Bayesian point estimation of quantitative trait loci

In this article, we consider the problem of the estimation of quantitative trait loci (QTL), those chromosomal regions at which genetic information affecting some quantitative trait is encoded. Generally the number of such encoding sites is unknown, and associations between neutral molecular marker genotypes and observed trait phenotypes are sought to locate them. We consider a Bayesian model for simple experimental designs, and discuss the existing approaches to inference for this problem. In particular, we focus on locating positions of the best candidate markers segregating for the trait, a situation which is of primary interest in comparative mapping. We introduce a loss function for estimating both the number of QTL and their location, and we illustrate its application via simulated and real data.     

Bayesian shrinkage estimation of quantitative trait loci parameters

Mapping multiple QTL is a typical problem of variable selection in an oversaturated model because the potential number of QTL can be substantially larger than the sample size. Currently, model selection is still the most effective approach to mapping multiple QTL, although further research is needed. An alternative approach to analyzing an oversaturated model is the shrinkage estimation in which all candidate variables are included in the model but their estimated effects are forced to shrink toward zero. In contrast to the usual shrinkage estimation where all model effects are shrunk by the same factor, we develop a Bayesian method that allows the shrinkage factor to vary across different effects. The new shrinkage method forces marker intervals that contain no QTL to have estimated effects close to zero whereas intervals containing notable QTL have estimated effects subject to virtually no shrinkage. We demonstrate the method using both simulated and real data for QTL mapping. A simulation experiment with 500 backcross (BC) individuals showed that the method can localize closely linked QTL and QTL with effects as small as 1% of the phenotypic variance of the trait. The method was also used to map QTL responsible for wound healing in a family of a (MRL/MPJ x SJL/J) cross with 633 F(2) mice derived from two inbred lines.     

Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling

A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a population-based sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the well-known Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest.     

Identifying causal genes and dysregulated pathways in complex diseases

In complex diseases, various combinations of genomic perturbations often lead to the same phenotype. On a molecular level, combinations of genomic perturbations are assumed to dys-regulate the same cellular pathways. Such a pathway-centric perspective is fundamental to understanding the mechanisms of complex diseases and the identification of potential drug targets. In order to provide an integrated perspective on complex disease mechanisms, we developed a novel computational method to simultaneously identify causal genes and dys-regulated pathways. First, we identified a representative set of genes that are differentially expressed in cancer compared to non-tumor control cases. Assuming that disease-associated gene expression changes are caused by genomic alterations, we determined potential paths from such genomic causes to target genes through a network of molecular interactions. Applying our method to sets of genomic alterations and gene expression profiles of 158 Glioblastoma multiforme (GBM) patients we uncovered candidate causal genes and causal paths that are potentially responsible for the altered expression of disease genes. We discovered a set of putative causal genes that potentially play a role in the disease. Combining an expression Quantitative Trait Loci (eQTL) analysis with pathway information, our approach allowed us not only to identify potential causal genes but also to find intermediate nodes and pathways mediating the information flow between causal and target genes. Our results indicate that different genomic perturbations indeed dys-regulate the same functional pathways, supporting a pathway-centric perspective of cancer. While copy number alterations and gene expression data of glioblastoma patients provided opportunities to test our approach, our method can be applied to any disease system where genetic variations play a fundamental causal role.     

Bayesian shrinkage estimation of high dimensional causal mediation effects in omics studies

Causal mediation analysis aims to examine the role of a mediator or a group of mediators that lie in the pathway between an exposure and an outcome. Recent biomedical studies often involve a large number of potential mediators based on high-throughput technologies. Most of the current analytic methods focus on settings with one or a moderate number of potential mediators. With the expanding growth of -omics data, joint analysis of molecular-level genomics data with epidemiological data through mediation analysis is becoming more common. However, such joint analysis requires methods that can simultaneously accommodate high-dimensional mediators and that are currently lacking. To address this problem, we develop a Bayesian inference method using continuous shrinkage priors to extend previous causal mediation analysis techniques to a high-dimensional setting. Simulations demonstrate that our method improves the power of global mediation analysis compared to simpler alternatives and has decent performance to identify true nonnull contributions to the mediation effects of the pathway. The Bayesian method also helps us to understand the structure of the composite null cases for inactive mediators in the pathway. We applied our method to Multi-Ethnic Study of Atherosclerosis and identified DNA methylation regions that may actively mediate the effect of socioeconomic status on cardiometabolic outcomes.     

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.     

