Semiparametric Bayesian variable selection for gene-environment interactions

BHAFT: Bayesian heredity-constrained accelerated failure time models for detecting gene-environment interactions in survival analysis

In addition to considering the main effects, understanding gene-environment (G × E) interactions is imperative for determining the etiology of diseases and the factors that affect their prognosis. In the existing statistical framework for censored survival outcomes, there are several challenges in detecting G × E interactions, such as handling high-dimensional omics data, diverse environmental factors, and algorithmic complications in survival analysis. The effect heredity principle has widely been used in studies involving interaction identification because it incorporates the dependence of the main and interaction effects. However, Bayesian survival models that incorporate the assumption of this principle have not been developed. Therefore, we propose Bayesian heredity-constrained accelerated failure time (BHAFT) models for identifying main and interaction (M-I) effects with novel spike-and-slab or regularized horseshoe priors to incorporate the assumption of effect heredity principle. The R package rstan was used to fit the proposed models. Extensive simulations demonstrated that BHAFT models had outperformed other existing models in terms of signal identification, coefficient estimation, and prognosis prediction. Biologically plausible G × E interactions associated with the prognosis of lung adenocarcinoma were identified using our proposed model. Notably, BHAFT models incorporating the effect heredity principle could identify both main and interaction effects, which are highly useful in exploring G × E interactions in high-dimensional survival analysis. The code and data used in our paper are available at https://github.com/SunNa-bayesian/BHAFT.

The Bayesian Regularized Quantile Varying Coefficient Model

The quantile varying coefficient (VC) model can flexibly capture dynamical patterns of regression coefficients. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the response variable, and can provide a more comprehensive picture of modeling via exploring the conditional quantiles of the response variable. Although extensive studies have been conducted to examine variable selection for the high-dimensional quantile varying coefficient models, the Bayesian analysis has been rarely developed. The Bayesian regularized quantile varying coefficient model has been proposed to incorporate robustness against data heterogeneity while accommodating the non-linear interactions between the effect modifier and predictors. Selecting important varying coefficients can be achieved through Bayesian variable selection. Incorporating the multivariate spike-and-slab priors further improves performance by inducing exact sparsity. The Gibbs sampler has been derived to conduct efficient posterior inference of the sparse Bayesian quantile VC model through Markov chain Monte Carlo (MCMC). The merit of the proposed model in selection and estimation accuracy over the alternatives has been systematically investigated in simulation under specific quantile levels and multiple heavy-tailed model errors. In the case study, the proposed model leads to identification of biologically sensible markers in a non-linear gene-environment interaction study using the NHS data.

Detection of Interaction Effects in a Nonparametric Concurrent Regression Model

Many methods have been developed to study nonparametric function-on-function regression models. Nevertheless, there is a lack of model selection approach to the regression function as a functional function with functional covariate inputs. To study interaction effects among these functional covariates, in this article, we first construct a tensor product space of reproducing kernel Hilbert spaces and build an analysis of variance (ANOVA) decomposition of the tensor product space. We then use a model selection method with the L1 criterion to estimate the functional function with functional covariate inputs and detect interaction effects among the functional covariates. The proposed method is evaluated using simulations and stroke rehabilitation data.

Robust Bayesian variable selection for gene-environment interactions

Gene-environment (G× E) interactions have important implications to elucidate the etiology of complex diseases beyond the main genetic and environmental effects. Outliers and data contamination in disease phenotypes of G× E studies have been commonly encountered, leading to the development of a broad spectrum of robust regularization methods. Nevertheless, within the Bayesian framework, the issue has not been taken care of in existing studies. We develop a fully Bayesian robust variable selection method for G× E interaction studies. The proposed Bayesian method can effectively accommodate heavy-tailed errors and outliers in the response variable while conducting variable selection by accounting for structural sparsity. In particular, for the robust sparse group selection, the spike-and-slab priors have been imposed on both individual and group levels to identify important main and interaction effects robustly. An efficient Gibbs sampler has been developed to facilitate fast computation. Extensive simulation studies, analysis of diabetes data with single-nucleotide polymorphism measurements from the Nurses' Health Study, and The Cancer Genome Atlas melanoma data with gene expression measurements demonstrate the superior performance of the proposed method over multiple competing alternatives.

