Bayesian Variable Selection Model Research Articles

GWABLUP: genome-wide association assisted best linear unbiased prediction of genetic values

BackgroundSince the very beginning of genomic selection, researchers investigated methods that improved upon SNP-BLUP (single nucleotide polymorphism best linear unbiased prediction). SNP-BLUP gives equal weight to all SNPs, whereas it is expected that many SNPs are not near causal variants and thus do not have substantial effects. A recent approach to remedy this is to use genome-wide association study (GWAS) findings and increase the weights of GWAS-top-SNPs in genomic predictions. Here, we employ a genome-wide approach to integrate GWAS results into genomic prediction, called GWABLUP.ResultsGWABLUP consists of the following steps: (1) performing a GWAS in the training data which results in likelihood ratios; (2) smoothing the likelihood ratios over the SNPs; (3) combining the smoothed likelihood ratio with the prior probability of SNPs having non-zero effects, which yields the posterior probability of the SNPs; (4) calculating a weighted genomic relationship matrix using the posterior probabilities as weights; and (5) performing genomic prediction using the weighted genomic relationship matrix. Using high-density genotypes and milk, fat, protein and somatic cell count phenotypes on dairy cows, GWABLUP was compared to GBLUP, GBLUP (topSNPs) with extra weights for GWAS top-SNPs, and BayesGC, i.e. a Bayesian variable selection model. The GWAS resulted in six, five, four, and three genome-wide significant peaks for milk, fat and protein yield and somatic cell count, respectively. GWABLUP genomic predictions were 10, 6, 7 and 1% more reliable than those of GBLUP for milk, fat and protein yield and somatic cell count, respectively. It was also more reliable than GBLUP (topSNPs) for all four traits, and more reliable than BayesGC for three of the traits. Although GWABLUP showed a tendency towards inflation bias for three of the traits, this was not statistically significant. In a multitrait analysis, GWABLUP yielded the highest accuracy for two of the traits. However, for SCC, which was relatively unrelated to the yield traits, including yield trait GWAS-results reduced the reliability compared to a single trait analysis.ConclusionsGWABLUP uses GWAS results to differentially weigh all the SNPs in a weighted GBLUP genomic prediction analysis. GWABLUP yielded up to 10% and 13% more reliable genomic predictions than GBLUP for single and multitrait analyses, respectively. Extension of GWABLUP to single-step analyses is straightforward.

Tumor radiogenomics in gliomas with Bayesian layered variable selection.

We propose a statistical framework to analyze radiological magnetic resonance imaging (MRI) and genomic data to identify the underlying radiogenomic associations in lower grade gliomas (LGG). We devise a novel imaging phenotype by dividing the tumor region into concentric spherical layers that mimics the tumor evolution process. MRI data within each layer is represented by voxel-intensity-based probability density functions which capture the complete information about tumor heterogeneity. Under a Riemannian-geometric framework these densities are mapped to a vector of principal component scores which act as imaging phenotypes. Subsequently, we build Bayesian variable selection models for each layer with the imaging phenotypes as the response and the genomic markers as predictors. Our novel hierarchical prior formulation incorporates the interior-to-exterior structure of the layers, and the correlation between the genomic markers. We employ a computationally-efficient Expectation-Maximization-based strategy for estimation. Simulation studies demonstrate the superior performance of our approach compared to other approaches. With a focus on the cancer driver genes in LGG, we discuss some biologically relevant findings. Genes implicated with survival and oncogenesis are identified as being associated with the spherical layers, which could potentially serve as early-stage diagnostic markers for disease monitoring, prior to routine invasive approaches. We provide a R package that can be used to deploy our framework to identify radiogenomic associations.

(Quasi) multitask support vector regression with heuristic hyperparameter optimization for whole-genome prediction of complex traits: a case study with carcass traits in broilers.

