advance of next-generation sequencing technologies in recent years, rare genetic variant data have now become available for genetic epidemiology studies. For family samples however, only a few statistical methods for association analysis of rare genetic variants have been developed. Rare variant approaches are of great interest particularly for family data because samples enriched for trait-relevant variants can be ascertained and rare variants are putatively enriched through segregation. To facilitate the evaluation of existing and new rare variant testing approaches for analyzing family data, Genetic Analysis Workshop 18 (GAW18) provided genotype and next-generation sequencing data and longitudinal blood pressure traits from extended pedigrees of Mexican-American families from the San Antonio Family Study. Our GAW18 group members analyzed real and simulated phenotype data from GAW18 by using generalized linear mixed-effects models or principal components to adjust for familial correlation or by testing binary traits using a correction factor for familial effects. With one exception, approaches dealt with the extended pedigrees in their original state using information based on the kinship matrix or alternative genetic similarity measures. For simulated data, our group demonstrated that the family-based kernel machine score test is superior in power to family-based single-marker or burden tests, except in a few specific scenarios. For real data, three contributions identified significant associations. They substantially reduced the number of tests before performing the association analysis. We conclude from our real data analyses that further development of strategies for targeted testing or more focused screening of genetic variants is strongly desirable.
PMCID: PMC4324976  PMID: 25112186
extended pedigrees; rare variant analysis; family-based association test; linear mixed effects model; kernel machine score test; principal components
6.  Comparison of scoring methods for the detection of causal genes with or without rare variants 
BMC Proceedings  2011;5(Suppl 9):S49.
Rare causal variants are believed to significantly contribute to the genetic basis of common diseases or quantitative traits. Appropriate statistical methods are required to discover the highest possible number of disease-relevant variants in a genome-wide screening study. The publicly available Genetic Analysis Workshop 17 data set consists of 697 individuals and 24,487 genetic variants. It includes a simulated complex disease model with intermediate quantitative phenotypes. We compare four gene-wise scoring methods with respect to ranking of causal genes under variable allele frequency thresholds for collapsing of rare variants and considering whether or not rare variants were included. We also compare causal genes for which the ranks differ clearly between scoring methods regarding such characteristics as number and strength of causal variants. We corroborated our findings with additional simulations. We found that the maximum statistics method was superior in assigning high ranks to genes with a single strong causal variant. Hotelling’s T2 test was superior for genes with several independent causal variants. This was consistent for all phenotypes and was confirmed by single-gene analyses and additional simulations. The multivariate analysis performed similarly to Hotelling’s T2 test. The least absolute shrinkage and selection operator (LASSO) analysis was widely comparable with the maximum statistics method. We conclude that the maximum statistics method is a superior alternative to Hotelling’s T2 test if one expects only one independent causal variant per gene with a dominating effect. Such a variant could also be a supermarker derived by collapsing rare variants. Because the true nature of the genetic effect is unknown for real data, both methods need to be taken into consideration.
PMCID: PMC3287886  PMID: 22373454
7.  Using the posterior distribution of deviance to measure evidence of association for rare susceptibility variants 
BMC Proceedings  2011;5(Suppl 9):S38.
Aitkin recently proposed an integrated Bayesian/likelihood approach that he claims is general and simple. We have applied this method, which does not rely on informative prior probabilities or large-sample results, to investigate the evidence of association between disease and the 16 variants in the KDR gene provided by Genetic Analysis Workshop 17. Based on the likelihood of logistic regression models and considering noninformative uniform prior probabilities on the coefficients of the explanatory variables, we used a random walk Metropolis algorithm to simulate the distributions of deviance and deviance difference. The distribution of probability values and the distribution of the proportions of positive deviance differences showed different locations, but the direction of the shift depended on the genetic factor. For the variant with the highest minor allele frequency and for any rare variant, standard logistic regression showed a higher power than the novel approach. For the two variants with the strongest effects on Q1 under a type I error rate of 1%, the integrated approach showed a higher power than standard logistic regression. The advantages and limitations of the integrated Bayesian/likelihood approach should be investigated using additional regions and considering alternative regression models and collapsing methods.