Springer: An R package for bi-level variable selection of high-dimensional longitudinal data

In high-dimensional data analysis, the bi-level (or the sparse group) variable selection can simultaneously conduct penalization on the group level and within groups, which has been developed for continuous, binary, and survival responses in the literature. Zhou et al. (2022) (PMID: 35766061) has further extended it under the longitudinal response by proposing a quadratic inference function-based penalization method in gene–environment interaction studies. This study introduces “springer,” an R package implementing the bi-level variable selection within the QIF framework developed in Zhou et al. (2022). In addition, R package “springer” has also implemented the generalized estimating equation-based sparse group penalization method. Alternative methods focusing only on the group level or individual level have also been provided by the package. In this study, we have systematically introduced the longitudinal penalization methods implemented in the “springer” package. We demonstrate the usage of the core and supporting functions, which is followed by the numerical examples and discussions. R package “springer” is available at https://cran.r-project.org/package=springer.

Interep: An R Package for High-Dimensional Interaction Analysis of the Repeated Measurement Data

We introduce interep, an R package for interaction analysis of repeated measurement data with high-dimensional main and interaction effects. In G × E interaction studies, the forms of environmental factors play a critical role in determining how structured sparsity should be imposed in the high-dimensional scenario to identify important effects. Zhou et al. (2019) (PMID: 31816972) proposed a longitudinal penalization method to select main and interaction effects corresponding to the individual and group structure, respectively, which requires a mixture of individual and group level penalties. The R package interep implements generalized estimating equation (GEE)-based penalization methods with this sparsity assumption. Moreover, alternative methods have also been implemented in the package. These alternative methods merely select effects on an individual level and ignore the group-level interaction structure. In this software article, we first introduce the statistical methodology corresponding to the penalized GEE methods implemented in the package. Next, we present the usage of the core and supporting functions, which is followed by a simulation example with R codes and annotations. The R package interep is available at The Comprehensive R Archive Network (CRAN).

Identifying Gene-Environment Interactions With Robust Marginal Bayesian Variable Selection

In high-throughput genetics studies, an important aim is to identify gene–environment interactions associated with the clinical outcomes. Recently, multiple marginal penalization methods have been developed and shown to be effective in G×E studies. However, within the Bayesian framework, marginal variable selection has not received much attention. In this study, we propose a novel marginal Bayesian variable selection method for G×E studies. In particular, our marginal Bayesian method is robust to data contamination and outliers in the outcome variables. With the incorporation of spike-and-slab priors, we have implemented the Gibbs sampler based on Markov Chain Monte Carlo (MCMC). The proposed method outperforms a number of alternatives in extensive simulation studies. The utility of the marginal robust Bayesian variable selection method has been further demonstrated in the case studies using data from the Nurse Health Study (NHS). Some of the identified main and interaction effects from the real data analysis have important biological implications.

Gene-gene interaction analysis incorporating network information via a structured Bayesian approach

Increasing evidence has shown that gene-gene interactions have important effects in biological processes of human diseases. Due to the high dimensionality of genetic measurements, interaction analysis usually suffers from a lack of sufficient information and has unsatisfactory results. Biological network information has been massively accumulated, allowing researchers to identify biomarkers while taking a system perspective, conducting network selection (of functionally related biomarkers), and accommodating network structures. In main-effect-only analysis, network information has been incorporated. However, effort has been limited in interaction analysis. Recently, link networks that describe the relationships between genetic interactions have been demonstrated as effective for revealing multiscale hierarchical organizations in networks and providing interesting findings beyond node networks. In this study, we develop a novel structured Bayesian interaction analysis approach to effectively incorporate network information. This study is among the first to identify gene-gene interactions with the assistance of network selection, while simultaneously accommodating the underlying network structures of both main effects and interactions. It innovatively respects multiple hierarchies among main effects, interactions, and networks. The Bayesian technique is adopted, which may be more informative for estimation and prediction over some other techniques. An efficient variational Bayesian expectation-maximization algorithm is developed to explore the posterior distribution. Extensive simulation studies demonstrate the practical superiority of the proposed approach. The analysis of TCGA data on melanoma and lung cancer leads to biologically sensible findings with satisfactory prediction accuracy and selection stability.