This study investigates nonlinear kernels for multitrait (MT) genomic prediction using support vector regression (SVR) models. We assessed the predictive ability delivered by single-trait (ST) and MT models for 2 carcass traits (CT1 and CT2) measured in purebred broiler chickens. The MT models also included information on indicator traits measured in vivo [Growth and feed efficiency trait (FE)]. We proposed an approach termed (quasi) multitask SVR (QMTSVR), with hyperparameter optimization performed via genetic algorithm. ST and MT Bayesian shrinkage and variable selection models [genomic best linear unbiased predictor (GBLUP), BayesC (BC), and reproducing kernel Hilbert space (RKHS) regression] were employed as benchmarks. MT models were trained using 2 validation designs (CV1 and CV2), which differ if the information on secondary traits is available in the testing set. Models' predictive ability was assessed with prediction accuracy (ACC; i.e. the correlation between predicted and observed values, divided by the square root of phenotype accuracy), standardized root-mean-squared error (RMSE*), and inflation factor (b). To account for potential bias in CV2-style predictions, we also computed a parametric estimate of accuracy (ACCpar). Predictive ability metrics varied according to trait, model, and validation design (CV1 or CV2), ranging from 0.71 to 0.84 for ACC, 0.78 to 0.92 for RMSE*, and between 0.82 and 1.34 for b. The highest ACC and smallest RMSE* were achieved with QMTSVR-CV2 in both traits. We observed that for CT1, model/validation design selection was sensitive to the choice of accuracy metric (ACC or ACCpar). Nonetheless, the higher predictive accuracy of QMTSVR over MTGBLUP and MTBC was replicated across accuracy metrics, besides the similar performance between the proposed method and the MTRKHS model. Results showed that the proposed approach is competitive with conventional MT Bayesian regression models using either Gaussian or spike-slab multivariate priors.

Bayesian outcome selection modeling.

In psychiatric and social epidemiology studies, it is common to measure multiple different outcomes using a comprehensive battery of tests thought to be related to an underlying construct of interest. In the research that motivates our work, researchers wanted to assess the impact of in utero alcohol exposure on child cognition and neuropsychological development, which are evaluated using a range of different psychometric tests. Statistical analysis of the resulting multiple outcomes data can be challenging, because the outcomes measured on the same individual are not independent. Moreover, it is unclear, a priori, which outcomes are impacted by the exposure under study. While researchers will typically have some hypotheses about which outcomes are important, a framework is needed to help identify outcomes that are sensitive to the exposure and to quantify the associated treatment or exposure effects of interest. We propose such a framework using a modification of stochastic search variable selection, a popular Bayesian variable selection model and use it to quantify an overall effect of the exposure on the affected outcomes. The performance of the method is investigated empirically and an illustration is given through application using data from our motivating study.

Multitrait Bayesian shrinkage and variable selection models with the BGLR-R package.

The BGLR-R package implements various types of single-trait shrinkage/variable selection Bayesian regressions. The package was first released in 2014, since then it has become a software very often used in genomic studies. We recently develop functionality for multitrait models. The implementation allows users to include an arbitrary number of random-effects terms. For each set of predictors, users can choose diffuse, Gaussian, and Gaussian–spike–slab multivariate priors. Unlike other software packages for multitrait genomic regressions, BGLR offers many specifications for (co)variance parameters (unstructured, diagonal, factor analytic, and recursive). Samples from the posterior distribution of the models implemented in the multitrait function are generated using a Gibbs sampler, which is implemented by combining code written in the R and C programming languages. In this article, we provide an overview of the models and methods implemented BGLR’s multitrait function, present examples that illustrate the use of the package, and benchmark the performance of the software.