PMCID: PMC3287874  PMID: 22373131
8.  Power of selective genotyping in genome-wide association studies of quantitative traits 
BMC Proceedings  2009;3(Suppl 7):S23.
The selective genotyping approach in quantitative genetics means genotyping only individuals with extreme phenotypes. This approach is considered an efficient way to perform gene mapping, and can be applied in both linkage and association studies. Selective genotyping in association mapping of quantitative trait loci was proposed to increase the power of detecting rare alleles of large effect. However, using this approach, only common variants have been detected. Studies on selective genotyping have been limited to single-locus scenarios. In this study we aim to investigate the power of selective genotyping in a genome-wide association study scenario, and we specifically study the impact of minor allele frequency of variants on the power of this approach. We use the Genetic Analysis Workshop 16 rheumatoid arthritis whole-genome data from the North American Rheumatoid Arthritis Consortium. Two quantitative traits, anti-cyclic citrullinated peptide and rheumatoid factor immunoglobulin M, and one binary trait, rheumatoid arthritis affection status, are used in the analysis. The power of selective genotyping is explored as a function of three parameters: sampling proportion, minor allele frequency of single-nucleotide polymorphism, and test level. The results show that the selective genotyping approach is more efficient in detecting common variants than detecting rare variants, and it is efficient only when the level of declaring significance is not stringent. In summary, the selective genotyping approach is most suitable for detecting common variants in candidate gene-based studies.
PMCID: PMC2795920  PMID: 20018013
9.  Identification of genes and variants associated with quantitative traits using Bayesian factor screening 
BMC Proceedings  2011;5(Suppl 9):S4.
We propose a factor-screening method based on a Bayesian model selection framework and apply it to Genetic Analysis Workshop 17 simulated data with unrelated individuals to identify genes and SNP variants associated with the quantitative trait Q1. A Metropolis-Hasting algorithm is implemented to generate a posterior distribution in a restricted model space and thus the marginal posterior distribution of each variant. Our framework provides flexibility to make inferences on either individual variants or genes. We obtained results for 10 simulated data sets. Our methods are able to identify FTP1 and KDR, two genes that are associated with Q1 in a majority of replicates.
PMCID: PMC3287876  PMID: 22373183
10.  Bayesian estimation of genetic parameters for multivariate threshold and continuous phenotypes and molecular genetic data in simulated horse populations using Gibbs sampling 
BMC Genetics  2007;8:19.
Requirements for successful implementation of multivariate animal threshold models including phenotypic and genotypic information are not known yet. Here simulated horse data were used to investigate the properties of multivariate estimators of genetic parameters for categorical, continuous and molecular genetic data in the context of important radiological health traits using mixed linear-threshold animal models via Gibbs sampling. The simulated pedigree comprised 7 generations and 40000 animals per generation. Additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits were simulated, resembling situations encountered in the Warmblood horse. Quantitative trait locus (QTL) effects and genetic marker information were simulated for one of the liabilities. Different scenarios with respect to recombination rate between genetic markers and QTL and polymorphism information content of genetic markers were studied. For each scenario ten replicates were sampled from the simulated population, and within each replicate six different datasets differing in number and distribution of animals with trait records and availability of genetic marker information were generated. (Co)Variance components were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. Residual variances were fixed to zero and a proper prior was used for the genetic covariance matrix.
Effective sample sizes (ESS) and biases of genetic parameters differed significantly between datasets. Bias of heritability estimates was -6% to +6% for the continuous trait, -6% to +10% for the binary traits of moderate heritability, and -21% to +25% for the binary traits of low heritability. Additive genetic correlations were mostly underestimated between the continuous trait and binary traits of low heritability, under- or overestimated between the continuous trait and binary traits of moderate heritability, and overestimated between two binary traits. Use of trait information on two subsequent generations of animals increased ESS and reduced bias of parameter estimates more than mere increase of the number of informative animals from one generation. Consideration of genotype information as a fixed effect in the model resulted in overestimation of polygenic heritability of the QTL trait, but increased accuracy of estimated additive genetic correlations of the QTL trait.
