{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T16:23:12Z","timestamp":1793636592492,"version":"4.5.1"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"9","license":[{"start":{"date-parts":[[2024,9,3]],"date-time":"2024-09-03T00:00:00Z","timestamp":1725321600000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["U24CA231846"],"award-info":[{"award-number":["U24CA231846"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["R35CA220523"],"award-info":[{"award-number":["R35CA220523"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000051","name":"National Human Genome Research Institute","doi-asserted-by":"publisher","award":["R01HG011393"],"award-info":[{"award-number":["R01HG011393"]}],"id":[{"id":"10.13039\/100000051","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Motivation<\/jats:title>\n                    <jats:p>Systems biology analyses often use correlations in gene expression profiles to infer co-expression networks that are then used as input for gene regulatory network inference or to identify functional modules of co-expressed or putatively co-regulated genes. While systematic biases, including batch effects, are known to induce spurious associations and confound differential gene expression analyses (DE), the impact of batch effects on gene co-expression has not been fully explored. Methods have been developed to adjust expression values, ensuring conditional independence of mean and variance from batch or other covariates for each gene, resulting in improved fidelity of DE analysis. However, such adjustments do not address the potential for spurious differential co-expression (DC) between groups. Consequently, uncorrected, artifactual DC can skew the correlation structure, leading to the identification of false, non-biological associations, even when the input data are corrected using standard batch correction.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>In this work, we demonstrate the persistence of confounders in covariance after standard batch correction using synthetic and real-world gene expression data examples. We then introduce Co-expression Batch Reduction Adjustment (COBRA), a method for computing a batch-corrected gene co-expression matrix based on estimating a conditional covariance matrix. COBRA estimates a reduced set of parameters expressing the co-expression matrix as a function of the sample covariates, allowing control for continuous and categorical covariates. COBRA is computationally efficient, leveraging the inherently modular structure of genomic data to estimate accurate gene regulatory associations and facilitate functional analysis for high-dimensional genomic data.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Availability and implementation<\/jats:title>\n                    <jats:p>COBRA is available under the GLP3 open source license in R and Python in netZoo (https:\/\/netzoo.github.io).<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btae531","type":"journal-article","created":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T18:50:12Z","timestamp":1725216612000},"source":"Crossref","is-referenced-by-count":11,"title":["Higher-order correction of persistent batch effects in correlation networks"],"prefix":"10.1093","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5402-9237","authenticated-orcid":false,"given":"Soel","family":"Micheletti","sequence":"first","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5127-4034","authenticated-orcid":false,"given":"Daniel","family":"Schlauch","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115,","place":["United States"]},{"name":"Department of Data Science, Dana-Farber Cancer Institute , Boston, MA 02215,","place":["United States"]},{"name":"Genospace, LLC , Boston, MA 02108,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2702-5879","authenticated-orcid":false,"given":"John","family":"Quackenbush","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115,","place":["United States"]},{"name":"Department of Data Science, Dana-Farber Cancer Institute , Boston, MA 02215,","place":["United States"]},{"name":"Channing Division of Network Medicine, Brigham and Women's Hospital , Boston, MA 02115,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5934-966X","authenticated-orcid":false,"given":"Marouen","family":"Ben Guebila","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Harvard T.H. Chan School of Public Health , Boston, MA 02115,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2024,9,3]]},"reference":[{"key":"2024093015203268200_btae531-B1","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.cell.2014.09.050","article-title":"Integrated genomic characterization of papillary thyroid carcinoma","volume":"159","author":"Agrawal","year":"2014","journal-title":"Cell"},{"key":"2024093015203268200_btae531-B2","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1093\/bioinformatics\/btw695","article-title":"EGAD: ultra-fast functional analysis of gene networks","volume":"33","author":"Ballouz","year":"2017","journal-title":"Bioinformatics"},{"key":"2024093015203268200_btae531-B3","doi-asserted-by":"crossref","first-page":"D610","DOI":"10.1093\/nar\/gkab778","article-title":"GRAND: a database of gene regulatory network models across human conditions","volume":"50","author":"Ben Guebila","year":"2022","journal-title":"Nucleic Acids Res"},{"key":"2024093015203268200_btae531-B4","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1038\/s41592-022-01479-2","article-title":"An online notebook resource for reproducible inference, analysis and publication of gene regulatory networks","volume":"19","author":"Ben Guebila","year":"2022","journal-title":"Nat Methods"},{"key":"2024093015203268200_btae531-B5","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1186\/s13059-023-02877-1","article-title":"The network zoo: a multilingual package for the inference and analysis of gene regulatory networks","volume":"24","author":"Ben Guebila","year":"2023","journal-title":"Genome Biol"},{"key":"2024093015203268200_btae531-B6","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1186\/s12859-015-0745-3","article-title":"Systematic noise degrades gene co-expression signals but can be corrected","volume":"16","author":"Freytag","year":"2015","journal-title":"BMC Bioinformatics"},{"key":"2024093015203268200_btae531-B7","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","article-title":"Sparse