Fine mapping and accurate prediction of complex traits using Bayesian Variable Selection models applied to biobank-size data

Modern GWAS studies use an enormous sample size and ultra-high density SNP genotypes. These conditions reduce the mapping resolution of marginal association tests–the method most often used in GWAS. Multi-locus Bayesian Variable Selection (BVS) offers a one-stop solution for powerful and precise mapping of risk variants and polygenic risk score (PRS) prediction. We show (with an extensive simulation) that multi-locus BVS methods can achieve high power with a low false discovery rate and a much better mapping resolution than marginal association tests. We demonstrate the performance of BVS for mapping and PRS prediction using data from blood biomarkers from the UK-Biobank (~300,000 samples and ~5.5 million SNPs). The article is accompanied by open-source R-software that implement the methods used in the study and scales to biobank-sized data.

Molecular Phylogenesis and Spatiotemporal Spread of SARS-CoV-2 in Southeast Asia.

Background: The ongoing coronavirus disease 2019 (COVID-19) pandemic has posed an unprecedented challenge to public health in Southeast Asia, a tropical region with limited resources. This study aimed to investigate the evolutionary dynamics and spatiotemporal patterns of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the region.Materials and Methods: A total of 1491 complete SARS-CoV-2 genome sequences from 10 Southeast Asian countries were downloaded from the Global Initiative on Sharing Avian Influenza Data (GISAID) database on November 17, 2020. The evolutionary relationships were assessed using maximum likelihood (ML) and time-scaled Bayesian phylogenetic analyses, and the phylogenetic clustering was tested using principal component analysis (PCA). The spatial patterns of SARS-CoV-2 spread within Southeast Asia were inferred using the Bayesian stochastic search variable selection (BSSVS) model. The effective population size (Ne) trajectory was inferred using the Bayesian Skygrid model.Results: Four major clades (including one potentially endemic) were identified based on the maximum clade credibility (MCC) tree. Similar clustering was yielded by PCA; the first three PCs explained 46.9% of the total genomic variations among the samples. The time to the most recent common ancestor (tMRCA) and the evolutionary rate of SARS-CoV-2 circulating in Southeast Asia were estimated to be November 28, 2019 (September 7, 2019 to January 4, 2020) and 1.446 × 10−3 (1.292 × 10−3 to 1.613 × 10−3) substitutions per site per year, respectively. Singapore and Thailand were the two most probable root positions, with posterior probabilities of 0.549 and 0.413, respectively. There were high-support transmission links (Bayes factors exceeding 1,000) in Singapore, Malaysia, and Indonesia; Malaysia involved the highest number (7) of inferred transmission links within the region. A twice-accelerated viral population expansion, followed by a temporary setback, was inferred during the early stages of the pandemic in Southeast Asia.Conclusions: With available genomic data, we illustrate the phylogeography and phylodynamics of SARS-CoV-2 circulating in Southeast Asia. Continuous genomic surveillance and enhanced strategic collaboration should be listed as priorities to curb the pandemic, especially for regional communities dominated by developing countries.

Bayesian variable selection for high‐dimensional rank data

AbstractThe study of microbiomes has become a topic of intense interest in last several decades as the development of new sequencing technologies has made DNA data accessible across disciplines. In this paper, we analyze a global dataset to investigate environmental factors that affect topsoil microbiome. As yet, much associated work has focused on linking indicators of microbial health to specific outcomes in various fields, rather than understanding how external factors may influence the microbiome composition itself. This is partially due to limited statistical methods to model abundance counts. The counts are high‐dimensional, overdispersed, often zero‐inflated, and exhibit complex dependence structures. Additionally, the raw counts are often noisy and compositional, and thus are not directly comparable across samples. Often, practitioners transform the counts to presence–absence indicators, but this transformation discards much of the data. As an alternative, we propose transforming to taxa ranks and develop a Bayesian variable selection model that uses ranks to identify covariates that influence microbiome composition. We show by simulation that the proposed model outperforms competitors across various settings and particular improvement in recall for small magnitude and low prevalence covariates. When applied to the topsoil data, the proposed method identifies several factors that affect microbiome composition.

