A comparison of Bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk.

We present the most comprehensive comparison to date of the predictive benefit of genetics in addition to currently used clinical variables, using genotype data for 33 single-nucleotide polymorphisms (SNPs) in 1,547 Caucasian men from the placebo arm of the REduction by DUtasteride of prostate Cancer Events (REDUCE®) trial. Moreover, we conducted a detailed comparison of three techniques for incorporating genetics into clinical risk prediction. The first method was a standard logistic regression model, which included separate terms for the clinical covariates and for each of the genetic markers. This approach ignores a substantial amount of external information concerning effect sizes for these Genome Wide Association Study (GWAS)-replicated SNPs. The second and third methods investigated two possible approaches to incorporating meta-analysed external SNP effect estimates - one via a weighted PCa 'risk' score based solely on the meta analysis estimates, and the other incorporating both the current and prior data via informative priors in a Bayesian logistic regression model. All methods demonstrated a slight improvement in predictive performance upon incorporation of genetics. The two methods that incorporated external information showed the greatest receiver-operating-characteristic AUCs increase from 0.61 to 0.64. The value of our methods comparison is likely to lie in observations of performance similarities, rather than difference, between three approaches of very different resource requirements. The two methods that included external information performed best, but only marginally despite substantial differences in complexity.

Comparative analysis of genome-wide association studies signals for lipids, diabetes, and coronary heart disease: Cardiovascular Biomarker Genetics Collaboration.

AIMS: To evaluate the associations of emergent genome-wide-association study-derived coronary heart disease (CHD)-associated single nucleotide polymorphisms (SNPs) with established and emerging risk factors, and the association of genome-wide-association study-derived lipid-associated SNPs with other risk factors and CHD events. METHODS AND RESULTS: Using two case-control studies, three cross-sectional, and seven prospective studies with up to 25 000 individuals and 5794 CHD events we evaluated associations of 34 genome-wide-association study-identified SNPs with CHD risk and 16 CHD-associated risk factors or biomarkers. The Ch9p21 SNPs rs1333049 (OR 1.17; 95% confidence limits 1.11-1.24) and rs10757274 (OR 1.17; 1.09-1.26), MIA3 rs17465637 (OR 1.10; 1.04-1.15), Ch2q36 rs2943634 (OR 1.08; 1.03-1.14), APC rs383830 (OR 1.10; 1.02, 1.18), MTHFD1L rs6922269 (OR 1.10; 1.03, 1.16), CXCL12 rs501120 (OR 1.12; 1.04, 1.20), and SMAD3 rs17228212 (OR 1.11; 1.05, 1.17) were all associated with CHD risk, but not with the CHD biomarkers and risk factors measured. Among the 20 blood lipid-related SNPs, LPL rs17411031 was associated with a lower risk of CHD (OR 0.91; 0.84-0.97), an increase in Apolipoprotein AI and HDL-cholesterol, and reduced triglycerides. SORT1 rs599839 was associated with CHD risk (OR 1.20; 1.15-1.26) as well as total- and LDL-cholesterol, and apolipoprotein B. ANGPTL3 rs12042319 was associated with CHD risk (OR 1.11; 1.03, 1.19), total- and LDL-cholesterol, triglycerides, and interleukin-6. CONCLUSION: Several SNPs predicting CHD events appear to involve pathways not currently indexed by the established or emerging risk factors; others involved changes in blood lipids including triglycerides or HDL-cholesterol as well as LDL-cholesterol. The overlapping association of SNPs with multiple risk factors and biomarkers supports the existence of shared points of regulation for these phenotypes.

Bayesian semiparametric meta-analysis for genetic association studies.