inverse covariance estimation with the graphical lasso","volume":"9","author":"Friedman","year":"2008","journal-title":"Biostatistics"},{"key":"2024093015203268200_btae531-B8","doi-asserted-by":"crossref","first-page":"e64832","DOI":"10.1371\/journal.pone.0064832","article-title":"Passing messages between biological networks to refine predicted interactions","volume":"8","author":"Glass","year":"2013","journal-title":"PLoS One"},{"key":"2024093015203268200_btae531-B9","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1093\/biostatistics\/kxj037","article-title":"Adjusting batch effects in microarray expression data using empirical bayes methods","volume":"8","author":"Johnson","year":"2007","journal-title":"Biostatistics"},{"key":"2024093015203268200_btae531-B10","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.isci.2019.03.021","article-title":"Estimating sample-specific regulatory networks","volume":"14","author":"Kuijjer","year":"2019","journal-title":"Iscience"},{"key":"2024093015203268200_btae531-B11","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1186\/1471-2105-9-559","article-title":"WGCNA: an R package for weighted correlation network analysis","volume":"1","author":"Langfelder","year":"2008","journal-title":"BMC Bioinformatics"},{"key":"2024093015203268200_btae531-B12","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1093\/bioinformatics\/bts034","article-title":"The SVA package for removing batch effects and other unwanted variation in high-throughput experiments","volume":"28","author":"Leek","year":"2012","journal-title":"Bioinformatics"},{"key":"2024093015203268200_btae531-B13","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/0-387-21679-0_5","volume-title":"The Analysis of Gene Expression Data: Methods and Software","author":"Li","year":"2003"},{"key":"2024093015203268200_btae531-B14","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1186\/s13059-014-0550-8","article-title":"Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2","volume":"15","author":"Love","year":"2014","journal-title":"Genome Biol"},{"key":"2024093015203268200_btae531-B15","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1038\/nature08872","article-title":"Understanding mechanisms underlying human gene expression variation with RNA sequencing","volume":"464","author":"Pickrell","year":"2010","journal-title":"Nature"},{"key":"2024093015203268200_btae531-B16","doi-asserted-by":"crossref","first-page":"e47","DOI":"10.1093\/nar\/gkv007","article-title":"limma powers differential expression analyses for RNA-sequencing and microarray studies","volume":"43","author":"Ritchie","year":"2015","journal-title":"Nucleic Acids Res"},{"key":"2024093015203268200_btae531-B17","author":"Schafer"},{"key":"2024093015203268200_btae531-B18","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1186\/s12918-017-0517-y","article-title":"Estimating drivers of cell state transitions using gene regulatory network models","volume":"11","author":"Schlauch","year":"2017","journal-title":"BMC Syst Biol"},{"key":"2024093015203268200_btae531-B19","doi-asserted-by":"crossref","first-page":"e15","DOI":"10.1093\/nar\/gkac1157","article-title":"Dragon: determining regulatory associations using graphical models on multi-omic networks","volume":"51","author":"Shutta","year":"2023","journal-title":"Nucleic Acids Res"},{"key":"2024093015203268200_btae531-B20","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1038\/s41592-019-0372-4","article-title":"Evaluating measures of association for single-cell transcriptomics","volume":"16","author":"Skinnider","year":"2019","journal-title":"Nat Methods"},{"key":"2024093015203268200_btae531-B21","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3349\/ymj.2022.63.6.591","article-title":"SOX12 promotes thyroid cancer cell proliferation and invasion by regulating the expression of POU2F1 and POU3F1","volume":"63","author":"Su","year":"2022","journal-title":"Yonsei Med J"},{"key":"2024093015203268200_btae531-B22","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.bbagrm.2016.02.007","article-title":"The Oct1 transcription factor and epithelial malignancies: old protein learns new tricks","volume":"1859","author":"V\u00e1zquez-Arregu\u00edn","year":"2016","journal-title":"Biochim Biophys Acta"},{"key":"2024093015203268200_btae531-B23","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1186\/s13059-021-02533-6","article-title":"recount3: summaries and queries for large-scale RNA-seq expression and splicing","volume":"22","author":"Wilks","year":"2021","journal-title":"Genome Biol"},{"key":"2024093015203268200_btae531-B24","first-page":"100141","article-title":"clusterprofiler 4.0: a universal enrichment tool for interpreting omics data","volume":"2","author":"Wu","year":"2021","journal-title":"Innovation"},{"key":"2024093015203268200_btae531-B25","doi-asserted-by":"crossref","first-page":"lqaa078","DOI":"10.1093\/nargab\/lqaa078","article-title":"ComBat-seq: batch effect adjustment for RNA-seq count data","volume":"2","author":"Zhang","year":"2020","journal-title":"NAR Genom Bioinform"},{"key":"2024093015203268200_btae531-B26","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1080\/01621459.2015.1131699","article-title":"Covariance regression analysis","volume":"112","author":"Zou","year":"2017","journal-title":"J Am Stat Assoc"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/advance-article-pdf\/doi\/10.1093\/bioinformatics\/btae531\/59004813\/btae531.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/40\/9\/btae531\/59459873\/btae531.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/40\/9\/btae531\/59459873\/btae531.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T11:20:52Z","timestamp":1727695252000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/doi\/10.1093\/bioinformatics\/btae531\/7748404"}},"subtitle":[],"editor":[{"given":"Pier Luigi","family":"Martelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":26,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2024,9,2]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btae531","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2023.12.28.573533","asserted-by":"object"}]},"ISSN":["1367-4811"],"issn-type":[{"value":"1367-4811","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2024,9]]},"published":{"date-parts":[[2024,9]]},"article-number":"btae531"}}