A Bayesian Latent Variable Selection Model for Nonignorable Missingness

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as leaving the data incomplete and failing to accommodate incomplete covariates with interactions, non-linear terms, and random slopes. We propose a Bayesian latent variable imputation approach to impute missing data due to MNAR (and other missingness mechanisms) and estimate the model of substantive interest simultaneously. In addition, even when the incomplete covariates involves interactions, non-linear terms, and random slopes, the proposed method can handle missingness appropriately. Computer simulation results suggested that the proposed Bayesian latent variable selection model (BLVSM) was quite effective when the outcome and/or covariates were MNAR. Except when the sample size was small, estimates from the proposed BLVSM tracked closely with those from the complete data analysis. With a small sample size, when the outcome was less predictable from the covariates, the missingness proportions of the covariates and the outcome were larger, and the missingness selection processes of the covariates and the outcome were more MNAR and MAR, the performance of BLVSM was less satisfactory. When the sample size was large, BLVSM always performed well. In contrast, the method with an MAR assumption provided biased estimates and undercoverage confidence intervals when the missingness was MNAR. The robustness and the implementation of BLVSM in real data were also illustrated. The proposed method is available in the Blimp software application, and the paper includes a data analysis example illustrating its use.

BayesSUR: An R Package for High-Dimensional Multivariate Bayesian Variable and Covariance Selection in Linear Regression

In molecular biology, advances in high-throughput technologies have made it possible to study complex multivariate phenotypes and their simultaneous associations with high-dimensional genomic and other omics data, a problem that can be studied with high-dimensional multi-response regression, where the response variables are potentially highly correlated. To this purpose, we recently introduced several multivariate Bayesian variable and covariance selection models, e.g., Bayesian estimation methods for sparse seemingly unrelated regression for variable and covariance selection. Several variable selection priors have been implemented in this context, in particular the hotspot detection prior for latent variable inclusion indicators, which results in sparse variable selection for associations between predictors and multiple phenotypes. We also propose an alternative, which uses a Markov random field (MRF) prior for incorporating prior knowledge about the dependence structure of the inclusion indicators. Inference of Bayesian seemingly unrelated regression (SUR) by Markov chain Monte Carlo methods is made computationally feasible by factorisation of the covariance matrix amongst the response variables. In this paper we present BayesSUR, an R package, which allows the user to easily specify and run a range of different Bayesian SUR models, which have been implemented in C++ for computational efficiency. The R package allows the specification of the models in a modular way, where the user chooses the priors for variable selection and for covariance selection separately. We demonstrate the performance of sparse SUR models with the hotspot prior and spike-and-slab MRF prior on synthetic and real data sets representing eQTL or mQTL studies and in vitro anti-cancer drug screening studies as examples for typical applications.

A mixtures approach to assessing relationships between environmental and social determinants of health and neonatal size and body composition in the Healthy Start cohort

Background: Previous studies have identified neighborhood-level environmental and social exposures associated with birth weight, but no studies have quantified the effects of simultaneous exposures across these domains. Here we used Bayesian Kernel Machine Regression (BKMR) to estimate the independent and joint effects of environmental and social exposures on birth weight in the Healthy Start cohort in Denver, CO.Methods: The initial selection of exposures was guided by an environmental justice screening tool developed for California. Data on neighborhood-level environmental (e.g., fine particulate matter, traffic counts, impervious surfaces) and social (e.g., hospitalization rates, educational attainment, and crime rates) exposures were assigned to pregnant mothers based on their census tract at enrollment. Birth weight was abstracted from medical records. We used a two-step approach to fit our model. First, we used a Bayesian nonparametric variable selection model to reduce the number of candidate exposures. Second, we fit a BKMR model with the exposures, interaction terms for all exposure pairs, and individual-level covariates.Results: We had complete data on birth weight, exposures, and covariates for 792 infants. Out of 19 exposures originally considered, the non-parametric Bayesian model selected 9 (3 environmental and 6 social). BKMR results showed a mixture with all exposures above the median was associated with decreased birth weight. The mixture components selected most frequently by the model were respiratory hospitalization rate and the percentage of households in poverty. Respiratory hospitalization rates had the greatest effect on birth weight (β = -0.03, SE = 0.06) when all other exposures were held at the 75th percentile. For some exposures (e.g., fine particulate matter), relationships with birth weight appeared non-linear.Conclusions: We identified joint effects of environmental and social exposures on birth weight. Results suggest that analyses within one domain may limit the identification of important interactions that are associated with neonatal outcomes.