Combined use of phenotype and genotype information on parents and offspring will help to identify agonistic and antagonistic genetic correlations between traits of interests, facilitating design of effective multiple trait selection schemes.
PMCID: PMC1876470  PMID: 17490471
11.  Enriching rare variants using family-specific linkage information 
BMC Proceedings  2011;5(Suppl 9):S82.
Genome-wide association studies have been successful in identifying common variants for common complex traits in recent years. However, common variants have generally failed to explain substantial proportions of the trait heritabilities. Rare variants, structural variations, and gene-gene and gene-environment interactions, among others, have been suggested as potential sources of the so-called missing heritability. With the advent of exome-wide and whole-genome next-generation sequencing technologies, finding rare variants in functionally important sites (e.g., protein-coding regions) becomes feasible. We investigate the role of linkage information to select families enriched for rare variants using the simulated Genetic Analysis Workshop 17 data. In each replicate of simulated phenotypes Q1 and Q2 on 697 subjects in 8 extended pedigrees, we select one pedigree with the largest family-specific LOD score. Across all 200 replications, we compare the probability that rare causal alleles will be carried in the selected pedigree versus a randomly chosen pedigree. One example of successful enrichment was exhibited for gene VEGFC. The causal variant had minor allele frequency of 0.0717% in the simulated unrelated individuals and explained about 0.1% of the phenotypic variance. However, it explained 7.9% of the phenotypic variance in the eight simulated pedigrees and 23.8% in the family that carried the minor allele. The carrier’s family was selected in all 200 replications. Thus our results show that family-specific linkage information is useful for selecting families for sequencing, thus ensuring that rare functional variants are segregating in the sequencing samples.
PMCID: PMC3287923  PMID: 22373363
12.  Identification of multiple rare variants associated with a disease 
BMC Proceedings  2011;5(Suppl 9):S103.
Identifying rare variants that are responsible for complex disease has been promoted by advances in sequencing technologies. However, statistical methods that can handle the vast amount of data generated and that can interpret the complicated relationship between disease and these variants have lagged. We apply a zero-inflated Poisson regression model to take into account the excess of zeros caused by the extremely low frequency of the 24,487 exonic variants in the Genetic Analysis Workshop 17 data. We grouped the 697 subjects in the data set as Europeans, Asians, and Africans based on principal components analysis and found the total number of rare variants per gene for each individual. We then analyzed these collapsed variants based on the assumption that rare variants are enriched in a group of people affected by a disease compared to a group of unaffected people. We also tested the hypothesis with quantitative traits Q1, Q2, and Q4. Analyses performed on the combined 697 individuals and on each ethnic group yielded different results. For the combined population analysis, we found that UGT1A1, which was not part of the simulation model, was associated with disease liability and that FLT1, which was a causal locus in the simulation model, was associated with Q1. Of the causal loci in the simulation models, FLT1 and KDR were associated with Q1 and VNN1 was correlated with Q2. No significant genes were associated with Q4. These results show the feasibility and capability of our new statistical model to detect multiple rare variants influencing disease risk.
PMCID: PMC3287826  PMID: 22373445
13.  Genetic Association Mapping via Evolution-Based Clustering of Haplotypes 
PLoS Genetics  2007;3(7):e111.
