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Gamarnik D, Zadik I. Sparse high-dimensional linear regression. Estimating squared error and a phase transition. Ann Stat 2022. [DOI: 10.1214/21-aos2130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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2
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Savino A, Provero P, Poli V. Differential Co-Expression Analyses Allow the Identification of Critical Signalling Pathways Altered during Tumour Transformation and Progression. Int J Mol Sci 2020; 21:E9461. [PMID: 33322692 PMCID: PMC7764314 DOI: 10.3390/ijms21249461] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Revised: 12/02/2020] [Accepted: 12/09/2020] [Indexed: 02/02/2023] Open
Abstract
Biological systems respond to perturbations through the rewiring of molecular interactions, organised in gene regulatory networks (GRNs). Among these, the increasingly high availability of transcriptomic data makes gene co-expression networks the most exploited ones. Differential co-expression networks are useful tools to identify changes in response to an external perturbation, such as mutations predisposing to cancer development, and leading to changes in the activity of gene expression regulators or signalling. They can help explain the robustness of cancer cells to perturbations and identify promising candidates for targeted therapy, moreover providing higher specificity with respect to standard co-expression methods. Here, we comprehensively review the literature about the methods developed to assess differential co-expression and their applications to cancer biology. Via the comparison of normal and diseased conditions and of different tumour stages, studies based on these methods led to the definition of pathways involved in gene network reorganisation upon oncogenes' mutations and tumour progression, often converging on immune system signalling. A relevant implementation still lagging behind is the integration of different data types, which would greatly improve network interpretability. Most importantly, performance and predictivity evaluation of the large variety of mathematical models proposed would urgently require experimental validations and systematic comparisons. We believe that future work on differential gene co-expression networks, complemented with additional omics data and experimentally tested, will considerably improve our insights into the biology of tumours.
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Affiliation(s)
- Aurora Savino
- Molecular Biotechnology Center, Department of Molecular Biotechnology and Health Sciences, University of Turin, Via Nizza 52, 10126 Turin, Italy
| | - Paolo Provero
- Department of Neurosciences “Rita Levi Montalcini”, University of Turin, Corso Massimo D’Ázeglio 52, 10126 Turin, Italy;
- Center for Omics Sciences, Ospedale San Raffaele IRCCS, Via Olgettina 60, 20132 Milan, Italy
| | - Valeria Poli
- Molecular Biotechnology Center, Department of Molecular Biotechnology and Health Sciences, University of Turin, Via Nizza 52, 10126 Turin, Italy
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3
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Zhou Y. Set-based differential covariance testing for genomics. Stat (Int Stat Inst) 2019; 8:e235. [PMID: 31763041 PMCID: PMC6853199 DOI: 10.1002/sta4.235] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Accepted: 04/25/2019] [Indexed: 01/08/2023]
Abstract
The problem of detecting the changes in covariance for a single pair of genomic features has been studied in some detail but may be limited in importance or general applicability. For testing equality of covariance matrices of a set of features, many methods have been limited to the two-sample problem and involve varying assumptions on the number of features p versus the sample size n. More general covariance regression approaches are appealing but have been insufficiently structured to provide interpretable testing. To address these deficiencies, we propose a simple uniform framework to test association of covariance matrices with an experimental variable, whether discrete or continuous. We describe four different summary statistics, to ensure power and flexibility under various alternatives, including a new "connectivity" statistic that is sensitive to the changes in overall covariance magnitude. For continuous experimental variables, a natural individual "risk score" is associated with several of the statistics. We establish asymptotic results applicable to both continuous and discrete responses, with relatively mild conditions and allowing for situations where p>n. We also show that the proposed statistics are permutationally equivalent to some existing methods in the two-sample special case. We demonstrate the power and utility of our approaches via simulation and analysis of real data. The R package CorDiff is published on R CRAN.
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Affiliation(s)
- Yi‐Hui Zhou
- Department of Biological Sciences and Bioinformatics Research CenterNorth Carolina State UniversityRaleigh27695North CarolinaUSA
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4
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Zhou C, Han F, Zhang XS, Liu H. An extreme-value approach for testing the equality of large U-statistic based correlation matrices. BERNOULLI 2019. [DOI: 10.3150/18-bej1027] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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5
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Bodwin BK, Zhang K, Nobel A. A TESTING BASED APPROACH TO THE DISCOVERY OF DIFFERENTIALLY CORRELATED VARIABLE SETS. Ann Appl Stat 2018; 12:1180-1203. [PMID: 31871518 PMCID: PMC6927674 DOI: 10.1214/17-aoas1083] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
Given data obtained under two sampling conditions, it is often of interest to identify variables that behave differently in one condition than in the other. We introduce a method for differential analysis of second-order behavior called Differential Correlation Mining (DCM). The DCM method identifies differentially correlated sets of variables, with the property that the average pairwise correlation between variables in a set is higher under one sample condition than the other. DCM is based on an iterative search procedure that adaptively updates the size and elements of a candidate variable set. Updates are performed via hypothesis testing of individual variables, based on the asymptotic distribution of their average differential correlation. We investigate the performance of DCM by applying it to simulated data as well as to recent experimental datasets in genomics and brain imaging.