Semiparametric Bayesian variable selection for gene-environment interactions.

Many complex diseases are known to be affected by the interactions between genetic variants and environmental exposures beyond the main genetic and environmental effects. Study of gene-environment (G×E) interactions is important for elucidating the disease etiology. Existing Bayesian methods for G×E interaction studies are challenged by the high-dimensional nature of the study and the complexity of environmental influences. Many studies have shown the advantages of penalization methods in detecting G×E interactions in "large p, small n" settings. However, Bayesian variable selection, which can provide fresh insight into G×E study, has not been widely examined. We propose a novel and powerful semiparametric Bayesian variable selection model that can investigate linear and nonlinear G×E interactions simultaneously. Furthermore, the proposed method can conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. Spike-and-slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. The proposed method conducts Bayesian variable selection more efficiently than existing methods. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. The proposed Bayesian method leads to the identification of main and interaction effects with important implications in a high-throughput profiling study with high-dimensional SNP data.

Use of a Bayesian model including QTL markers increases prediction reliability when test animals are distant from the reference population

Relatedness between reference and test animals has an important effect on the reliability of genomic prediction for test animals. Because genomic prediction has been widely applied in practical cattle breeding and bulls have been selected according to genomic breeding value without progeny testing, the sires or grandsires of candidates might not have phenotypic information and might not be in the reference population when the candidates are selected. The objective of this study was to investigate the decreasing trend of the reliability of genomic prediction given distant reference populations, using genomic best linear unbiased prediction (GBLUP) and Bayesian variable selection models with or without including the quantitative trait locus (QTL) markers detected from sequencing data. The data used in this study consisted of 22,242 bulls genotyped using the 54K SNP array from EuroGenomics. Among them, 1,444 Danish bulls born from 2006 to 2010 were selected as test animals. Different reference populations with varying relationships to test animals were created according to pedigree-based relationships. The reference individuals having a relationship with one or more test animals higher than 0.4 (scenario ρ < 0.4), 0.2 (ρ < 0.2), or 0.1 (ρ < 0.1, where ρ = relationship coefficient) were removed from reference sets; these represented the distance between reference and test animals being 2 generations, 3 generations, and 4 generations, respectively. Imputed whole-genome sequencing data of bulls from Denmark were used to conduct a genome-wide association study (GWAS). A small number of significant variants (QTL markers) from the GWAS were added to the array data. To compare the effects of different models, the basic GBLUP model, a Bayesian selection variable model, a GBLUP model with 2 components of genetic effects, and a Bayesian model with pooled array data and QTL markers were used for estimating genomic estimated breeding values (GEBV) of test animals. The reliability of genomic prediction decreased when the test animals were more generations away from the reference population. The reliability of genomic prediction was 0.461 for 1 generation away and 0.396 for 3 generations away, with the same number of individuals in the reference set, using a GBLUP model with chip markers only. The results showed that using the Bayesian method and QTL markers improved the reliability of genomic prediction in all scenarios of relationship between test and reference animals, in a range of 1.3% and 65.1% (4 generations away with only 841 individuals in the reference set). However, most gains were for predictions of milk yield and fat yield. There was little improvement for predictions of protein yield and mastitis, and no improvement for prediction of fertility, except for scenario ρ < 0.1, in which there was a large improvement for predictions of all traits. On the other hand, models including more than 10% polygenic effect decreased prediction reliability when the relationship between test and reference animals was distant.

