Bayesian Variable Selection Method Research Articles

Multivariate Bayesian variable selection for multi-trait genetic fine mapping

Abstract Genome-wide association studies (GWAS) have identified thousands of single-nucleotide polymorphisms (SNPs) associated with complex traits, but determining the underlying causal variants remains challenging. Fine mapping aims to pinpoint the potentially causal variants from a large number of correlated SNPs possibly with group structure in GWAS-enriched genomic regions using variable selection approaches. In multi-trait fine mapping, we are interested in identifying the causal variants for multiple related traits. Existing multivariate variable selection methods for fine mapping select variables for all responses without considering the possible heterogeneity across different responses. Here, we develop a novel multivariate Bayesian variable selection method for multi-trait fine mapping to select causal variants from a large number of grouped SNPs that target at multiple correlated and possibly heterogeneous traits. Our new method is featured by its selection at multiple levels, incorporation of prior biological knowledge to guide selection and identification of best subset of traits the variants target at. We showed the advantage of our method over existing methods via comprehensive simulations that mimic typical fine-mapping settings and a real-world fine-mapping example in UK Biobank, where we identified critical causal variants potentially targeting at different subsets of addictive behaviours and risk factors.

Automated Bayesian variable selection methods for binary regression models with missing covariate data

Data collection and the availability of large data sets has increased over the last decades. In both statistical and machine learning frameworks, two methodological issues typically arise when performing regression analysis on large data sets. First, variable selection is crucial in regression modeling, as it helps to identify an appropriate model with respect to the considered set of conditioning variables. Second, especially in the context of survey data, handling of missing values is important for estimation, which occur even with state-of-the-art data collection and processing methods. Within this paper, we provide an Bayesian approach based on a spike-and-slab prior for the regression coefficients, which allows for simultaneous handling of variable selection and estimation in combination with handling of missing values in covariate data. The paper also discusses the implementation of the approach using Markov chain Monte Carlo techniques and provides results for simulated data sets and an empirical illustration based on data from the German National Educational Panel Study. The suggested Bayesian approach is compared to other statistical and machine learning frameworks such as Lasso, ridge regression, and Elastic net, and is shown to perform well in terms of estimation performance and variable selection accuracy. The simulation results demonstrate that ignoring the handling of missing values in data sets can lead to the generation of biased selection results. Overall, the proposed Bayesian method offers a holistic, flexible, and powerful framework for variable selection in the presence of missing covariate data.

Task-Dependent Brain Activity in Generalized Anxiety Disorder Determined By Bayesian Spatio-Temporal Single Case Model

Introduction: Data obtained from functional magnetic resonance imaging (fMRI) have a complex structure. Considering the special features of this type of data in analyses is of particular importance. Previous studies on generalized anxiety disorder (GAD) as a prevalent mental disorder using functional neuroimaging have had conflicting results. In this study, we apply a Bayesian spatiotemporal model to this type of data which considers both spatial and temporal dependence among regions which is one of the most essential features to consider. Methods: In this single-subject study, we analyze data from a patient with GAD and a healthy participant. Both participants are 24-year-old women who are assigned an emotion reactivity task (matching neutral and negative facial expressions) inside a scanner. The spatial Bayesian variable selection method is used to detect blood oxygen level-dependent activation in fMRI data. Results: Activation areas in neutral and negative facial expressions are provided for both participants by posterior probability map. The results of our study show a greater level of activity in the GAD participant in comparison to the healthy participant in responding to the negative matching task. Conclusion: the GAD patient showed more neural activity in response to negative facial expressions than the healthy participant in brain regions related to emotional response in the areas of the frontal Pole, middle frontal gyrus, insular cortex, and frontal orbital cortex. Moreover, the inferior frontal gyrus in the patient with GAD showed more reaction to negative emotional stimuli.

Using encrypted genotypes and phenotypes for collaborative genomic analyses to maintain data confidentiality.