We present a Bayesian semiparametric model for the meta-analysis of candidate gene studies with a binary outcome. Such studies often report results from association tests for different, possibly study-specific and non-overlapping genetic markers in the same genetic region. Meta-analyses of the results at each marker in isolation are seldom appropriate as they ignore the correlation that may exist between markers due to linkage disequilibrium (LD) and cannot assess the relative importance of variants at each marker. Also such marker-wise meta-analyses are restricted to only those studies that have typed the marker in question, with a potential loss of power. A better strategy is one which incorporates information about the LD between markers so that any combined estimate of the effect of each variant is corrected for the effect of other variants, as in multiple regression. Here we develop a Bayesian semiparametric model which models the observed genotype group frequencies conditional to the case/control status and uses pairwise LD measurements between markers as prior information to make posterior inference on adjusted effects. The approach allows borrowing of strength across studies and across markers. The analysis is based on a mixture of Dirichlet processes model as the underlying semiparametric model. Full posterior inference is performed through Markov chain Monte Carlo algorithms. The approach is demonstrated on simulated and real data.

Multilocus Bayesian meta-analysis of gene-disease associations.

Meta-analysis is a vital tool in genetic epidemiology. However, meta-analyses to identify gene-disease associations are compromised when contributing studies have typed partially overlapping sets of markers. Currently, only marginal analyses are possible, and these are restricted to the subset of studies typing that marker. This does not allow full use of available data and leads to the confounding of marker effects by closely associated markers. We present a Bayesian approach that exploits prior information on underlying haplotypes to allow multi-marker analysis incorporating data from all relevant studies of a gene or region, irrespective of the markers typed. We present results from application of our approach to data on a possible association between PDE4D and ischemic stroke.

Searching for genotype-phenotype structure: using hierarchical log-linear models in Crohn disease.

There has been considerable recent success in the detection of gene-disease associations. We consider here the development of tools that facilitate the more detailed characterization of the effect of a genetic variant on disease. We replace the simplistic classification of individuals according to a single binary disease indicator with classification according to a number of subphenotypes. This more accurately reflects the underlying biological complexity of the disease process, but it poses additional analytical difficulties. Notably, the subphenotypes that make up a particular disease are typically highly associated, and it becomes difficult to distinguish which genes might be causing which subphenotypes. Such problems arise in many complex diseases. Here, we concentrate on an application to Crohn disease (CD). We consider this problem as one of model selection based upon log-linear models, fitted in a Bayesian framework via reversible-jump Metropolis-Hastings approach. We evaluate the performance of our suggested approach with a simple simulation study and then apply the method to a real data example in CD, revealing a sparse disease structure. Most notably, the associated NOD2.908G-->R mutation appears to be directly related to more severe disease behaviors, whereas the other two associated NOD2 variants, 1007L-->FS and 702R-->W, are more generally related to disease in the small bowel (ileum and jejenum). The ATG16L1.300T-->A variant appears to be directly associated with only disease of the small bowel.

Gene-centric association signals for lipids and apolipoproteins identified via the HumanCVD BeadChip.

Blood lipids are important cardiovascular disease (CVD) risk factors with both genetic and environmental determinants. The Whitehall II study (n=5592) was genotyped with the gene-centric HumanCVD BeadChip (Illumina). We identified 195 SNPs in 16 genes/regions associated with 3 major lipid fractions and 2 apolipoprotein components at p<10(-5), with the associations being broadly concordant with prior genome-wide analysis. SNPs associated with LDL cholesterol and apolipoprotein B were located in LDLR, PCSK9, APOB, CELSR2, HMGCR, CETP, the TOMM40-APOE-C1-C2-C4 cluster, and the APOA5-A4-C3-A1 cluster; SNPs associated with HDL cholesterol and apolipoprotein AI were in CETP, LPL, LIPC, APOA5-A4-C3-A1, and ABCA1; and SNPs associated with triglycerides in GCKR, BAZ1B, MLXIPL, LPL, and APOA5-A4-C3-A1. For 48 SNPs in previously unreported loci that were significant at p<10(-4) in Whitehall II, in silico analysis including the British Women's Heart and Health Study, BRIGHT, ASCOT, and NORDIL studies (total n>12,500) revealed previously unreported associations of SH2B3 (p<2.2x10(-6)), BMPR2 (p<2.3x10(-7)), BCL3/PVRL2 (flanking APOE; p<4.4x10(-8)), and SMARCA4 (flanking LDLR; p<2.5x10(-7)) with LDL cholesterol. Common alleles in these genes explained 6.1%-14.7% of the variance in the five lipid-related traits, and individuals at opposite tails of the additive allele score exhibited substantial differences in trait levels (e.g., >1 mmol/L in LDL cholesterol [approximately 1 SD of the trait distribution]). These data suggest that multiple common alleles of small effect can make important contributions to individual differences in blood lipids potentially relevant to the assessment of CVD risk. These genes provide further insights into lipid metabolism and the likely effects of modifying the encoded targets therapeutically.