Bayesian variable selection for multivariate zero-inflated models: Application to microbiome count data.

Microorganisms play critical roles in human health and disease. They live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical covariates, such as treatment effects, joint (multivariate) statistical models are preferred. Multivariate models allow one to estimate and exploit complex interdependencies among multiple taxa, yielding more powerful tests of exposure or treatment effects than application of taxon-specific univariate analyses. Analysis of microbial count data also requires special attention because data commonly exhibit zero inflation, i.e., more zeros than expected from a standard count distribution. To meet these needs, we developed a Bayesian variable selection model for multivariate count data with excess zeros that incorporates information on the covariance structure of the outcomes (counts for multiple taxa), while estimating associations with the mean levels of these outcomes. Though there has been much work on zero-inflated models for longitudinal data, little attention has been given to high-dimensional multivariate zero-inflated data modeled via a general correlation structure. Through simulation, we compared performance of the proposed method to that of existing univariate approaches, for both the binary ("excess zero") and count parts of the model. When outcomes were correlated the proposed variable selection method maintained type I error while boosting the ability to identify true associations in the binary component of the model. For the count part of the model, in some scenarios the univariate method had higher power than the multivariate approach. This higher power was at a cost of a highly inflated false discovery rate not observed with the proposed multivariate method. We applied the approach to oral microbiome data from the Pediatric HIV/AIDS Cohort Oral Health Study and identified five (of 44) species associated with HIV infection.

Bayesian Spatiotemporal Modeling Using Hierarchical Spatial Priors, with Applications to Functional Magnetic Resonance Imaging (with Discussion)

We propose a spatiotemporal Bayesian variable selection model for detecting activation in functional magnetic resonance imaging (fMRI) settings. Following recent research in this area, we use binary indicator variables for classifying active voxels. We assume that the spatial dependence in the images can be accommodated by applying an areal model to parcels of voxels. The use of parcellation and a spatial hierarchical prior (instead of the popular Ising prior) results in a posterior distribution amenable to exploration with an efficient Markov chain Monte Carlo (MCMC) algorithm. We study the properties of our approach by applying it to simulated data and an fMRI data set.

Short communication: Improving the accuracy of genomic prediction of body conformation traits in Chinese Holsteins using markers derived from high-density marker panels

This study investigated the efficiency of genomic prediction with adding the markers identified by genome-wide association study (GWAS) using a data set of imputed high-density (HD) markers from 54K markers in Chinese Holsteins. Among 3,056 Chinese Holsteins with imputed HD data, 2,401 individuals born before October 1, 2009, were used for GWAS and a reference population for genomic prediction, and the 220 younger cows were used as a validation population. In total, 1,403, 1,536, and 1,383 significant single nucleotide polymorphisms (SNP; false discovery rate at 0.05) associated with conformation final score, mammary system, and feet and legs were identified, respectively. About 2 to 3% genetic variance of 3 traits was explained by these significant SNP. Only a very small proportion of significant SNP identified by GWAS was included in the 54K marker panel. Three new marker sets (54K+) were herein produced by adding significant SNP obtained by linear mixed model for each trait into the 54K marker panel. Genomic breeding values were predicted using a Bayesian variable selection (BVS) model. The accuracies of genomic breeding value by BVS based on the 54K+ data were 2.0 to 5.2% higher than those based on the 54K data. The imputed HD markers yielded 1.4% higher accuracy on average (BVS) than the 54K data. Both the 54K+ and HD data generated lower bias of genomic prediction, and the 54K+ data yielded the lowest bias in all situations. Our results show that the imputed HD data were not very useful for improving the accuracy of genomic prediction and that adding the significant markers derived from the imputed HD marker panel could improve the accuracy of genomic prediction and decrease the bias of genomic prediction.