To adhere to and capitalize on the benefits of the FAIR (findable, accessible, interoperable, and reusable) principles in agricultural genome-to-phenome studies, it is crucial to address privacy and intellectual property issues that prevent sharing and reuse of data in research and industry. Direct sharing of genotype and phenotype data is often prohibited due to intellectual property and privacy concerns. Thus, there is a pressing need for encryption methods that obscure confidential aspects of the data, without affecting the outcomes of certain statistical analyses. A homomorphic encryption method for genotypes and phenotypes (HEGP) has been proposed for single-marker regression in genome-wide association studies (GWAS) using linear mixed models with Gaussian errors. This methodology permits frequentist likelihood-based parameter estimation and inference. In this paper, we extend HEGP to broader applications in genome-to-phenome analyses. We show that HEGP is suited to commonly used linear mixed models for genetic analyses of quantitative traits including genomic best linear unbiased prediction (GBLUP) and ridge-regression best linear unbiased prediction (RR-BLUP), as well as Bayesian variable selection methods (e.g. those in Bayesian Alphabet), for genetic parameter estimation, genomic prediction, and GWAS. By advancing the capabilities of HEGP, we offer researchers and industry professionals a secure and efficient approach for collaborative genomic analyses while preserving data confidentiality.

Application of statistical machine learning in biomarker selection

In the recent JAVELIN Bladder 100 phase 3 trial, avelumab plus best supportive care significantly prolonged overall survival relative to best supportive care alone as first-line maintenance therapy following first-line platinum-based chemotherapy in patients with advanced urothelial cancer (aUC). Discovering biomarkers using genomic profiling to understand potential patient heterogeneity is essential to help improve patient care with precision medicine. For the JAVELIN Bladder 100 trial, it is unclear which variable selection methods can most reliably identify biomarkers to inform patient care because the dataset is characterized by high collinearity and low signal. The aim of this paper was to evaluate available selection methods and their ability to discover prognostic and predictive biomarkers in patients with aUC receiving first-line maintenance therapy. A simulation study evaluated the performance of popular variable selection approaches for high-dimensional data including penalized regression models, random survival forests, and Bayesian variable selection methods. For Bayesian variable selection methods, a modified Bayesian Information Criterion (BIC) thresholding rule was proposed in addition to the traditional BIC thresholding rule. These methods were applied to the JAVELIN Bladder 100 dataset to investigate potential biomarkers associated with survival benefit. Results from the simulations demonstrated the strengths and limitations of the different methods. The variable selection methods demonstrated low false discovery rates under different conditions. However, their performance declined in the presence of high collinearity. Using the JAVELIN Bladder 100 data, we identified some potentially significant biomarkers across multiple models. Several lasso-related methods were able to identify potentially biologically meaningful variables in the trial. Some variable selection methods (such as stochastic search variable selection and random survival forest) may not be well suited to this type of data due to the presence of extreme collinearity and low signal. Future research should explore novel variable selection methods that may be more suitable for identifying prognostic and predictive biomarkers in this population.Trial registration: ClinicalTrials.gov Identifier: NCT02603432.

Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data

Quantile regression models are remarkable structures for conducting regression analyses when the data are subject to missingness. Missing values occur because of various factors like missing completely at random, missing at random, or missing not at random. All these may result from system malfunction during data collection or human error during data preprocessing. Nevertheless, it is important to deal with missing values before analyzing data since ignoring or omitting missing values may result in biased or misinformed analysis. This paper studies quantile regressions from a Bayesian perspective. By proposing a hierarchical model framework, we develop an alternative approach based on deterministic variational Bayes approximations. Logistic and probit models are adopted to specify propensity scores for missing manifests and covariates, respectively. Bayesian variable selection method is proposed to recognize significant covariates. Several simulation studies and real examples illustrate the advantages of the proposed methodology and offer some possible future research directions.

Bayesian bi-level variable selection for genome-wide survival study.

Mild cognitive impairment (MCI) is a clinical syndrome characterized by the onset and evolution of cognitive impairments, often considered a transitional stage to Alzheimer's disease (AD). The genetic traits of MCI patients who experience a rapid progression to AD can enhance early diagnosis capabilities and facilitate drug discovery for AD. While a genome-wide association study (GWAS) is a standard tool for identifying single nucleotide polymorphisms (SNPs) related to a disease, it fails to detect SNPs with small effect sizes due to stringent control for multiple testing. Additionally, the method does not consider the group structures of SNPs, such as genes or linkage disequilibrium blocks, which can provide valuable insights into the genetic architecture. To address the limitations, we propose a Bayesian bi-level variable selection method that detects SNPs associated with time of conversion from MCI to AD. Our approach integrates group inclusion indicators into an accelerated failure time model to identify important SNP groups. Additionally, we employ data augmentation techniques to impute censored time values using a predictive posterior. We adapt Dirichlet-Laplace shrinkage priors to incorporate the group structure for SNP-level variable selection. In the simulation study, our method outperformed other competing methods regarding variable selection. The analysis of Alzheimer's Disease Neuroimaging Initiative (ADNI) data revealed several genes directly or indirectly related to AD, whereas a classical GWAS did not identify any significant SNPs.