Identifying differentially expressed genes in meta-analysis via Bayesian model-based clustering

A Bayesian model-based clustering approach is proposed for identifying differentially expressed genes in meta-analysis. A Bayesian hierarchical model is used as a scientific tool for combining information from different studies, and a mixture prior is used to separate differentially expressed genes from non-differentially expressed genes. Posterior estimation of the parameters and missing observations are done by using a simple Markov chain Monte Carlo method. From the estimated mixture model, useful measure of significance of a test such as the Bayesian false discovery rate (FDR), the local FDR (Efron et al., 2001), and the integration-driven discovery rate (IDR; Choi et al., 2003) can be easily computed. The model-based approach is also compared with commonly used permutation methods, and it is shown that the model-based approach is superior to the permutation methods when there are excessive under-expressed genes compared to over-expressed genes or vice versa. The proposed method is applied to four publicly available prostate cancer gene expression data sets and simulated data sets.     

Beyond the proportional frailty model: Bayesian estimation of individual heterogeneity on mortality parameters

Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz–Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.     

Bayesian nonparametric functional data analysis through density estimation

In many modern experimental settings, observations are obtainedin the form of functions and interest focuses on inferencesabout a collection of such functions. We propose a hierarchicalmodel that allows us simultaneously to estimate multiple curvesnonparametrically by using dependent Dirichlet process mixturesof Gaussian distributions to characterize the joint distributionof predictors and outcomes. Function estimates are then inducedthrough the conditional distribution of the outcome given thepredictors. The resulting approach allows for flexible estimationand clustering, while borrowing information across curves. Wealso show that the function estimates we obtain are consistenton the space of integrable functions. As an illustration, weconsider an application to the analysis of conductivity andtemperature at depth data in the north Atlantic.     

Identifying novel genes for atherosclerosis through mouse-human comparative genetics

Susceptibility to atherosclerosis is determined by both environmental and genetic factors. Its genetic determinants have been studied by use of quantitative-trait-locus (QTL) analysis. So far, 21 atherosclerosis QTLs have been identified in the mouse: 7 in a high-fat-diet model only, 9 in a sensitized model (apolipoprotein E- or LDL [low-density lipoprotein] receptor-deficient mice) only, and 5 in both models, suggesting that different gene sets operate in each model and that a subset operates in both. Among the 27 human atherosclerosis QTLs reported, 17 (63%) are located in regions homologous (concordant) to mouse QTLs, suggesting that these mouse and human atherosclerosis QTLs have the same underlying genes. Therefore, genes regulating human atherosclerosis will be found most efficiently by first finding their orthologs in concordant mouse QTLs. Novel mouse QTL genes will be found most efficiently by using a combination of the following strategies: identifying QTLs in new crosses performed with previously unused parental strains; inducing mutations in large-scale, high-throughput mutagenesis screens; and using new genomic and bioinformatics tools. Once QTL genes are identified in mice, they can be tested in human association studies for their relevance in human atherosclerotic disease.     

On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty

Summary .   We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture–recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs 62, 1–135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model-averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.     

Localization of a quantitative trait locus via a Bayesian approach

A Bayesian approach to the direct mapping of a quantitative trait locus (QTL), fully utilizing information from multiple linked gene markers, is presented in this paper. The joint posterior distribution (a mixture distribution modeling the linkage between a biallelic QTL and N gene markers) is computationally challenging and invites exploration via Markov chain Monte Carlo methods. The parameter's complete marginal posterior densities are obtained, allowing a diverse range of inferences. Parameters estimated include the QTL genotype probabilities for the sires and the offspring, the allele frequencies for the QTL, and the position and additive and dominance effects of the QTL. The methodology is applied through simulation to a half-sib design to form an outbred pedigree structure where there is an entire class of missing information. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.     

A Bayesian nonparametric model for zero‐inflated outcomes: Prediction,clustering, and causal estimation

Researchers are often interested in predicting outcomes, detecting distinct subgroups of their data, or estimating causal treatment effects. Pathological data distributions that exhibit skewness and zero‐inflation complicate these tasks—requiring highly flexible, data‐adaptive modeling. In this paper, we present a multipurpose Bayesian nonparametric model for continuous, zero‐inflated outcomes that simultaneously predicts structural zeros, captures skewness, and clusters patients with similar joint data distributions. The flexibility of our approach yields predictions that capture the joint data distribution better than commonly used zero‐inflated methods. Moreover, we demonstrate that our model can be coherently incorporated into a standardization procedure for computing causal effect estimates that are robust to such data pathologies. Uncertainty at all levels of this model flow through to the causal effect estimates of interest—allowing easy point estimation, interval estimation, and posterior predictive checks verifying positivity, a required causal identification assumption. Our simulation results show point estimates to have low bias and interval estimates to have close to nominal coverage under complicated data settings. Under simpler settings, these results hold while incurring lower efficiency loss than comparator methods. We use our proposed method to analyze zero‐inflated inpatient medical costs among endometrial cancer patients receiving either chemotherapy or radiation therapy in the SEER‐Medicare database.     