Multilocus analysis of single nucleotide polymorphism haplotypes is a promising approach to dissecting the genetic basis of complex diseases. We propose a coalescent-based model for association mapping that potentially increases the power to detect disease-susceptibility variants in genetic association studies. The approach uses Bayesian partition modelling to cluster haplotypes with similar disease risks by exploiting evolutionary information. We focus on candidate gene regions with densely spaced markers and model chromosomal segments in high linkage disequilibrium therein assuming a perfect phylogeny. To make this assumption more realistic, we split the chromosomal region of interest into sub-regions or windows of high linkage disequilibrium. The haplotype space is then partitioned into disjoint clusters, within which the phenotype–haplotype association is assumed to be the same. For example, in case-control studies, we expect chromosomal segments bearing the causal variant on a common ancestral background to be more frequent among cases than controls, giving rise to two separate haplotype clusters. The novelty of our approach arises from the fact that the distance used for clustering haplotypes has an evolutionary interpretation, as haplotypes are clustered according to the time to their most recent common ancestor. Our approach is fully Bayesian and we develop a Markov Chain Monte Carlo algorithm to sample efficiently over the space of possible partitions. We compare the proposed approach to both single-marker analyses and recently proposed multi-marker methods and show that the Bayesian partition modelling performs similarly in localizing the causal allele while yielding lower false-positive rates. Also, the method is computationally quicker than other multi-marker approaches. We present an application to real genotype data from the CYP2D6 gene region, which has a confirmed role in drug metabolism, where we succeed in mapping the location of the susceptibility variant within a small error.
Author Summary
Genetic association studies offer great promise in dissecting the genetic contribution to complex diseases. The underlying idea of such studies is to search for genetic variants along the genome that appear to be associated with a trait of interest, e.g., disease status for a binary trait. One then proceeds by genotyping unrelated individuals at several marker sites, searching for positions where single markers or combinations of multiple markers on the paternally and maternally inherited chromosomes (or haplotypes) appear to discriminate among affected and unaffected individuals, flagging genomic regions that may harbour disease susceptibility variants. The statistical analysis of such studies, however, poses several challenges, such as multiplicity and false-positives issue, due to the large number of markers considered. Focusing on case-control studies, we present a novel evolution-based Bayesian partition model that clusters haplotypes with similar disease risks. The novelty of this approach lies in the use of perfect phylogenies, which offers a sensible and computationally efficient approximation of the ancestry of a sample of chromosomes. We show that the incorporation of phylogenetic information leads to low false-positive rates, while our model fitting offers computational advantages over similar recently proposed coalescent-based haplotype clustering methods.
PMCID: PMC1913101  PMID: 17616979
14.  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
15.  Analysis and Optimal Design for Association Studies Using Next-Generation Sequencing With Case-Control Pools 
Genetic epidemiology  2012;36(8):870-881.
With its potential to discover a much greater amount of genetic variation, next-generation sequencing is fast becoming an emergent tool for genetic association studies. However, the cost of sequencing all individuals in a large-scale population study is still high in comparison to most alternative genotyping options. While the ability to identify individual-level data is lost (without bar-coding), sequencing pooled samples can substantially lower costs without compromising the power to detect significant associations.We propose a hierarchical Bayesian model that estimates the association of each variant using pools of cases and controls, accounting for the variation in read depth across pools and sequencing error. To investigate the performance of our method across a range of number of pools, number of individuals within each pool, and average coverage, we undertook extensive simulations varying effect sizes, minor allele frequencies, and sequencing error rates. In general, the number of pools and pool size have dramatic effects on power while the total depth of coverage per pool has only a moderate impact. This information can guide the selection of a study design that maximizes power subject to cost, sample size, or other laboratory constraints. We provide an R package (hiPOD: hierarchical Pooled Optimal Design) to find the optimal design, allowing the user to specify a cost function, cost, and sample size limitations, and distributions of effect size, minor allele frequency, and sequencing error rate.
PMCID: PMC4139478  PMID: 22972696
genetic association studies; sequencing; rare variants
16.  A Bayesian hierarchical gene model on latent genotypes for genome-wide association studies 
BMC Proceedings  2014;8(Suppl 1):S45.
The primary goal of genome-wide association studies is to determine which genetic markers are associated with genetic traits, most commonly human diseases. As a result of the "large p, small n" nature of genome-wide association study data sets, and especially because of the collinearity due to linkage disequilibrium, multivariate regression results in an ill-posed problem. To overcome these obstacles, we propose preprocessing single-nucleotide polymorphisms to adjust for linkage disequilibrium, and a novel Bayesian statistical model that exploits a hierarchical structure between single-nucleotide polymorphisms and genes. We obtain posterior samples using a hybrid Metropolis-within-Gibbs sampler, and further conduct inference on single-nucleotide polymorphism and gene associations using centroid estimation. Finally, we illustrate the proposed model and estimation procedure and discuss results obtained on the data provided for the Genetic Analysis Workshop 18.
