Bayesian Variable Selection for Gaussian Copula Regression Models

Alexopoulos, Angelos; Bottolo, Leonardo

doi:10.1080/10618600.2020.1840997

Cited by 13 publications

(8 citation statements)

References 57 publications

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“…Zhang et al, 2019). For nonlinear models, a novel and efficient MCMC algorithm was proposed by Alexopoulos and Bottolo (2020), which can explore the high-dimensional model space and estimate the structure among multiple responses of diverse types (i.e., low-intensity counts, binary, ordinal and continuous variables). S3.1 if using the median probability model.…”

Section: Discussionmentioning

confidence: 99%

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Zhao¹,

Banterle²,

Lewin³

et al. 2021

Preprint

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It is becoming increasingly common to study the complex association between multiple outcomes and high-dimensional predictors in biomedicine. However, the related multiple outcomes and related high-dimensional predictors require flexible and efficient joint statistical models. We propose a multivariate structured Bayesian variable selection model to identify sparse predictors associated with multiple outcomes. The approach uses a known structure prior between the multiple outcomes and predictors via a Markov random field (MRF) prior for the latent indicator variables of the coefficient matrix of a sparse seemingly unrelated regression. The prior knowledge in the MRF prior has the potential to generate new structure knowledge. In addition, we employ random effects to capture sample heterogeneity of grouped data. The proposed approach is validated by simulation studies and a large-scale pharmacogenomic study which includes a pharmacological profiling and multi-omics data from in vitro anti-cancer drug screening.

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Section: Discussionmentioning

confidence: 99%

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Zhao¹,

Banterle²,

Lewin³

et al. 2021

Preprint

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“…MR 2 is based on a recently proposed Bayesian method to select important predictors in regression models with multiple responses of any type [40]. Specifically, a sparse Gaussian copula regression (GCR) model [41] is used to account for the multivariate dependencies between the Gaussian responses 13 β Y once their direct causal association with a set of important exposures β X is estimated.…”

Section: Bayesian Multi-response Mrmentioning

confidence: 99%

“…A detailed discussion of the Bayesian formulation of the GCR model in eq. ( 10) with multiple responses of any type is presented in [40]. In the following, we summarise the main aspects of the proposed multi-response multivariable MR model when all margins are univariate Gaussian.…”

Section: Bayesian Multi-response Mrmentioning

confidence: 99%

Multi-response Mendelian randomization: Identification of shared and distinct exposures for multimorbidity and multiple related disease outcomes

Zuber

Lewin

Levin

et al. 2023

Preprint

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The existing framework of Mendelian randomization (MR) infers the causal effect of one or multiple exposures on one single outcome. It is not designed to jointly model multiple outcomes, as would be necessary to detect causes of more than one outcome and would be relevant to model multimorbidity or other related disease outcomes. Here, we introduce Multi-response Mendelian randomization (MR2), a novel MR method specifically designed for multiple outcomes to identify exposures that cause more than one outcome or, conversely, exposures that exert their effect on distinct responses. MR2uses a sparse Bayesian Gaussian copula regression framework to detect causal effects while estimating the residual correlation between summary-level outcomes, i.e., the correlation that cannot be explained by the exposures, andviceversa. We show both theoretically and in a comprehensive simulation study how unmeasured shared pleiotropy induces residual correlation. We also reveal how non-genetic factors that affect more than one outcome contribute to their correlation. We demonstrate that by accounting for residual correlation, MR2has higher power to detect shared exposures causing more than one outcome. It also provides more accurate causal effect estimates than existing methods that ignore the dependence between related responses. Finally, we illustrate how MR2detects shared and distinct causal exposures for five cardiovascular diseases in two applications considering cardiometabolic and lipidomic exposures and uncovers residual correlation between summary-level outcomes reflecting known relationships between cardiovascular diseases.

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“…In this set‐up, the proposal and target densities cancel out in the Metropolis–Hastings acceptance ratios. This is known as ‘implicit marginalisation’ (Alexopoulos & Bottolo, 2020; Holmes & Held, 2006) since the resulting acceptance ratio does not contain the current and proposed values of

β_{γ}

{{bold-italicσ}^{2}

, ρ } and it has been shown to greatly improve mixing of the structural parameters γ and J which are in our case the main focus of inference.…”

Section: Posterior Computationsmentioning

confidence: 99%

A Computationally Efficient Bayesian Seemingly Unrelated Regressions Model for High-Dimensional Quantitative Trait Loci Discovery

Bottolo

Banterle

Richardson

et al. 2021

Journal of the Royal Statistical Society Series C: Applied Statistics

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Our work is motivated by the search for metabolite quantitative trait loci (QTL) in a cohort of more than 5000 people. There are 158 metabolites measured by NMR spectroscopy in the 31‐year follow‐up of the Northern Finland Birth Cohort 1966 (NFBC66). These metabolites, as with many multivariate phenotypes produced by high‐throughput biomarker technology, exhibit strong correlation structures. Existing approaches for combining such data with genetic variants for multivariate QTL analysis generally ignore phenotypic correlations or make restrictive assumptions about the associations between phenotypes and genetic loci. We present a computationally efficient Bayesian seemingly unrelated regressions model for high‐dimensional data, with cell‐sparse variable selection and sparse graphical structure for covariance selection. Cell sparsity allows different phenotype responses to be associated with different genetic predictors and the graphical structure is used to represent the conditional dependencies between phenotype variables. To achieve feasible computation of the large model space, we exploit a factorisation of the covariance matrix. Applying the model to the NFBC66 data with 9000 directly genotyped single nucleotide polymorphisms, we are able to simultaneously estimate genotype–phenotype associations and the residual dependence structure among the metabolites. The R package BayesSUR with full documentation is available at https://cran.r-project.org/web/packages/BayesSUR/

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Bayesian Variable Selection for Gaussian Copula Regression Models

Cited by 13 publications

References 57 publications

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Multivariate Bayesian structured variable selection for pharmacogenomic studies

Multi-response Mendelian randomization: Identification of shared and distinct exposures for multimorbidity and multiple related disease outcomes

A Computationally Efficient Bayesian Seemingly Unrelated Regressions Model for High-Dimensional Quantitative Trait Loci Discovery

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