Comparative efficacy of three Bayesian variable selection methods in the context of weight loss in obese women.

The use of high-dimensional data has expanded in many fields, including in clinical research, thus making variable selection methods increasingly important compared to traditional statistical approaches. The work aims to compare the performance of three supervised Bayesian variable selection methods to detect the most important predictors among a high-dimensional set of variables and to provide useful and practical guidelines of their use. We assessed the variable selection ability of: (1) Bayesian Kernel Machine Regression (BKMR), (2) Bayesian Semiparametric Regression (BSR), and (3) Bayesian Least Absolute Shrinkage and Selection Operator (BLASSO) regression on simulated data of different dimensions and under three scenarios with disparate predictor-response relationships and correlations among predictors. This is the first study describing when one model should be preferred over the others and when methods achieve comparable results. BKMR outperformed all other models with small synthetic datasets. BSR was strongly dependent on the choice of its own intrinsic parameter, but its performance was comparable to BKMR with large datasets. BLASSO should be preferred only when it is reasonable to hypothesise the absence of synergies between predictors and the presence of monotonous predictor-outcome relationships. Finally, we applied the models to a real case study and assessed the relationships among anthropometric, biochemical, metabolic, cardiovascular, and inflammatory variables with weight loss in 755 hospitalised obese women from the Follow Up OBese patients at AUXOlogico institute (FUOBAUXO) cohort.

A Bayesian genomic selection approach incorporating prior feature ordering and population structures with application to coronary artery disease.

Coronary artery disease is one of the most common types of cardiovascular disease. Death from coronary heart disease is influenced by genetic factors in both women and men. In this article, we propose a novel Bayesian variable selection framework for the identification of important genetic variants associated with coronary artery disease disease status. Instead of treating each feature independently as in conventional Bayesian variable selection methods, we propose an innovative prior for the inclusion probabilities of genetic variants that accounts for their ordering structure. We assume that neighboring variants are more likely to be selected together as they tend to be highly correlated and have similar biological functions. Additionally, we propose to group participating subjects based on underlying population structure and fit separate regressions, so that the regression coefficients can better reflect different disease risks in different population groups. Our approach borrows strength across regression models through an innovative prior inspired by the Markov random fields. The proposed framework can improve variable selection and prediction performances as demonstrated in the simulation studies. We also apply the proposed framework to the CATHeterization GENetics data with binary Coronary artery disease disease status.

BGWAS: Bayesian variable selection in linear mixed models with nonlocal priors for genome-wide association studies

BackgroundGenome-wide association studies (GWAS) seek to identify single nucleotide polymorphisms (SNPs) that cause observed phenotypes. However, with highly correlated SNPs, correlated observations, and the number of SNPs being two orders of magnitude larger than the number of observations, GWAS procedures often suffer from high false positive rates.ResultsWe propose BGWAS, a novel Bayesian variable selection method based on nonlocal priors for linear mixed models specifically tailored for genome-wide association studies. Our proposed method BGWAS uses a novel nonlocal prior for linear mixed models (LMMs). BGWAS has two steps: screening and model selection. The screening step scans through all the SNPs fitting one LMM for each SNP and then uses Bayesian false discovery control to select a set of candidate SNPs. After that, a model selection step searches through the space of LMMs that may have any number of SNPs from the candidate set. A simulation study shows that, when compared to popular GWAS procedures, BGWAS greatly reduces false positives while maintaining the same ability to detect true positive SNPs. We show the utility and flexibility of BGWAS with two case studies: a case study on salt stress in plants, and a case study on alcohol use disorder.ConclusionsBGWAS maintains and in some cases increases the recall of true SNPs while drastically lowering the number of false positives compared to popular SMA procedures.

Study of Bayesian variable selection method on mixed linear regression models.