PMCID: PMC4143727  PMID: 25519327
17.  Hierarchical likelihood opens a new way of estimating genetic values using genome-wide dense marker maps 
BMC Proceedings  2011;5(Suppl 3):S14.
Genome-wide dense markers have been used to detect genes and estimate relative genetic values. Among many methods, Bayesian techniques have been widely used and shown to be powerful in genome-wide breeding value estimation and association studies. However, computation is known to be intensive under the Bayesian framework, and specifying a prior distribution for each parameter is always required for Bayesian computation. We propose the use of hierarchical likelihood to solve such problems.
Using double hierarchical generalized linear models, we analyzed the simulated dataset provided by the QTLMAS 2010 workshop. Marker-specific variances estimated by double hierarchical generalized linear models identified the QTL with large effects for both the quantitative and binary traits. The QTL positions were detected with very high accuracy. For young individuals without phenotypic records, the true and estimated breeding values had Pearson correlation of 0.60 for the quantitative trait and 0.72 for the binary trait, where the quantitative trait had a more complicated genetic architecture involving imprinting and epistatic QTL.
Hierarchical likelihood enables estimation of marker-specific variances under the likelihoodist framework. Double hierarchical generalized linear models are powerful in localizing major QTL and computationally fast.
PMCID: PMC3103199  PMID: 21624170
18.  Search for compound heterozygous effects in exome sequence of unrelated subjects 
BMC Proceedings  2011;5(Suppl 9):S95.
To enable the assessment of compound heterozygosity, we propose a simple approach for incorporating genotype phase in a rare variant collapsing procedure for the analysis of DNA sequence data. When multiple variants are identified within a gene, knowing the phase of each variant may provide additional statistical power to detect associations with phenotypes that follow a recessive or additive inheritance pattern. We begin by phasing all marker data; then, we collapse nonsynonymous single-nucleotide polymorphisms within genes on each phased haplotype, resulting in a single diploid genotype for each gene, which represents whether one or both haplotypes carry a nonsynonymous variant allele. A recessive or additive association test can then be used to assess the relationship between the collapsed genotype and the phenotype of interest. We apply this approach to the unrelated individuals data from Genetic Analysis Workshop 17 and compare the results of the additive test with a dominant test in which phase is not informative. Analysis of the first phenotype replicate shows that the FLT1 gene is significantly associated with both Q1 and the binary affection status phenotype. This association was detected by both the additive and dominant tests, although the additive phase-informed test resulted in a smaller p-value. No false-positive results were detected in the first phenotype replicate. Analysis of the average values of all phenotype replicates correctly identified five other genes important to the simulation, but with an increase in false-positive rates. The accuracy of our method is contingent on correct phase determination.
PMCID: PMC3287937  PMID: 22373223
19.  A bivariate quantitative genetic model for a threshold trait and a survival trait 
Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.
PMCID: PMC2689264  PMID: 17129560
bivariate genetic model; survival trait; ordered categorical trait; Bayesian analysis
20.  SNP calling by sequencing pooled samples 
BMC Bioinformatics  2012;13:239.
Performing high throughput sequencing on samples pooled from different individuals is a strategy to characterize genetic variability at a small fraction of the cost required for individual sequencing. In certain circumstances some variability estimators have even lower variance than those obtained with individual sequencing. SNP calling and estimating the frequency of the minor allele from pooled samples, though, is a subtle exercise for at least three reasons. First, sequencing errors may have a much larger relevance than in individual SNP calling: while their impact in individual sequencing can be reduced by setting a restriction on a minimum number of reads per allele, this would have a strong and undesired effect in pools because it is unlikely that alleles at low frequency in the pool will be read many times. Second, the prior allele frequency for heterozygous sites in individuals is usually 0.5 (assuming one is not analyzing sequences coming from, e.g. cancer tissues), but this is not true in pools: in fact, under the standard neutral model, singletons (i.e. alleles of minimum frequency) are the most common class of variants because P(f) ∝ 1/f and they occur more often as the sample size increases. Third, an allele appearing only once in the reads from a pool does not necessarily correspond to a singleton in the set of individuals making up the pool, and vice versa, there can be more than one read – or, more likely, none – from a true singleton.
