1
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Zhou F, Ren J, Ma S, Wu C. The Bayesian Regularized Quantile Varying Coefficient Model. Comput Stat Data Anal 2023; 187:107808. [PMID: 38746689 PMCID: PMC11090482 DOI: 10.1016/j.csda.2023.107808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/19/2024]
Abstract
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.
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Affiliation(s)
- Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, KS
| | - Jie Ren
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN
| | - Shuangge Ma
- Department of Biostatistics, Yale University, New Haven, CT
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS
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2
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Jin X, Shi G. Cauchy combination methods for the detection of gene-environment interactions for rare variants related to quantitative phenotypes. Heredity (Edinb) 2023; 131:241-252. [PMID: 37481617 PMCID: PMC10539363 DOI: 10.1038/s41437-023-00640-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 07/09/2023] [Accepted: 07/12/2023] [Indexed: 07/24/2023] Open
Abstract
The characterization of gene-environment interactions (GEIs) can provide detailed insights into the biological mechanisms underlying complex diseases. Despite recent interest in GEIs for rare variants, published GEI tests are underpowered for an extremely small proportion of causal rare variants in a gene or a region. By extending the aggregated Cauchy association test (ACAT), we propose three GEI tests to address this issue: a Cauchy combination GEI test with fixed main effects (CCGEI-F), a Cauchy combination GEI test with random main effects (CCGEI-R), and an omnibus Cauchy combination GEI test (CCGEI-O). ACAT was applied to combine p values of single-variant GEI analyses to obtain CCGEI-F and CCGEI-R and p values of multiple GEI tests were combined in CCGEI-O. Through numerical simulations, for small numbers of causal variants, CCGEI-F, CCGEI-R and CCGEI-O provided approximately 5% higher power than the existing GEI tests INT-FIX and INT-RAN; however, they had slightly higher power than the existing GEI test TOW-GE. For large numbers of causal variants, although CCGEI-F and CCGEI-R exhibited comparable or slightly lower power values than the competing tests, the results were still satisfactory. Among all simulation conditions evaluated, CCGEI-O provided significantly higher power than that of competing GEI tests. We further applied our GEI tests in genome-wide analyses of systolic blood pressure or diastolic blood pressure to detect gene-body mass index (BMI) interactions, using whole-exome sequencing data from UK Biobank. At a suggestive significance level of 1.0 × 10-4, KCNC4, GAR1, FAM120AOS and NT5C3B showed interactions with BMI by our GEI tests.
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Affiliation(s)
- Xiaoqin Jin
- State Key Laboratory of Integrated Services Networks, Xidian University, 2 South Taibai Road, Xi'an, Shaanxi, 710071, China.
| | - Gang Shi
- State Key Laboratory of Integrated Services Networks, Xidian University, 2 South Taibai Road, Xi'an, Shaanxi, 710071, China
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3
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Zhou F, Liu Y, Ren J, Wang W, Wu C. Springer: An R package for bi-level variable selection of high-dimensional longitudinal data. Front Genet 2023; 14:1088223. [PMID: 37091810 PMCID: PMC10117642 DOI: 10.3389/fgene.2023.1088223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 02/28/2023] [Indexed: 04/09/2023] Open
Abstract
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.