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Affiliation(s)
| | - Kai Zhang
- The University of North Carolina at Chapel Hill
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6
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Feature selection method based on support vector machine and shape analysis for high-throughput medical data. Comput Biol Med 2017; 91:103-111. [PMID: 29049908 DOI: 10.1016/j.compbiomed.2017.10.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Revised: 09/24/2017] [Accepted: 10/08/2017] [Indexed: 12/12/2022]
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7
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Xia Y. Testing and support recovery of multiple high-dimensional covariance matrices with false discovery rate control. TEST-SPAIN 2017. [DOI: 10.1007/s11749-017-0533-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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8
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Sheng E, Witten D, Zhou XH. Hypothesis testing for differentially correlated features. Biostatistics 2016; 17:677-91. [PMID: 27044327 DOI: 10.1093/biostatistics/kxw013] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2014] [Accepted: 01/12/2016] [Indexed: 11/12/2022] Open
Abstract
In a multivariate setting, we consider the task of identifying features whose correlations with the other features differ across conditions. Such correlation shifts may occur independently of mean shifts, or differences in the means of the individual features across conditions. Previous approaches for detecting correlation shifts consider features simultaneously, by computing a correlation-based test statistic for each feature. However, since correlations involve two features, such approaches do not lend themselves to identifying which feature is the culprit. In this article, we instead consider a serial testing approach, by comparing columns of the sample correlation matrix across two conditions, and removing one feature at a time. Our method provides a novel perspective and favorable empirical results compared with competing approaches.
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Affiliation(s)
- Elisa Sheng
- Department of Biostatistics, University of Washington, Seattle, WA, USA
| | - Daniela Witten
- Department of Biostatistics, University of Washington, Seattle, Washington, USA and Department of Statistics, University of Washington, Seattle, Washington, USA
| | - Xiao-Hua Zhou
- Department of Biostatistics, University of Washington, Seattle, Washington, USA and Veterans Affairs Seattle Medical Center, Seattle, Washington, USA
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9
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Qiu X, Hu R, Wu Z. Evaluation of bias-variance trade-off for commonly used post-summarizing normalization procedures in large-scale gene expression studies. PLoS One 2014; 9:e99380. [PMID: 24941114 PMCID: PMC4062409 DOI: 10.1371/journal.pone.0099380] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Accepted: 05/12/2014] [Indexed: 11/26/2022] Open
Abstract
Normalization procedures are widely used in high-throughput genomic data analyses to remove various technological noise and variations. They are known to have profound impact to the subsequent gene differential expression analysis. Although there has been some research in evaluating different normalization procedures, few attempts have been made to systematically evaluate the gene detection performances of normalization procedures from the bias-variance trade-off point of view, especially with strong gene differentiation effects and large sample size. In this paper, we conduct a thorough study to evaluate the effects of normalization procedures combined with several commonly used statistical tests and MTPs under different configurations of effect size and sample size. We conduct theoretical evaluation based on a random effect model, as well as simulation and biological data analyses to verify the results. Based on our findings, we provide some practical guidance for selecting a suitable normalization procedure under different scenarios.
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Affiliation(s)
- Xing Qiu
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, United States of America
- * E-mail:
| | - Rui Hu
- Department of Biostatistics and Computational Biology, University of Rochester, Rochester, New York, United States of America
| | - Zhixin Wu
- Math Department, DePauw University, Greencastle, Indiana, United States of America
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Hardin J, Garcia SR, Golan D. A method for generating realistic correlation matrices. Ann Appl Stat 2013. [DOI: 10.1214/13-aoas638] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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11
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Cai T, Liu W, Xia Y. Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings. J Am Stat Assoc 2013. [DOI: 10.1080/01621459.2012.758041] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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12
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Wu S, Wu H. More powerful significant testing for time course gene expression data using functional principal component analysis approaches. BMC Bioinformatics 2013; 14:6. [PMID: 23323795 PMCID: PMC3617096 DOI: 10.1186/1471-2105-14-6] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2012] [Accepted: 11/07/2012] [Indexed: 11/24/2022] Open
Abstract
BACKGROUND One of the fundamental problems in time course gene expression data analysis is to identify genes associated with a biological process or a particular stimulus of interest, like a treatment or virus infection. Most of the existing methods for this problem are designed for data with longitudinal replicates. But in reality, many time course gene experiments have no replicates or only have a small number of independent replicates. RESULTS We focus on the case without replicates and propose a new method for identifying differentially expressed genes by incorporating the functional principal component analysis (FPCA) into a hypothesis testing framework. The data-driven eigenfunctions allow a flexible and parsimonious representation of time course gene expression trajectories, leaving more degrees of freedom for the inference compared to that using a prespecified basis. Moreover, the information of all genes is borrowed for individual gene inferences. CONCLUSION The proposed approach turns out to be more powerful in identifying time course differentially expressed genes compared to the existing methods. The improved performance is demonstrated through simulation studies and a real data application to the Saccharomyces cerevisiae cell cycle data.