Production of novel allelic variation for genes involved in starch biosynthesis through mutagenesis

Given the important role that starch plays in food and non-food uses of many crops, particularly wheat, efforts are being made to manipulate its composition through modification of the amylose/amylopectin ratio. Approaches used to achieve this goal include the manipulation of the genes involved in the starch biosynthetic pathway using natural or induced mutations and transgenic methods. The use of mutagenesis to produce novel allelic variation represents a powerful tool to increase genetic diversity and this approach seems particularly appropriate for starch synthase genes for which limited variation exists. In this work, an EMS-mutagenised population of bread wheat cv. Cadenza has been screened by combining SDS–PAGE analysis of granule bound starch proteins with a TILLING (Targeting Induced Local Lesions IN Genomes) approach at the gene level. In particular we have focused on two groups of synthase genes, those encoding the starch synthase II (Sgp-1) and those corresponding to the waxy proteins (Wx). SDS–PAGE analysis of granule bound proteins allowed the identification of single null genotypes associated with each of the three homoeologous loci. Molecular characterization of induced mutants has been performed using genome specific primer pairs for Sgp-1 and Wx genes. Additional novel allelic variation has also been detected at the different Sgp-1 homoeoloci by using a reverse genetic approach (TILLING). In particular single nucleotide substitutions, introducing a premature stop codon and creating amino acid substitutions, have been identified.     

Bayesian classification and non-Bayesian label estimation via EM algorithm to identify differentially expressed genes: a comparative study

Gene classification problem is studied considering the ratio of gene expression levels, X, in two-channel microarrays and a non-observed categorical variable indicating how differentially expressed the gene is: non differentially expressed, down-regulated or up-regulated. Supposing X from a mixture of Gamma distributions, two methods are proposed and results are compared. The first method is based on an hierarchical Bayesian model. The conditional predictive probability of a gene to belong to each group is calculated and the gene is assigned to the group for which this conditional probability is higher. The second method uses EM algorithm to estimate the most likely group label for each gene, that is, to assign the gene to the group which contains it with the higher estimated probability.     

Matrix heterogeneity affects population size of the harvest mice: Bayesian estimation of matrix resistance and model validation

It has been increasingly recognized that landscape matrices are an important factor determining patch connectivity and hence the population size of organisms living in highly fragmented landscapes. However, most previous studies estimated the effect of matrix heterogeneity using prior information regarding dispersal or habitat preferences of a focal organism. Here we estimated matrix resistance of harvest mice in agricultural landscapes using a novel pattern‐oriented modeling with Bayesian estimation and no prior information, and then conducted model validation using data sets independent from those used for model construction. First, we investigated the distribution patterns of harvest mice for approximately 400 habitat patches, and estimated matrix resistance for different matrix types using statistical models incorporating patch size, patch environment, and patch connectivity. We used Bayesian estimation with a Markov chain Monte Carlo algorithm, and searched for appropriate matrix resistance that best explained the distribution pattern. Patch connectivity as well as patch quality was an important determinant of local population size for the harvest mice. Moreover, matrix resistance was far from uniform, with rice and crop fields exhibiting low resistance and forests, creeks, roads and residential areas showing much higher resistance. The deviance explained by this model (heterogeneous matrix model) was much larger than that obtained by the model with no consideration of matrix heterogeneity (homogeneous matrix model). Second, we obtained distribution data from five additional landscapes that were more fragmented than that used for model construction, and used them for model validation. The heterogeneous matrix model well predicted the population size for four out of five landscapes. In contrast, the homogeneous model considerably overestimated population sizes in all cases. Our approach is widely applicable to species living in fragmented landscapes, especially those for which prior information regarding movement or dispersal is difficult to obtain.     

Genome‐wide expression quantitative trait locus studies facilitate isolation of causal genes controlling panicle structure

The morphology of rice (Oryza sativa L.) panicles is an important determinant of grain yield, and elucidation of the genetic control of panicle structure is very important for fulfilling the demand for high yield in breeding programs. In a quantitative trait locus (QTL) study using 82 backcross inbred lines (BILs) derived from Koshihikari and Habataki, 68 QTLs for 25 panicle morphological traits were identified. Gene expression profiling from inflorescence meristems of BILs was obtained. A combination of phenotypic QTL (pQTL) and expression QTL (eQTL) analysis revealed co‐localization between pQTLs and eQTLs, consistent with significant correlations between phenotypic traits and gene expression levels. By combining pQTL and eQTL data, two genes were identified as controlling panicle structure: OsMADS18 modulates the average length of the primary rachis and OsFTL1 has pleiotropic effects on the total number of secondary rachides, number of grains per panicle, plant height and the length of flag leaves. Phenotypes were confirmed in RNA interference knocked‐down plants and overexpressor lines. The combination of pQTL and eQTL analysis could facilitate identification of genes involved in rice panicle formation.