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Affiliation(s)
- Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, KS, United States
| | - Yuwen Liu
- Department of Statistics, Kansas State University, Manhattan, KS, United States
| | - Jie Ren
- Department of Biostatistics and Health Data Sciences, Indiana University School of Medicine, Indianapolis, IN, United States
| | - Weiqun Wang
- Department of Food, Nutrition, Dietetics and Health, Kansas State University, Manhattan, KS, United States
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS, United States
- *Correspondence: Cen Wu,
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4
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Guan S, Zhao M, Cui Y. Variable selection for single-index varying-coefficients models with applications to synergistic G × E interactions. Electron J Stat 2023. [DOI: 10.1214/23-ejs2117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
Affiliation(s)
- Shunjie Guan
- Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA
| | - Mingtao Zhao
- School of Statistics and Applied Mathematics, Anhui University of Finance & Economics, Bengbu, Anhui, 233000, China
| | - Yuehua Cui
- Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA
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5
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Zhou F, Lu X, Ren J, Fan K, Ma S, Wu C. Sparse group variable selection for gene-environment interactions in the longitudinal study. Genet Epidemiol 2022; 46:317-340. [PMID: 35766061 DOI: 10.1002/gepi.22461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Revised: 01/31/2022] [Accepted: 03/15/2022] [Indexed: 11/06/2022]
Abstract
Penalized variable selection for high-dimensional longitudinal data has received much attention as it can account for the correlation among repeated measurements while providing additional and essential information for improved identification and prediction performance. Despite the success, in longitudinal studies, the potential of penalization methods is far from fully understood for accommodating structured sparsity. In this article, we develop a sparse group penalization method to conduct the bi-level gene-environment (G × $\times $ E) interaction study under the repeatedly measured phenotype. Within the quadratic inference function framework, the proposed method can achieve simultaneous identification of main and interaction effects on both the group and individual levels. Simulation studies have shown that the proposed method outperforms major competitors. In the case study of asthma data from the Childhood Asthma Management Program, we conduct G × $\times $ E study by using high-dimensional single nucleotide polymorphism data as genetic factors and the longitudinal trait, forced expiratory volume in 1 s, as the phenotype. Our method leads to improved prediction and identification of main and interaction effects with important implications.
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Affiliation(s)
- Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, Kansas, 66506, USA
| | - Xi Lu
- Department of Statistics, Kansas State University, Manhattan, Kansas, 66506, USA
| | - Jie Ren
- Department of Biostatistics and Health Data Sciences, Indiana University School of Medicine, Indianapolis, Indiana, 46202, USA
| | - Kun Fan
- Department of Statistics, Kansas State University, Manhattan, Kansas, 66506, USA
| | - Shuangge Ma
- Department of Biostatistics, Yale University, New Haven, Connecticut, 06520, USA
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, Kansas, 66506, USA
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6
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Identification of Generators’ Economic Withholding Behavior Based on a SCAD-Logit Model in Electricity Spot Market. ENERGIES 2022. [DOI: 10.3390/en15114135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The effective identification of the economic withholding behavior of the generators can help ensure the fair operation of the electricity market. A SCAD-logit model is proposed to improve the performance of the logit model for the massive data of electricity market. First, a social network analysis method is used to construct an equity relationship graph of the generators to obtain a set of key monitoring generators. An indicator system for identifying the economic withholding behavior of the generators is constructed based on structure conduct performance (SCP) theory. The indicators are screened by the smoothed clipped absolute deviation (SCAD) penalty regression method to reduce the collinearity and improve identification efficiency. Then, a SCAD-logit model is established to identify the economic withholding of key monitoring generators, so that the boundary contributions of each indicator to the economic withholding behavior are obtained. The confusion matrix, ROC curve, and AUC values are used to evaluate the model’s performance. Finally, the model is applied to the electricity spot market, and the method can identify the generators that exercise economic withholding behavior with a correct rate of 96.83%. Indicators such as market share, quotation fluctuation degree, high quotation index, and volume price index can be used as important indicators for identifying the economic withholding behavior.
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7
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Luo Z, Zhang Y, Sun Y. A Penalization Method for Estimating Heterogeneous Covariate Effects in Cancer Genomic Data. Genes (Basel) 2022; 13:genes13040702. [PMID: 35456506 PMCID: PMC9025588 DOI: 10.3390/genes13040702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 04/08/2022] [Accepted: 04/09/2022] [Indexed: 11/16/2022] Open
Abstract
In high-throughput profiling studies, extensive efforts have been devoted to searching for the biomarkers associated with the development and progression of complex diseases. The heterogeneity of covariate effects associated with the outcomes across subjects has been noted in the literature. In this paper, we consider a scenario where the effects of covariates change smoothly across subjects, which are ordered by a known auxiliary variable. To this end, we develop a penalization-based approach, which applies a penalization technique to simultaneously select important covariates and estimate their unique effects on the outcome variables of each subject. We demonstrate that, under the appropriate conditions, our method shows selection and estimation consistency. Additional simulations demonstrate its superiority compared to several competing methods. Furthermore, applying the proposed approach to two The Cancer Genome Atlas datasets leads to better prediction performance and higher selection stability.