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Affiliation(s)
- Shuang Wu
- Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Avenue, Rochester, NY, 14642, USA
| | - Hulin Wu
- Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Avenue, Rochester, NY, 14642, USA
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Exploiting identifiability and intergene correlation for improved detection of differential expression. ISRN BIOINFORMATICS 2013; 2013:404717. [PMID: 25937946 PMCID: PMC4393076 DOI: 10.1155/2013/404717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/13/2012] [Accepted: 11/19/2012] [Indexed: 11/23/2022]
Abstract
Accurate differential analysis of microarray data strongly depends on effective treatment of intergene correlation. Such dependence is ordinarily accounted for in terms of its effect on significance cutoffs. In this paper, it is shown that correlation can, in fact, be exploited to share information across tests and reorder expression differentials for increased statistical power, regardless of the threshold. Significantly improved differential analysis is the result of two simple measures: (i) adjusting test statistics to exploit information from identifiable genes (the large subset of genes represented on a microarray that can be classified a priori as nondifferential with very high confidence], but (ii) doing so in a way that accounts for linear dependencies among identifiable and nonidentifiable genes. A method is developed that builds upon the widely used two-sample t-statistic approach and uses analysis in Hilbert space to decompose the nonidentified gene vector into two components that are correlated and uncorrelated with the identified set. In the application to data derived from a widely studied prostate cancer database, the proposed method outperforms some of the most highly regarded approaches published to date. Algorithms in MATLAB and in R are available for public download.
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14
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Zhang JG, Li J, Tang W, Deng HW. Fusing Gene Interaction to Improve Disease Discrimination on Classification Analysis. ADVANCES IN GENETICS 2012; 1:1000102. [PMID: 23814698 DOI: 10.4172/age.1000102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
It is usually observed that among genes there exist strong statistical interactions associated with diseases of public health importance. Gene interactions can potentially contribute to the improvement of disease classification accuracy. Especially when gene expression differs across different classes are not great enough, it is more important to take use of gene interactions for disease classification analyses. However, most gene selection algorithms in classification analyses merely focus on genes whose expression levels show differences across classes, and ignore the discriminatory information from gene interactions. In this study, we develop a two-stage algorithm that can take gene interaction into account during a gene selection procedure. Its biggest advantage is that it can take advantage of discriminatory information from gene interactions as well as gene expression differences, by using "Bayes error" as a gene selection criterion. Using simulated and real microarray data sets, we demonstrate the ability of gene interactions for classification accuracy improvement, and present that the proposed algorithm can yield small informative sets of genes while leading to highly accurate classification results. Thus our study may give a novel sight for future gene selection algorithms of human diseases discrimination.
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Affiliation(s)
- Ji-Gang Zhang
- Center for Bioinformatics and Genomics, Department of Biostatistics and Bioinformatics, School of Public Health and Tropical Medicine, Tulane University, USA
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15
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Deller JR, Radha H, McCormick JJ, Wang H. Nonlinear dependence in the discovery of differentially expressed genes. ISRN BIOINFORMATICS 2012; 2012:564715. [PMID: 25937940 PMCID: PMC4393074 DOI: 10.5402/2012/564715] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/16/2011] [Accepted: 11/09/2011] [Indexed: 11/23/2022]
Abstract
Microarray data are used to determine which genes are active in response to a changing cell environment. Genes are “discovered” when they are significantly differentially expressed in the microarray data collected under the differing conditions. In one prevalent approach, all genes are assumed to satisfy a null hypothesis, ℍ0, of no difference in expression. A false discovery (type
1 error) occurs when ℍ0 is incorrectly rejected. The quality of a detection algorithm is assessed by estimating its number of false
discoveries, 𝔉. Work involving the second-moment modeling of the z-value histogram (representing gene expression differentials) has
shown significantly deleterious effects of intergene expression correlation on the estimate of 𝔉. This paper suggests that nonlinear
dependencies could likewise be important. With an applied emphasis, this paper extends the “moment framework” by including
third-moment skewness corrections in an estimator of 𝔉. This estimator combines observed correlation (corrected for sampling
fluctuations) with the information from easily identifiable null cases. Nonlinear-dependence modeling reduces the estimation error
relative to that of linear estimation. Third-moment calculations involve empirical densities of 3 × 3 covariance matrices estimated using very few samples. The principle of entropy maximization is employed to connect estimated moments to 𝔉 inference. Model results are tested with BRCA and HIV data sets and with carefully constructed simulations.