A novel protective prion protein variant that colocalizes with kuru exposure.

BACKGROUND: Kuru is a devastating epidemic prion disease that affected a highly restricted geographic area of the Papua New Guinea highlands; at its peak, it predominantly affected adult women and children of both sexes. Its incidence has steadily declined since the cessation of its route of transmission, endocannibalism. METHODS: We performed genetic and selected clinical and genealogic assessments of more than 3000 persons from Eastern Highland populations, including 709 who participated in cannibalistic mortuary feasts, 152 of whom subsequently died of kuru. RESULTS: Persons who were exposed to kuru and survived the epidemic in Papua New Guinea are predominantly heterozygotes at the known resistance factor at codon 129 of the prion protein gene (PRNP). We now report a novel PRNP variant--G127V--that was found exclusively in people who lived in the region in which kuru was prevalent and that was present in half of the otherwise susceptible women from the region of highest exposure who were homozygous for methionine at PRNP codon 129. Although this allele is common in the area with the highest incidence of kuru, it is not found in patients with kuru and in unexposed population groups worldwide. Genealogic analysis reveals a significantly lower incidence of kuru in pedigrees that harbor the protective allele than in geographically matched control families. CONCLUSIONS: The 127V polymorphism is an acquired prion disease resistance factor selected during the kuru epidemic, rather than a pathogenic mutation that could have triggered the kuru epidemic. Variants at codons 127 and 129 of PRNP demonstrate the population genetic response to an epidemic of prion disease and represent a powerful episode of recent selection in humans.

Bayesian meta-analysis of genetic association studies with different sets of markers.

Robust assessment of genetic effects on quantitative traits or complex-disease risk requires synthesis of evidence from multiple studies. Frequently, studies have genotyped partially overlapping sets of SNPs within a gene or region of interest, hampering attempts to combine all the available data. By using the example of C-reactive protein (CRP) as a quantitative trait, we show how linkage disequilibrium in and around its gene facilitates use of Bayesian hierarchical models to integrate informative data from all available genetic association studies of this trait, irrespective of the SNP typed. A variable selection scheme, followed by contextualization of SNPs exhibiting independent associations within the haplotype structure of the gene, enhanced our ability to infer likely causal variants in this region with population-scale data. This strategy, based on data from a literature based systematic review and substantial new genotyping, facilitated the most comprehensive evaluation to date of the role of variants governing CRP levels, providing important information on the minimal subset of SNPs necessary for comprehensive evaluation of the likely causal relevance of elevated CRP levels for coronary-heart-disease risk by Mendelian randomization. The same method could be applied to evidence synthesis of other quantitative traits, whenever the typed SNPs vary among studies, and to assist fine mapping of causal variants.

Genetic association mapping via evolution-based clustering of haplotypes.

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.

Genetic risk factors for variant Creutzfeldt-Jakob disease: a genome-wide association study.