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Affiliation(s)
- Ziye Luo
- School of Statistics, Renmin University of China, No. 59 Zhongguancun Street, Beijing 100872, China; (Z.L.); (Y.Z.)
| | - Yuzhao Zhang
- School of Statistics, Renmin University of China, No. 59 Zhongguancun Street, Beijing 100872, China; (Z.L.); (Y.Z.)
| | - Yifan Sun
- Center for Applied Statistics, School of Statistics, Renmin University of China, No. 59 Zhongguancun Street, Beijing 100872, China
- Correspondence:
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8
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Zhou F, Ren J, Liu Y, Li X, Wang W, Wu C. Interep: An R Package for High-Dimensional Interaction Analysis of the Repeated Measurement Data. Genes (Basel) 2022; 13:genes13030544. [PMID: 35328097 PMCID: PMC8950762 DOI: 10.3390/genes13030544] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2022] [Revised: 03/12/2022] [Accepted: 03/13/2022] [Indexed: 02/05/2023] Open
Abstract
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).
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Affiliation(s)
- Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA; (F.Z.); (Y.L.); (X.L.)
| | - Jie Ren
- Department of Biostatistics and Health Data Sciences, Indiana University School of Medicine, Indianapolis, IN 46202, USA;
| | - Yuwen Liu
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA; (F.Z.); (Y.L.); (X.L.)
| | - Xiaoxi Li
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA; (F.Z.); (Y.L.); (X.L.)
| | - Weiqun Wang
- Department of Food, Nutrition, Dietetics and Health, Kansas State University, Manhattan, KS 66506, USA;
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA; (F.Z.); (Y.L.); (X.L.)
- Correspondence: ; Tel.: +1-7855322231
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9
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Lu X, Fan K, Ren J, Wu C. Identifying Gene-Environment Interactions With Robust Marginal Bayesian Variable Selection. Front Genet 2021; 12:667074. [PMID: 34956304 PMCID: PMC8693717 DOI: 10.3389/fgene.2021.667074] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Accepted: 07/13/2021] [Indexed: 01/02/2023] Open
Abstract
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.
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Affiliation(s)
- Xi Lu
- Department of Statistics, Kansas State University, Manhattan, KS, United States
| | - Kun Fan
- Department of Statistics, Kansas State University, Manhattan, KS, United States
| | - Jie Ren
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, United States
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS, United States
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10
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Wang H, Ye M, Fu Y, Dong A, Zhang M, Feng L, Zhu X, Bo W, Jiang L, Griffin CH, Liang D, Wu R. Modeling genome-wide by environment interactions through omnigenic interactome networks. Cell Rep 2021; 35:109114. [PMID: 33979624 DOI: 10.1016/j.celrep.2021.109114] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Revised: 03/11/2021] [Accepted: 04/21/2021] [Indexed: 10/21/2022] Open
Abstract
How genes interact with the environment to shape phenotypic variation and evolution is a fundamental question intriguing to biologists from various fields. Existing linear models built on single genes are inadequate to reveal the complexity of genotype-environment (G-E) interactions. Here, we develop a conceptual model for mechanistically dissecting G-E interplay by integrating previously disconnected theories and methods. Under this integration, evolutionary game theory, developmental modularity theory, and a variable selection method allow us to reconstruct environment-induced, maximally informative, sparse, and casual multilayer genetic networks. We design and conduct two mapping experiments by using a desert-adapted tree species to validate the biological application of the model proposed. The model identifies previously uncharacterized molecular mechanisms that mediate trees' response to saline stress. Our model provides a tool to comprehend the genetic architecture of trait variation and evolution and trace the information flow of each gene toward phenotypes within omnigenic networks.