Multibreed genomic prediction using multitrait genomic residual maximum likelihood and multitask Bayesian variable selection

Genomic prediction is applicable to individuals of different breeds. Empirical results to date, however, show limited benefits in using information on multiple breeds in the context of genomic prediction. We investigated a multitask Bayesian model, presented previously by others, implemented in a Bayesian stochastic search variable selection (BSSVS) model. This model allowed for evidence of quantitative trait loci (QTL) to be accumulated across breeds or for both QTL that segregate across breeds and breed-specific QTL. In both cases, single nucleotide polymorphism effects were estimated with information from a single breed. Other models considered were a single-trait and multitrait genomic residual maximum likelihood (GREML) model, with breeds considered as different traits, and a single-trait BSSVS model. All single-trait models were applied to each of the 2 breeds separately and to the pooled data of both breeds. The data used included a training data set of 6,278 Holstein and 722 Jersey bulls, as well as 374 Jersey validation bulls. All animals had genotypes for 474,773 single nucleotide polymorphisms after editing and phenotypes for milk, fat, and protein yields. Using the same training data, BSSVS consistently outperformed GREML. The multitask BSSVS, however, did not outperform single-trait BSSVS, which used pooled Holstein and Jersey data for training. Thus, the rigorous assumption that the traits are the same in both breeds yielded a slightly better prediction than a model that had to estimate the correlation between the breeds from the data. Adding the Holstein data significantly increased the accuracy of the single-trait GREML and BSSVS in predicting the Jerseys for milk and protein, in line with estimated correlations between the breeds of 0.66 and 0.47 for milk and protein yields, whereas only the BSSVS model significantly improved the accuracy for fat yield with an estimated correlation between breeds of only 0.05. The relatively high genetic correlations for milk and protein yields, and the superiority of the pooling strategy, is likely the result of the observed admixture between both breeds in our data. The Bayesian model was able to detect several QTL in Holsteins, which likely enabled it to outperform GREML. The inability of the multitask Bayesian models to outperform a simple pooling strategy may be explained by the fact that the pooling strategy assumes equal effects in both breeds; furthermore, this assumption may be valid for moderate- to large-sized QTL, which are important for multibreed genomic prediction.

Diagnosing pregnancy status using infrared spectra and milk composition in dairy cows

Data on Holstein (16,890), Brown Swiss (31,441), Simmental (25,845), and Alpine Grey (12,535) cows reared in northeastern Italy were used to assess the ability of milk components (fat, protein, casein, and lactose) and Fourier transform infrared (FTIR) spectral data to diagnose pregnancy. Pregnancy status was defined as whether a pregnancy was confirmed by a subsequent calving and no other subsequent inseminations within 90 d of the breeding of specific interest. Milk samples were analyzed for components and FTIR full-spectrum data using a MilkoScan FT+ 6000 (Foss Electric, Hillerød, Denmark). The spectrum covered 1,060 wavenumbers (wn) from 5,010 to 925 cm-1. Pregnancy status was predicted using generalized linear models with fat, protein, lactose, casein, and individual FTIR spectral bands or wavelengths as predictors. We also fitted a generalized linear model as a simultaneous function of all wavelengths (1,060 wn) with a Bayesian variable selection model using the BGLR R-package (https://r-forge.r-project.org/projects/bglr/). Prediction accuracy was determined using the area under a receiver operating characteristic curve based on a 10-fold cross-validation (CV-AUC) assessment based on sensitivities and specificities of phenotypic predictions. Overall, the best prediction accuracies were obtained for the model that included the complete FTIR spectral data. We observed similar patterns across breeds with small differences in prediction accuracy. The highest CV-AUC value was obtained for Alpine Grey cows (CV-AUC = 0.645), whereas Brown Swiss and Simmental cows had similar performance (CV-AUC = 0.630 and 0.628, respectively), followed by Holsteins (CV-AUC = 0.607). For single-wavelength analyses, important peaks were detected at wn 2,973 to 2,872 cm-1 where Fat-B (C-H stretch) is usually filtered, wn 1,773 cm-1 where Fat-A (C=O stretch) is filtered, wn 1,546 cm-1 where protein is filtered, wn 1,468 cm-1 associated with urea and fat, wn 1,399 and 1,245 cm-1 associated with acetone, and wn 1,025 to 1,013 cm-1 where lactose is filtered. In conclusion, this research provides new insight into alternative strategies for pregnancy screening of dairy cows.