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Affiliation(s)
- J R Deller
- Department of Electrical and Computer Engineering, Michigan State University, 2120 EB, East Lansing, MI 48824, USA
| | - Hayder Radha
- Department of Electrical and Computer Engineering, Michigan State University, 2120 EB, East Lansing, MI 48824, USA
| | - J Justin McCormick
- Carcinogenesis Laboratory, Department of Molecular Biology and Biochemistry, Michigan State University, 341 FST, East Lansing, MI 48824, USA
| | - Huiyan Wang
- College of Computer Science and Information Engineering, Zhejiang Gongshang University, 18 Xuezheng Street, Zhejiang Province Hangzhou, 310018, China
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16
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Dawson JA, Kendziorski C. An empirical Bayesian approach for identifying differential coexpression in high-throughput experiments. Biometrics 2011; 68:455-65. [PMID: 22004327 DOI: 10.1111/j.1541-0420.2011.01688.x] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A common goal of microarray and related high-throughput genomic experiments is to identify genes that vary across biological condition. Most often this is accomplished by identifying genes with changes in mean expression level, so called differentially expressed (DE) genes, and a number of effective methods for identifying DE genes have been developed. Although useful, these approaches do not accommodate other types of differential regulation. An important example concerns differential coexpression (DC). Investigations of this class of genes are hampered by the large cardinality of the space to be interrogated as well as by influential outliers. As a result, existing DC approaches are often underpowered, exceedingly prone to false discoveries, and/or computationally intractable for even a moderately large number of pairs. To address this, an empirical Bayesian approach for identifying DC gene pairs is developed. The approach provides a false discovery rate controlled list of significant DC gene pairs without sacrificing power. It is applicable within a single study as well as across multiple studies. Computations are greatly facilitated by a modification to the expectation-maximization algorithm and a procedural heuristic. Simulations suggest that the proposed approach outperforms existing methods in far less computational time; and case study results suggest that the approach will likely prove to be a useful complement to current DE methods in high-throughput genomic studies.
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Affiliation(s)
- John A Dawson
- Department of Statistics, University of Wisconsin, Madison, Wisconsin 53706, USA
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Needham M, Hu R, Dwarkadas S, Qiu X. Hierarchical parallelization of gene differential association analysis. BMC Bioinformatics 2011; 12:374. [PMID: 21936916 PMCID: PMC3248234 DOI: 10.1186/1471-2105-12-374] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2011] [Accepted: 09/21/2011] [Indexed: 01/24/2023] Open
Abstract
Background Microarray gene differential expression analysis is a widely used technique that deals with high dimensional data and is computationally intensive for permutation-based procedures. Microarray gene differential association analysis is even more computationally demanding and must take advantage of multicore computing technology, which is the driving force behind increasing compute power in recent years. In this paper, we present a two-layer hierarchical parallel implementation of gene differential association analysis. It takes advantage of both fine- and coarse-grain (with granularity defined by the frequency of communication) parallelism in order to effectively leverage the non-uniform nature of parallel processing available in the cutting-edge systems of today. Results Our results show that this hierarchical strategy matches data sharing behavior to the properties of the underlying hardware, thereby reducing the memory and bandwidth needs of the application. The resulting improved efficiency reduces computation time and allows the gene differential association analysis code to scale its execution with the number of processors. The code and biological data used in this study are downloadable from http://www.urmc.rochester.edu/biostat/people/faculty/hu.cfm. Conclusions The performance sweet spot occurs when using a number of threads per MPI process that allows the working sets of the corresponding MPI processes running on the multicore to fit within the machine cache. Hence, we suggest that practitioners follow this principle in selecting the appropriate number of MPI processes and threads within each MPI process for their cluster configurations. We believe that the principles of this hierarchical approach to parallelization can be utilized in the parallelization of other computationally demanding kernels.
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Affiliation(s)
- Mark Needham
- Department of Computer Science, University of Rochester, New York 14627, USA
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