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Affiliation(s)
- Haojie Wang
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Meixia Ye
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Yaru Fu
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Ang Dong
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Miaomiao Zhang
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Li Feng
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Xuli Zhu
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Wenhao Bo
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Libo Jiang
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Christopher H Griffin
- Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802, USA
| | - Dan Liang
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China
| | - Rongling Wu
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, College of Biological Sciences and Technology, Beijing Forestry University, Beijing 100083, China; Center for Statistical Genetics, Departments of Public Health Sciences and Statistics, The Pennsylvania State University, Hershey, PA 17033, USA.
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11
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Du Y, Fan K, Lu X, Wu C. Integrating Multi–Omics Data for Gene-Environment Interactions. BIOTECH 2021; 10:biotech10010003. [PMID: 35822775 PMCID: PMC9245467 DOI: 10.3390/biotech10010003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Revised: 01/22/2021] [Accepted: 01/22/2021] [Indexed: 01/05/2023] Open
Abstract
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.
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12
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Zhou F, Ren J, Lu X, Ma S, Wu C. Gene-Environment Interaction: A Variable Selection Perspective. Methods Mol Biol 2021; 2212:191-223. [PMID: 33733358 DOI: 10.1007/978-1-0716-0947-7_13] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
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.
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Affiliation(s)
- Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, KS, USA
| | - Jie Ren
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, USA
| | - Xi Lu
- Department of Statistics, Kansas State University, Manhattan, KS, USA
| | - Shuangge Ma
- Department of Biostatistics, School of Public Health, Yale University, New Haven, CT, USA
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS, USA.
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13
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Yao Z, Zhang J, Zou X. A general index for linear and nonlinear correlations for high dimensional genomic data. BMC Genomics 2020; 21:846. [PMID: 33256599 PMCID: PMC7706065 DOI: 10.1186/s12864-020-07246-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 11/18/2020] [Indexed: 01/23/2023] Open
Abstract
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.
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Affiliation(s)
- Zhihao Yao
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 China
- Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072 China
| | - Jing Zhang
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 China
- Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072 China
| | - Xiufen Zou
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 China
- Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072 China
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14
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Lai P, Wang F, Zhu T, Zhang Q. Model identification and selection for single-index varying-coefficient models. ANN I STAT MATH 2020. [DOI: 10.1007/s10463-020-00757-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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15
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Ren J, Zhou F, Li X, Chen Q, Zhang H, Ma S, Jiang Y, Wu C. Semiparametric Bayesian variable selection for gene-environment interactions. Stat Med 2020; 39:617-638. [PMID: 31863500 PMCID: PMC7467082 DOI: 10.1002/sim.8434] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2019] [Revised: 09/26/2019] [Accepted: 11/02/2019] [Indexed: 11/06/2022]
Abstract
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.
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Affiliation(s)
- Jie Ren
- Department of Statistics, Kansas State University, Manhattan, Kansas
| | - Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, Kansas
| | - Xiaoxi Li
- Department of Statistics, Kansas State University, Manhattan, Kansas
| | - Qi Chen
- Department of Pharmacology, Toxicology and Therapeutics, University of Kansas Medical Center, Kansas City, Kansas
| | - Hongmei Zhang
- Division of Epidemiology, Biostatistics and Environmental Health, School of Public Health, University of Memphis, Memphis, Tennessee
| | - Shuangge Ma
- Department of Biostatistics, Yale University, New Haven, Connecticut
| | - Yu Jiang
- Division of Epidemiology, Biostatistics and Environmental Health, School of Public Health, University of Memphis, Memphis, Tennessee
| | - Cen Wu
- Department of Statistics, Kansas State University, Manhattan, Kansas
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16
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Penalized Variable Selection for Lipid-Environment Interactions in a Longitudinal Lipidomics Study. Genes (Basel) 2019; 10:genes10121002. [PMID: 31816972 PMCID: PMC6947406 DOI: 10.3390/genes10121002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 11/26/2019] [Indexed: 12/20/2022] Open
Abstract
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.