Variable selection has always been an important issue in statistics. When a linear regression model is used to fit data, selecting appropriate explanatory variables that strongly impact the response variables has a significant effect on the model prediction accuracy and interpretation effect. redThis study introduces the Bayesian adaptive group Lasso method to solve the variable selection problem under a mixed linear regression model with a hidden state and explanatory variables with a grouping structure. First, the definition of the implicit state mixed linear regression model is presented. Thereafter, the Bayesian adaptive group Lasso method is used to determine the penalty function and parameters, after which each parameter's specific form of the fully conditional posterior distribution is calculated. Moreover, the Gibbs algorithm design is outlined. Simulation experiments are conducted to compare the variable selection and parameter estimation effects in different states. Finally, a dataset of Alzheimer's Disease is used for application analysis. The results demonstrate that the proposed method can identify the observation from different hidden states, but the results of the variable selection in different states are obviously different.

Variable selection for quantile autoregressive model: Bayesian methods versus classical methods

In this article, we introduce three Bayesian variable selection methods for the quantile autoregressive model with explanatory variables. The Gibbs sampling algorithms are developed for each method by setting different priors. The numerical simulations suggest that the Gibbs sampling algorithms converge fast and Bayesian variable selection methods are reliable. A real example is given to analysis the relationship between the count of total rental bikes and five explanatory variables. Both simulations and data example indicate that the proposed methods are feasible, reliable, and appropriate for analyzing the Bike Sharing data set.

A Bayesian Variable Selection Method for Spatial Autoregressive Quantile Models

In this paper, a Bayesian variable selection method for spatial autoregressive (SAR) quantile models is proposed on the basis of spike and slab prior for regression parameters. The SAR quantile models, which are more generalized than SAR models and quantile regression models, are specified by adopting the asymmetric Laplace distribution for the error term in the classical SAR models. The proposed approach could perform simultaneously robust parametric estimation and variable selection in the context of SAR quantile models. Bayesian statistical inferences are implemented by a detailed Markov chain Monte Carlo (MCMC) procedure that combines Gibbs samplers with a probability integral transformation (PIT) algorithm. In the end, empirical numerical examples including several simulation studies and a Boston housing price data analysis are employed to demonstrate the newly developed methodologies.

Correlation scenarios and correlation stress testing

We develop a general approach for stress testing correlations of financial asset portfolios. The correlation matrix of asset returns is specified in a parametric form, where correlations are represented as a function of risk factors, such as country and industry factors. A sparse factor structure linking assets and risk factors is built using Bayesian variable selection methods. Regular calibration yields a joint distribution of economically meaningful stress scenarios of the factors. As such, the method also lends itself as a reverse stress testing framework: using the Mahalanobis distance or Highest Density Regions (HDR) on the joint risk factor distribution allows to infer worst-case correlation scenarios. We give examples of stress tests on a large portfolio of European and North American stocks.

Bayesian forecast combination using time-varying features

In this work, we propose a novel framework for density forecast combination by constructing time-varying weights based on time-varying features. Our framework estimates weights in the forecast combination via Bayesian log predictive scores, in which the optimal forecast combination is determined by time series features from historical information. In particular, we use an automatic Bayesian variable selection method to identify the importance of different features. To this end, our approach has better interpretability compared to other black-box forecasting combination schemes. We apply our framework to stock market data and M3 competition data. Based on our structure, a simple maximum-a-posteriori scheme outperforms benchmark methods, and Bayesian variable selection can further enhance the accuracy for both point forecasts and density forecasts.

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.

A Bayesian method for identifying associations between response variables and bacterial community composition.