Multi-breed genomic prediction using Bayes R with sequence data and dropping variants with a small effect

BackgroundThe increasing availability of whole-genome sequence data is expected to increase the accuracy of genomic prediction. However, results from simulation studies and analysis of real data do not always show an increase in accuracy from sequence data compared to high-density (HD) single nucleotide polymorphism (SNP) chip genotypes. In addition, the sheer number of variants makes analysis of all variants and accurate estimation of all effects computationally challenging. Our objective was to find a strategy to approximate the analysis of whole-sequence data with a Bayesian variable selection model. Using a simulated dataset, we applied a Bayes R hybrid model to analyse whole-sequence data, test the effect of dropping a proportion of variants during the analysis, and test how the analysis can be split into separate analyses per chromosome to reduce the elapsed computing time. We also investigated the effect of imputation errors on prediction accuracy. Subsequently, we applied the approach to a dataset that contained imputed sequences and records for production and fertility traits for 38,492 Holstein, Jersey, Australian Red and crossbred bulls and cows.ResultsWith the simulated dataset, we found that prediction accuracy was highly increased for a breed that was not represented in the training population for sequence data compared to HD SNP data. Either dropping part of the variants during the analysis or splitting the analysis into separate analyses per chromosome decreased accuracy compared to analysing whole-sequence data. First, dropping variants from each chromosome and reanalysing the retained variants together resulted in an accuracy similar to that obtained when analysing whole-sequence data. Adding imputation errors decreased prediction accuracy, especially for errors in the validation population. With real data, using sequence variants resulted in accuracies that were similar to those obtained with the HD SNPs.ConclusionsWe present an efficient approach to approximate analysis of whole-sequence data with a Bayesian variable selection model. The lack of increase in prediction accuracy when applied to real data could be due to imputation errors, which demonstrates the importance of developing more accurate methods of imputation or directly genotyping sequence variants that have a major effect in the prediction equation.

A Scalable Bayesian Method for Integrating Functional Information in Genome-wide Association Studies

Genome-wide association studies (GWASs) have identified many complex loci. However, most loci reside in noncoding regions and have unknown biological functions. Integrative analysis that incorporates known functional information into GWASs can help elucidate the underlying biological mechanisms and prioritize important functional variants. Hence, we develop a flexible Bayesian variable selection model with efficient computational techniques for such integrative analysis. Different from previous approaches, our method models the effect-size distribution and probability of causality for variants with different annotations and jointly models genome-wide variants to account for linkage disequilibrium (LD), thus prioritizing associations based on the quantification of the annotations and allowing for multiple associated variants per locus. Our method dramatically improves both computational speed and posterior sampling convergence by taking advantage of the block-wise LD structures in human genomes. In simulations, our method accurately quantifies the functional enrichment and performs more powerfully for prioritizing the true associations than alternative methods, where the power gain is especially apparent when multiple associated variants in LD reside in the same locus. We applied our method to an in-depth GWAS of age-related macular degeneration with 33,976 individuals and 9,857,286 variants. We find the strongest enrichment for causality among non-synonymous variants (54× more likely to be causal, 1.4× larger effect sizes) and variants in transcription, repressed Polycomb, and enhancer regions, as well as identify five additional candidate loci beyond the 32 known AMD risk loci. In conclusion, our method is shown to efficiently integrate functional information in GWASs, helping identify functional associated-variants and underlying biology.