To improve upon existing theory and software packages, we have developed a Bayesian approach for minor allele frequency (MAF) computation and SNP calling in pools (and implemented it in a program called snape): the approach takes into account sequencing errors and allows users to choose different priors. We also set up a pipeline which can simulate the coalescence process giving rise to the SNPs, the pooling procedure and the sequencing. We used it to compare the performance of snape to that of other packages.
We present a software which helps in calling SNPs in pooled samples: it has good power while retaining a low false discovery rate (FDR). The method also provides the posterior probability that a SNP is segregating and the full posterior distribution of f for every SNP. In order to test the behaviour of our software, we generated (through simulated coalescence) artificial genomes and computed the effect of a pooled sequencing protocol, followed by SNP calling. In this setting, snape has better power and False Discovery Rate (FDR) than the comparable packages samtools, PoPoolation, Varscan : for N = 50 chromosomes, snape has power ≈ 35%and FDR ≈ 2.5%. snape is available at (source code and precompiled binaries).
PMCID: PMC3475117  PMID: 22992255
21.  Hierarchical Generalized Linear Models for Multiple Groups of Rare and Common Variants: Jointly Estimating Group and Individual-Variant Effects 
PLoS Genetics  2011;7(12):e1002382.
Complex diseases and traits are likely influenced by many common and rare genetic variants and environmental factors. Detecting disease susceptibility variants is a challenging task, especially when their frequencies are low and/or their effects are small or moderate. We propose here a comprehensive hierarchical generalized linear model framework for simultaneously analyzing multiple groups of rare and common variants and relevant covariates. The proposed hierarchical generalized linear models introduce a group effect and a genetic score (i.e., a linear combination of main-effect predictors for genetic variants) for each group of variants, and jointly they estimate the group effects and the weights of the genetic scores. This framework includes various previous methods as special cases, and it can effectively deal with both risk and protective variants in a group and can simultaneously estimate the cumulative contribution of multiple variants and their relative importance. Our computational strategy is based on extending the standard procedure for fitting generalized linear models in the statistical software R to the proposed hierarchical models, leading to the development of stable and flexible tools. The methods are illustrated with sequence data in gene ANGPTL4 from the Dallas Heart Study. The performance of the proposed procedures is further assessed via simulation studies. The methods are implemented in a freely available R package BhGLM (
Author Summary
Complex diseases and traits are likely influenced by many common and rare genetic variants and environmental factors. Next-generation sequencing technologies have provided unparalleled tools to sequence a large number of individuals, allowing for comprehensive studies of both common and rare variants. However, detecting disease-associated rare variants and common variants of small effects poses unique statistical challenges. We propose here a comprehensive hierarchical generalized linear model framework for simultaneously analyzing multiple groups of rare and common variants and relevant covariates. The proposed hierarchical generalized linear models introduce a group effect and a genetic score for each group of variants, and jointly they estimate the group effects and the weights of the genetic scores. This framework includes various previous methods as special cases, and it can effectively deal with both risk and protective variants in a group and can simultaneously estimate the cumulative contribution of multiple variants and their relative importance. The methods are illustrated with sequence data in gene ANGPTL4 from the Dallas Heart Study and are further assessed via simulation studies. The methods have been implemented in a freely available R package BhGLM (
PMCID: PMC3228815  PMID: 22144906
22.  BiomeNet: A Bayesian Model for Inference of Metabolic Divergence among Microbial Communities 
PLoS Computational Biology  2014;10(11):e1003918.
Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model (metabolic reactions, subnetworks, and networks) are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host's nutrient-based mechanism for bacterial partner selection.
