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.

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.

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.

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.

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.