Determining associations between intestinal bacteria and continuously measured physiological outcomes is important for understanding the bacteria-host relationship but is not straightforward since abundance data (compositional data) are not normally distributed. To address this issue, we developed a fully Bayesian linear regression model (BRACoD; Bayesian Regression Analysis of Compositional Data) with physiological measurements (continuous data) as a function of a matrix of relative bacterial abundances. Bacteria can be classified as operational taxonomic units or by taxonomy (genus, family, etc.). Bacteria associated with the physiological measurement were identified using a Bayesian variable selection method: Stochastic Search Variable Selection. The output is a list of inclusion probabilities () and coefficients that indicate the strength of the association () for each bacterial taxa. Tests with simulated communities showed that adopting a cut point value of ≥ 0.3 for identifying included bacteria optimized the true positive rate (TPR) while maintaining a false positive rate (FPR) of ≤ 5%. At this point, the chances of identifying non-contributing bacteria were low and all well-established contributors were included. Comparison with other methods showed that BRACoD (at ≥ 0.3) had higher precision and a higher TPR than a commonly used center log transformed LASSO procedure (clr-LASSO) as well as higher TPR than an off-the-shelf Spike and Slab method after center log transformation (clr-SS). BRACoD was also less likely to include non-contributing bacteria that merely correlate with contributing bacteria. Analysis of a rat microbiome experiment identified 47 operational taxonomic units that contributed to fecal butyrate levels. Of these, 31 were positively and 16 negatively associated with butyrate. Consistent with their known role in butyrate metabolism, most of these fell within the Lachnospiraceae and Ruminococcaceae. We conclude that BRACoD provides a more precise and accurate method for determining bacteria associated with a continuous physiological outcome compared to clr-LASSO. It is more sensitive than a generalized clr-SS algorithm, although it has a higher FPR. Its ability to distinguish genuine contributors from correlated bacteria makes it better suited to discriminating bacteria that directly contribute to an outcome. The algorithm corrects for the distortions arising from compositional data making it appropriate for analysis of microbiome data.

Accuracy of genomic prediction of maternal traits in pigs using Bayesian variable selection methods.

The aim of this study was to compare three methods of genomic prediction: GBLUP, BayesC and BayesGC for genomic prediction of six maternal traits in Landrace sows using a panel of 660 K SNPs. The effects of different priors for the Bayesian methods were also investigated. GBLUP does not take the genetic architecture into account as all SNPs are assumed to have equally sized effects and relies heavily on the relationships between the animals for accurate predictions. Bayesian approaches rely on both fitting SNPs that describe relationships between animals in addition to fitting single SNP effects directly. Both the relationship between the animals and single SNP effects are important for accurate predictions. Maternal traits in sows are often more difficult to record and have lower heritabilities. BayesGC was generally the method with the higher accuracy, although its accuracy was for some traits matched by that of GBLUP and for others by that of BayesC. For piglet mortality within 3 weeks, BayesGC achieved up to 9.2% higher accuracy. For many of the traits, however, the methods did not show significant differences in accuracies.

Variational Bayes for high-dimensional proportional hazards models with applications within gene expression.

MotivationFew Bayesian methods for analyzing high-dimensional sparse survival data provide scalable variable selection, effect estimation and uncertainty quantification. Such methods often either sacrifice uncertainty quantification by computing maximum a posteriori estimates, or quantify the uncertainty at high (unscalable) computational expense.ResultsWe bridge this gap and develop an interpretable and scalable Bayesian proportional hazards model for prediction and variable selection, referred to as sparse variational Bayes. Our method, based on a mean-field variational approximation, overcomes the high computational cost of Markov chain Monte Carlo, whilst retaining useful features, providing a posterior distribution for the parameters and offering a natural mechanism for variable selection via posterior inclusion probabilities. The performance of our proposed method is assessed via extensive simulations and compared against other state-of-the-art Bayesian variable selection methods, demonstrating comparable or better performance. Finally, we demonstrate how the proposed method can be used for variable selection on two transcriptomic datasets with censored survival outcomes, and how the uncertainty quantification offered by our method can be used to provide an interpretable assessment of patient risk.Availability and implementationour method has been implemented as a freely available R package survival.svb (https://github.com/mkomod/survival.svb).Supplementary information Supplementary data are available at Bioinformatics online.

Bayesian flexible beta regression model with functional covariate

Standard parametric regression models are unsuitable when the aim is to predict a bounded continuous response, such as a proportion/percentage or a rate. A possible solution is the flexible beta regression model which is based on a special mixture of betas designed to cope with (though not limited to) bimodality, heavy tails, and outlying observations. This work introduces such a model in the case of a functional covariate, motivated by a spectrometric analysis on milk specimens. Estimation issues are dealt with through a combination of standard basis expansion and Markov chains Monte Carlo techniques. Specifically, the selection of the most significant coefficients of the expansion is done through Bayesian variable selection methods that take advantage of shrinkage priors. The effectiveness of the proposal is illustrated with simulation studies and the application on spectrometric data.