Bayesian variable selection for understanding mixtures in environmental exposures

Social and environmental stressors are crucial factors in child development. However, there exists a multitude of measurable social and environmental factors-the effects of which may be cumulative, interactive, or null. Using a comprehensive cohort of children in North Carolina, we study the impact of social and environmental variables on 4th end-of-grade exam scores in reading and mathematics. To identify the essential factors that predict these educational outcomes, we design new tools for Bayesian linear variable selection using decision analysis. We extract a predictive optimal subset of explanatory variables by coupling a loss function with a novel model-based penalization scheme, which leads to coherent Bayesian decision analysis and empirically improves variable selection, estimation, and prediction on simulated data. The Bayesian linear model propagates uncertainty quantification to all predictive evaluations, which is important for interpretable and robust model comparisons. These predictive comparisons are conducted out-of-sample with a customized approximation algorithm that avoids computationally intensive model refitting. We apply our variable selection techniques to identify the joint collection of social and environmental stressors-and their interactions-that offer clear and quantifiable improvements in prediction of reading and mathematics exam scores.

GEInter: an R package for robust gene-environment interaction analysis

SUMMARY

For understanding complex diseases, gene-environment (G-E) interactions have important implications beyond main G and E effects. Most of the existing analysis approaches and software packages cannot accommodate data contamination/long-tailed distribution. We develop GEInter, a comprehensive R package tailored to robust G-E interaction analysis. For both marginal and joint analysis, for data without and with missingness, for continuous and censored survival responses, it comprehensively conducts identification, estimation, visualization, and prediction. It can fill an important gap in the existing literature and enjoy broad applicability.

AVAILABILITY AND IMPLEMENTATION

https://cran.r-project.org/web/packages/GEInter/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

EnRank: An Ensemble Method to Detect Pulmonary Hypertension Biomarkers Based on Feature Selection and Machine Learning Models

Pulmonary hypertension (PH) is a common disease that affects the normal functioning of the human pulmonary arteries. The peripheral blood mononuclear cells (PMBCs) served as an ideal source for a minimally invasive disease diagnosis. This study hypothesized that the transcriptional fluctuations in the PMBCs exposed to the PH arteries may stably reflect the disease. However, the dimension of a human transcriptome is much higher than the number of samples in all the existing datasets. So, an ensemble feature selection algorithm, EnRank, was proposed to integrate the ranking information of four popular feature selection algorithms, i.e., T-test (Ttest), Chi-squared test (Chi2), ridge regression (Ridge), and Least Absolute Shrinkage and Selection Operator (Lasso). Our results suggested that the EnRank-detected biomarkers provided useful information from these four feature selection algorithms and achieved very good prediction accuracy in predicting the PH patients. Many of the EnRank-detected biomarkers were also supported by the literature.

The relationship between occupational stress, musculoskeletal disorders and the mental health of coal miners: The interaction between BDNF gene, TPH2 gene polymorphism and the environment

OBJECTIVE

Mental disorders are prevalent among the population and seriously endanger people's working ability as well as their physical and mental health. This study employed stratified cluster random sampling to examine occupational stress, musculoskeletal disorders (MSDs) and the mental health status of 1675 coal miners in Xinjiang.

METHODS

A cross-sectional investigation was carried out, and BDNF (rs6265, rs10835210) gene polymorphism and TPH2(rs4570625, rs4131347) gene polymorphism were identified in 30% of the study's participants. This study aimed to analyze the relationship between mental disorders, occupational stress and MSDs, and to explore the role of gene-gene and gene-environment interactions in respect to the incidence of psychological disorders. On this basis, the risk prediction model of mental disorders was constructed.

RESULTS

The study identified the following risk factors for mental disorders among coal miners: Female, age, four shifts, coal miners, college education or above, single, occupational stress, and MSDs. MSDs, BDNF gene (rs6265) and TPH2 gene (rs4570625) are directly related to mental disorders, and interactions were found between MSDs and BDNF gene (rs6265),TPH2 gene (rs4570625), affecting the incidence of mental disorders. The Bayesian network model of mental disorders showed that MSDs, educational level, TPH2 gene (rs4570625) and marital status had a higher influence on mental disorders. Monthly income and educational level can indirectly affect mental disorders through occupational stress. BDNF gene (rs6265) and TPH2 gene (rs4570625) can indirectly affect mental disorders through MSDs. There may be an interaction between MSDs and educational level.

CONCLUSIONS

Besides demographic characteristics, occupational stress and musculoskeletal disorders are also factors affecting the mental health of coal miners. It was found that BDNF rs10835210, TPH2 rs4570625 and TPH2 rs4131347 interact with each other, increasing the risk of mental disorders among coal miners.