Author Summary
Metagenomic studies of microbial communities yield enormous numbers of gene sequences that have a known enzymatic function, and thus have potential to contribute to community-level metabolic activities. Ecologically divergent microbial communities are presumed to differ in metabolic repertoire and function, but detecting such differences is challenging because the required analytical methodology is complex. Here, we present a novel Bayesian model suitable for this task. Our model, BiomeNet, does not assume that microbiome samples of a certain type are the same; rather, a sample is modeled as a unique mixture of complex metabolic systems referred to as “metabosystems”. The metabosystems are composed of mixtures of subnetworks, where subnetworks are mixtures of reactions related by function. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among IBD patients. We inferred that this metabosystem is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an important antioxidant, possibly contributing to gut inflammation associated with IBD.
PMCID: PMC4238953  PMID: 25412107
23.  Gene-Based Tests of Association 
PLoS Genetics  2011;7(7):e1002177.
Genome-wide association studies (GWAS) are now used routinely to identify SNPs associated with complex human phenotypes. In several cases, multiple variants within a gene contribute independently to disease risk. Here we introduce a novel Gene-Wide Significance (GWiS) test that uses greedy Bayesian model selection to identify the independent effects within a gene, which are combined to generate a stronger statistical signal. Permutation tests provide p-values that correct for the number of independent tests genome-wide and within each genetic locus. When applied to a dataset comprising 2.5 million SNPs in up to 8,000 individuals measured for various electrocardiography (ECG) parameters, this method identifies more validated associations than conventional GWAS approaches. The method also provides, for the first time, systematic assessments of the number of independent effects within a gene and the fraction of disease-associated genes housing multiple independent effects, observed at 35%–50% of loci in our study. This method can be generalized to other study designs, retains power for low-frequency alleles, and provides gene-based p-values that are directly compatible for pathway-based meta-analysis.
Author Summary
Genome-wide association studies (GWAS) have successfully identified genetic variants associated with complex human phenotypes. Despite a proliferation of analysis methods, most studies rely on simple, robust SNP–by–SNP univariate tests with ever-larger population sizes. Here we introduce a new test motivated by the biological hypothesis that a single gene may contain multiple variants that contribute independently to a trait. Applied to simulated phenotypes with real genotypes, our new method, Gene-Wide Significance (GWiS), has better power to identify true associations than traditional univariate methods, previous Bayesian methods, popular L1 regularized (LASSO) multivariate regression, and other approaches. GWiS retains power for low-frequency alleles that are increasingly important for personal genetics, and it is the only method tested that accurately estimates the number of independent effects within a gene. When applied to human data for multiple ECG traits, GWiS identifies more genome-wide significant loci (verified by meta-analyses of much larger populations) than any other method. We estimate that 35%–50% of ECG trait loci are likely to have multiple independent effects, suggesting that our method will reveal previously unidentified associations when applied to existing data and will improve power for future association studies.
PMCID: PMC3145613  PMID: 21829371
24.  Huvariome: a web server resource of whole genome next-generation sequencing allelic frequencies to aid in pathological candidate gene selection 
Next generation sequencing provides clinical research scientists with direct read out of innumerable variants, including personal, pathological and common benign variants. The aim of resequencing studies is to determine the candidate pathogenic variants from individual genomes, or from family-based or tumor/normal genome comparisons. Whilst the use of appropriate controls within the experimental design will minimize the number of false positive variations selected, this number can be reduced further with the use of high quality whole genome reference data to minimize false positives variants prior to candidate gene selection. In addition the use of platform related sequencing error models can help in the recovery of ambiguous genotypes from lower coverage data.