BACKGROUND: Human and animal prion diseases are under genetic control, but apart from PRNP (the gene that encodes the prion protein), we understand little about human susceptibility to bovine spongiform encephalopathy (BSE) prions, the causal agent of variant Creutzfeldt-Jakob disease (vCJD). METHODS: We did a genome-wide association study of the risk of vCJD and tested for replication of our findings in samples from many categories of human prion disease (929 samples) and control samples from the UK and Papua New Guinea (4254 samples), including controls in the UK who were genotyped by the Wellcome Trust Case Control Consortium. We also did follow-up analyses of the genetic control of the clinical phenotype of prion disease and analysed candidate gene expression in a mouse cellular model of prion infection. FINDINGS: The PRNP locus was strongly associated with risk across several markers and all categories of prion disease (best single SNP [single nucleotide polymorphism] association in vCJD p=2.5 x 10(-17); best haplotypic association in vCJD p=1 x 10(-24)). Although the main contribution to disease risk was conferred by PRNP polymorphic codon 129, another nearby SNP conferred increased risk of vCJD. In addition to PRNP, one technically validated SNP association upstream of RARB (the gene that encodes retinoic acid receptor beta) had nominal genome-wide significance (p=1.9 x 10(-7)). A similar association was found in a small sample of patients with iatrogenic CJD (p=0.030) but not in patients with sporadic CJD (sCJD) or kuru. In cultured cells, retinoic acid regulates the expression of the prion protein. We found an association with acquired prion disease, including vCJD (p=5.6 x 10(-5)), kuru incubation time (p=0.017), and resistance to kuru (p=2.5 x 10(-4)), in a region upstream of STMN2 (the gene that encodes SCG10). The risk genotype was not associated with sCJD but conferred an earlier age of onset. Furthermore, expression of Stmn2 was reduced 30-fold post-infection in a mouse cellular model of prion disease. INTERPRETATION: The polymorphic codon 129 of PRNP was the main genetic risk factor for vCJD; however, additional candidate loci have been identified, which justifies functional analyses of these biological pathways in prion disease.

Bayesian survival analysis in genetic association studies.

MOTIVATION: Large-scale genetic association studies are carried out with the hope of discovering single nucleotide polymorphisms involved in the etiology of complex diseases. There are several existing methods in the literature for performing this kind of analysis for case-control studies, but less work has been done for prospective cohort studies. We present a Bayesian method for linking markers to censored survival outcome by clustering haplotypes using gene trees. Coalescent-based approaches are promising for LD mapping, as the coalescent offers a good approximation to the evolutionary history of mutations. RESULTS: We compare the performance of the proposed method in simulation studies to the univariate Cox regression and to dimension reduction methods, and we observe that it performs similarly in localizing the causal site, while offering a clear advantage in terms of false positive associations. Moreover, it offers computational advantages. Applying our method to a real prospective study, we observe potential association between candidate ABC transporter genes and epilepsy treatment outcomes. AVAILABILITY: R codes are available upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

An abundance of rare functional variants in 202 drug target genes sequenced in 14,002 people.

Rare genetic variants contribute to complex disease risk; however, the abundance of rare variants in human populations remains unknown. We explored this spectrum of variation by sequencing 202 genes encoding drug targets in 14,002 individuals. We find rare variants are abundant (1 every 17 bases) and geographically localized, so that even with large sample sizes, rare variant catalogs will be largely incomplete. We used the observed patterns of variation to estimate population growth parameters, the proportion of variants in a given frequency class that are putatively deleterious, and mutation rates for each gene. We conclude that because of rapid population growth and weak purifying selection, human populations harbor an abundance of rare variants, many of which are deleterious and have relevance to understanding disease risk.

Defining the true sensitivity of culture for the diagnosis of melioidosis using Bayesian latent class models.