Integrating Multi–Omics Data for Gene-Environment Interactions

Gene-environment (G×E) interaction is critical for understanding the genetic basis of complex disease beyond genetic and environment main effects. In addition to existing tools for interaction studies, penalized variable selection emerges as a promising alternative for dissecting G×E interactions. Despite the success, variable selection is limited in terms of accounting for multidimensional measurements. Published variable selection methods cannot accommodate structured sparsity in the framework of integrating multiomics data for disease outcomes. In this paper, we have developed a novel variable selection method in order to integrate multi-omics measurements in G×E interaction studies. Extensive studies have already revealed that analyzing omics data across multi-platforms is not only sensible biologically, but also resulting in improved identification and prediction performance. Our integrative model can efficiently pinpoint important regulators of gene expressions through sparse dimensionality reduction, and link the disease outcomes to multiple effects in the integrative G×E studies through accommodating a sparse bi-level structure. The simulation studies show the integrative model leads to better identification of G×E interactions and regulators than alternative methods. In two G×E lung cancer studies with high dimensional multi-omics data, the integrative model leads to an improved prediction and findings with important biological implications.

Gene-Environment Interaction: A Variable Selection Perspective

Gene-environment interactions have important implications for elucidating the genetic basis of complex diseases beyond the joint function of multiple genetic factors and their interactions (or epistasis). In the past, G × E interactions have been mainly conducted within the framework of genetic association studies. The high dimensionality of G × E interactions, due to the complicated form of environmental effects and the presence of a large number of genetic factors including gene expressions and SNPs, has motivated the recent development of penalized variable selection methods for dissecting G × E interactions, which has been ignored in the majority of published reviews on genetic interaction studies. In this article, we first survey existing studies on both gene-environment and gene-gene interactions. Then, after a brief introduction to the variable selection methods, we review penalization and relevant variable selection methods in marginal and joint paradigms, respectively, under a variety of conceptual models. Discussions on strengths and limitations, as well as computational aspects of the variable selection methods tailored for G × E studies, have also been provided.

A general index for linear and nonlinear correlations for high dimensional genomic data

BACKGROUND

With the advance of high throughput sequencing, high-dimensional data are generated. Detecting dependence/correlation between these datasets is becoming one of most important issues in multi-dimensional data integration and co-expression network construction. RNA-sequencing data is widely used to construct gene regulatory networks. Such networks could be more accurate when methylation data, copy number aberration data and other types of data are introduced. Consequently, a general index for detecting relationships between high-dimensional data is indispensable.

RESULTS

We proposed a Kernel-Based RV-coefficient, named KBRV, for testing both linear and nonlinear correlation between two matrices by introducing kernel functions into RV2 (the modified RV-coefficient). Permutation test and other validation methods were used on simulated data to test the significance and rationality of KBRV. In order to demonstrate the advantages of KBRV in constructing gene regulatory networks, we applied this index on real datasets (ovarian cancer datasets and exon-level RNA-Seq data in human myeloid differentiation) to illustrate its superiority over vector correlation.

CONCLUSIONS

We concluded that KBRV is an efficient index for detecting both linear and nonlinear relationships in high dimensional data. The correlation method for high dimensional data has possible applications in the construction of gene regulatory network.

Penalized Variable Selection for Lipid-Environment Interactions in a Longitudinal Lipidomics Study

Lipid species are critical components of eukaryotic membranes. They play key roles in many biological processes such as signal transduction, cell homeostasis, and energy storage. Investigations of lipid-environment interactions, in addition to the lipid and environment main effects, have important implications in understanding the lipid metabolism and related changes in phenotype. In this study, we developed a novel penalized variable selection method to identify important lipid-environment interactions in a longitudinal lipidomics study. An efficient Newton-Raphson based algorithm was proposed within the generalized estimating equation (GEE) framework. We conducted extensive simulation studies to demonstrate the superior performance of our method over alternatives, in terms of both identification accuracy and prediction performance. As weight control via dietary calorie restriction and exercise has been demonstrated to prevent cancer in a variety of studies, analysis of the high-dimensional lipid datasets collected using 60 mice from the skin cancer prevention study identified meaningful markers that provide fresh insight into the underlying mechanism of cancer preventive effects.