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Li Y, Li R, Lin C, Qin Y, Ma S. Penalized integrative semiparametric interaction analysis for multiple genetic datasets. Stat Med 2019; 38:3221-3242. [PMID: 30993736 DOI: 10.1002/sim.8172] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2018] [Revised: 02/08/2019] [Accepted: 03/27/2019] [Indexed: 12/19/2022]
Abstract
In this article, we consider a semiparametric additive partially linear interaction model for the integrative analysis of multiple genetic datasets. The goals are to identify important genetic predictors and gene-gene interactions and to estimate the nonparametric functions that describe the environmental effects at the same time. To find the similarities and differences of the genetic effects across different datasets, we impose a group structure on the regression coefficients matrix under the homogeneity assumption, ie, models for different datasets share the same sparsity structure, but the coefficients may differ across datasets. We develop an iterative approach to estimate the parameters of main effects, interactions and nonparametric functions, where a reparametrization of interaction parameters is implemented to meet the strong hierarchy assumption. We demonstrate the advantages of the proposed method in identification, estimation, and prediction in a series of numerical studies. We also apply the proposed method to the Skin Cutaneous Melanoma data and the lung cancer data from the Cancer Genome Atlas.
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Affiliation(s)
- Yang Li
- Center for Applied Statistics, Renmin University of China, Beijing, China.,School of Statistics, Renmin University of China, Beijing, China.,Statistical Consulting Center, Renmin University of China, Beijing, China
| | - Rong Li
- School of Statistics, Renmin University of China, Beijing, China.,Statistical Consulting Center, Renmin University of China, Beijing, China
| | - Cunjie Lin
- Center for Applied Statistics, Renmin University of China, Beijing, China.,School of Statistics, Renmin University of China, Beijing, China.,Statistical Consulting Center, Renmin University of China, Beijing, China
| | - Yichen Qin
- Department of Operations, Business Analytics and Information Systems, University of Cincinnati, Cincinatti, Ohio
| | - Shuangge Ma
- School of Statistics, Renmin University of China, Beijing, China.,Department of Biostatistics, Yale University, New Haven, Connecticut
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Wu C, Zhou F, Ren J, Li X, Jiang Y, Ma S. A Selective Review of Multi-Level Omics Data Integration Using Variable Selection. High Throughput 2019; 8:E4. [PMID: 30669303 PMCID: PMC6473252 DOI: 10.3390/ht8010004] [Citation(s) in RCA: 114] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Revised: 12/24/2018] [Accepted: 01/10/2019] [Indexed: 01/02/2023] Open
Abstract
High-throughput technologies have been used to generate a large amount of omics data. In the past, single-level analysis has been extensively conducted where the omics measurements at different levels, including mRNA, microRNA, CNV and DNA methylation, are analyzed separately. As the molecular complexity of disease etiology exists at all different levels, integrative analysis offers an effective way to borrow strength across multi-level omics data and can be more powerful than single level analysis. In this article, we focus on reviewing existing multi-omics integration studies by paying special attention to variable selection methods. We first summarize published reviews on integrating multi-level omics data. Next, after a brief overview on variable selection methods, we review existing supervised, semi-supervised and unsupervised integrative analyses within parallel and hierarchical integration studies, respectively. The strength and limitations of the methods are discussed in detail. No existing integration method can dominate the rest. The computation aspects are also investigated. The review concludes with possible limitations and future directions for multi-level omics data integration.
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Affiliation(s)
- Cen Wu
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA.
| | - Fei Zhou
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA.
| | - Jie Ren
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA.
| | - Xiaoxi Li
- Department of Statistics, Kansas State University, Manhattan, KS 66506, USA.
| | - Yu Jiang
- Division of Epidemiology, Biostatistics and Environmental Health, School of Public Health, University of Memphis, Memphis, TN 38152, USA.
| | - Shuangge Ma
- Department of Biostatistics, School of Public Health, Yale University, New Haven, CT 06510, USA.
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