BACKGROUND: Culture remains the diagnostic gold standard for many bacterial infections, and the method against which other tests are often evaluated. Specificity of culture is 100% if the pathogenic organism is not found in healthy subjects, but the sensitivity of culture is more difficult to determine and may be low. Here, we apply Bayesian latent class models (LCMs) to data from patients with a single Gram-negative bacterial infection and define the true sensitivity of culture together with the impact of misclassification by culture on the reported accuracy of alternative diagnostic tests. METHODS/PRINCIPAL FINDINGS: Data from published studies describing the application of five diagnostic tests (culture and four serological tests) to a patient cohort with suspected melioidosis were re-analysed using several Bayesian LCMs. Sensitivities, specificities, and positive and negative predictive values (PPVs and NPVs) were calculated. Of 320 patients with suspected melioidosis, 119 (37%) had culture confirmed melioidosis. Using the final model (Bayesian LCM with conditional dependence between serological tests), the sensitivity of culture was estimated to be 60.2%. Prediction accuracy of the final model was assessed using a classification tool to grade patients according to the likelihood of melioidosis, which indicated that an estimated disease prevalence of 61.6% was credible. Estimates of sensitivities, specificities, PPVs and NPVs of four serological tests were significantly different from previously published values in which culture was used as the gold standard. CONCLUSIONS/SIGNIFICANCE: Culture has low sensitivity and low NPV for the diagnosis of melioidosis and is an imperfect gold standard against which to evaluate alternative tests. Models should be used to support the evaluation of diagnostic tests with an imperfect gold standard. It is likely that the poor sensitivity/specificity of culture is not specific for melioidosis, but rather a generic problem for many bacterial and fungal infections.

A spatial probit model for fine-scale mapping of disease genes.

We present a novel statistical method for linkage disequilibrium (LD) mapping of disease susceptibility loci in case-control studies. Such studies exploit the statistical correlation or LD that exist between variants physically close along the genome to identify those that correlate with disease status and might thus be close to a causative mutation, generally assumed unobserved. LD structure, however, varies markedly over short distances because of variation in local recombination rates, mutation and genetic drift among other factors. We propose a Bayesian multivariate probit model that flexibly accounts for the local spatial correlation between markers. In a case-control setting, we use a retrospective model that properly reflects the sampling scheme and identify regions where single- or multi-locus marker frequencies differ across cases and controls. We formally quantify these differences using information-theoretic distance measures while the fully Bayesian approach naturally accommodates unphased or missing genotype data. We demonstrate our approach on simulated data and on real data from the CYP2D6 region that has a confirmed role in drug metabolism.

Bayesian graphical models for genomewide association studies.

As the extent of human genetic variation becomes more fully characterized, the research community is faced with the challenging task of using this information to dissect the heritable components of complex traits. Genomewide association studies offer great promise in this respect, but their analysis poses formidable difficulties. In this article, we describe a computationally efficient approach to mining genotype-phenotype associations that scales to the size of the data sets currently being collected in such studies. We use discrete graphical models as a data-mining tool, searching for single- or multilocus patterns of association around a causative site. The approach is fully Bayesian, allowing us to incorporate prior knowledge on the spatial dependencies around each marker due to linkage disequilibrium, which reduces considerably the number of possible graphical structures. A Markov chain-Monte Carlo scheme is developed that yields samples from the posterior distribution of graphs conditional on the data from which probabilistic statements about the strength of any genotype-phenotype association can be made. Using data simulated under scenarios that vary in marker density, genotype relative risk of a causative allele, and mode of inheritance, we show that the proposed approach has better localization properties and leads to lower false-positive rates than do single-locus analyses. Finally, we present an application of our method to a quasi-synthetic data set in which data from the CYP2D6 region are embedded within simulated data on 100K single-nucleotide polymorphisms. Analysis is quick (<5 min), and we are able to localize the causative site to a very short interval.

Bayesian modelling of multivariate quantitative traits using seemingly unrelated regressions.

We investigate a Bayesian approach to modelling the statistical association between markers at multiple loci and multivariate quantitative traits. In particular, we describe the use of Bayesian Seemingly Unrelated Regressions (SUR) whereby genotypes at the different loci are allowed to have non-simultaneous effects on the phenotypes considered with residuals from each regression assumed correlated. We present results from simulations showing that, under rather general conditions that are likely to hold in real situations, the Bayesian SUR approach has increased probability of selecting the true model compared to univariate analyses. Finally, we apply our methods to data from subjects genotyped for 12 SNPs in the apolipoprotein E (APOE) gene. Phenotypes relate to response to treatment with atorvastatin and include changes in total cholesterol, low-density lipoprotein cholesterol, and triglycerides. Missing genotype data are naturally accommodated in our Bayesian framework by imputing them using a nested haplotype phasing algorithm.