We have developed a whole genome database of human genetic variations, Huvariome, determined by whole genome deep sequencing data with high coverage and low error rates. The database was designed to be sequencing technology independent but is currently populated with 165 individual whole genomes consisting of small pedigrees and matched tumor/normal samples sequenced with the Complete Genomics sequencing platform. Common variants have been determined for a Benelux population cohort and represented as genotypes alongside the results of two sets of control data (73 of the 165 genomes), Huvariome Core which comprises 31 healthy individuals from the Benelux region, and Diversity Panel consisting of 46 healthy individuals representing 10 different populations and 21 samples in three Pedigrees. Users can query the database by gene or position via a web interface and the results are displayed as the frequency of the variations as detected in the datasets. We demonstrate that Huvariome can provide accurate reference allele frequencies to disambiguate sequencing inconsistencies produced in resequencing experiments. Huvariome has been used to support the selection of candidate cardiomyopathy related genes which have a homozygous genotype in the reference cohorts. This database allows the users to see which selected variants are common variants (> 5% minor allele frequency) in the Huvariome core samples, thus aiding in the selection of potentially pathogenic variants by filtering out common variants that are not listed in one of the other public genomic variation databases. The no-call rate and the accuracy of allele calling in Huvariome provides the user with the possibility of identifying platform dependent errors associated with specific regions of the human genome.
Huvariome is a simple to use resource for validation of resequencing results obtained by NGS experiments. The high sequence coverage and low error rates provide scientists with the ability to remove false positive results from pedigree studies. Results are returned via a web interface that displays location-based genetic variation frequency, impact on protein function, association with known genetic variations and a quality score of the variation base derived from Huvariome Core and the Diversity Panel data. These results may be used to identify and prioritize rare variants that, for example, might be disease relevant. In testing the accuracy of the Huvariome database, alleles of a selection of ambiguously called coding single nucleotide variants were successfully predicted in all cases. Data protection of individuals is ensured by restricted access to patient derived genomes from the host institution which is relevant for future molecular diagnostics.
PMCID: PMC3549785  PMID: 23164068
Medical genetics; Medical genomics; Whole genome sequencing; Allele frequency; Cardiomyopathy
25.  Fusion of Large-Scale Genomic Knowledge and Frequency Data Computationally Prioritizes Variants in Epilepsy 
PLoS Genetics  2013;9(9):e1003797.
Curation and interpretation of copy number variants identified by genome-wide testing is challenged by the large number of events harbored in each personal genome. Conventional determination of phenotypic relevance relies on patterns of higher frequency in affected individuals versus controls; however, an increasing amount of ascertained variation is rare or private to clans. Consequently, frequency data have less utility to resolve pathogenic from benign. One solution is disease-specific algorithms that leverage gene knowledge together with variant frequency to aid prioritization. We used large-scale resources including Gene Ontology, protein-protein interactions and other annotation systems together with a broad set of 83 genes with known associations to epilepsy to construct a pathogenicity score for the phenotype. We evaluated the score for all annotated human genes and applied Bayesian methods to combine the derived pathogenicity score with frequency information from our diagnostic laboratory. Analysis determined Bayes factors and posterior distributions for each gene. We applied our method to subjects with abnormal chromosomal microarray results and confirmed epilepsy diagnoses gathered by electronic medical record review. Genes deleted in our subjects with epilepsy had significantly higher pathogenicity scores and Bayes factors compared to subjects referred for non-neurologic indications. We also applied our scores to identify a recently validated epilepsy gene in a complex genomic region and to reveal candidate genes for epilepsy. We propose a potential use in clinical decision support for our results in the context of genome-wide screening. Our approach demonstrates the utility of integrative data in medical genomics.
Author Summary
Improvements in sequencing and microarray technologies have increased the resolution and scope of genetic testing. As a result, millions of variations are identified in each personal genome of unrelated individuals. In the context of testing for genetic diseases, identifying the variant or variants contributing to illness among such a large number of candidates is difficult. Conventional studies to identify causative variants have relied on patterns of higher frequency in affected patients compared with individuals that are well. However, it is often the rarest variations that cause human disease, making frequency information alone less useful. Many groups have turned to computational analysis to aid in interpretation of genetic variants. Epilepsy is a disease where such tools would be useful, as only a fraction of patients with suspected genetic epilepsy have a specific genetic diagnosis. To help improve variant interpretation in epilepsy, we used computational analysis to combine knowledge about genes from large cloud information sources with mutation frequency from our diagnostic laboratory to score all genes as to how likely they are to be associated with epilepsy. We use these scores to identify possible candidate genes in epilepsy, and explore other downstream applications.
PMCID: PMC3784560  PMID: 24086149

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