{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:26:59Z","timestamp":1787020019916,"version":"build-2736575974"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T00:00:00Z","timestamp":1707091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Controlling the False Discovery Rate (FDR) in Multiple Comparison Procedures (MCPs) has widespread applications in many scientific fields. Previous studies show that the correlation structure between test statistics increases the variance and bias of FDR. The objective of this study is to modify the effect of correlation in MCPs based on the information theory. We proposed three modified procedures (M1, M2, and M3) under strong, moderate, and mild assumptions based on the conditional Fisher Information of the consecutive sorted test statistics for controlling the false discovery rate under arbitrary correlation structure. The performance of the proposed procedures was compared with the Benjamini\u2013Hochberg (BH) and Benjamini\u2013Yekutieli (BY) procedures in simulation study and real high-dimensional data of colorectal cancer gene expressions. In the simulation study, we generated 1000 differential multivariate Gaussian features with different levels of the correlation structure and screened the significance features by the FDR controlling procedures, with strong control on the Family Wise Error Rates.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>When there was no correlation between 1000 simulated features, the performance of the BH procedure was similar to the three proposed procedures. In low to medium correlation structures the BY procedure is too conservative. The BH procedure is too liberal, and the mean number of screened features was constant at the different levels of the correlation between features. The mean number of screened features by proposed procedures was between BY and BH procedures and reduced when the correlations increased. Where the features are highly correlated the number of screened features by proposed procedures reached the Bonferroni (BF) procedure, as expected. In real data analysis the BY, BH, M1, M2, and M3 procedures were done to screen gene expressions of colorectal cancer. To fit a predictive model based on the screened features the Efficient Bayesian Logistic Regression (EBLR) model was used. The fitted EBLR models based on the screened features by M1 and M2 procedures have minimum entropies and are more efficient than BY and BH procedures.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>The modified proposed procedures based on information theory, are much more flexible than BH and BY procedures for the amount of correlation between test statistics. The modified procedures avoided screening the non-informative features and so the number of screened features reduced with the increase in the level of correlation.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s12859-024-05678-w","type":"journal-article","created":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T01:02:24Z","timestamp":1707094944000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modifying the false discovery rate procedure based on the information theory under arbitrary correlation structure and its performance in high-dimensional genomic data"],"prefix":"10.1186","volume":"25","author":[{"given":"Sedighe","family":"Rastaghi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Azadeh","family":"Saki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hamed","family":"Tabesh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,2,5]]},"reference":[{"issue":"1","key":"5678_CR1","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1111\/j.1467-9868.2004.00439.x","volume":"66","author":"JD Storey","year":"2004","unstructured":"Storey JD, Taylor JE, Siegmund D. Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach. J Roy Stat Soc B. 2004;66(1):187\u2013205.","journal-title":"J Roy Stat Soc B"},{"issue":"1","key":"5678_CR2","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1111\/j.2517-6161.1995.tb02031.x","volume":"57","author":"Y Benjamini","year":"1995","unstructured":"Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J R Stat Soc Ser B (Methodol). 1995;57(1):289\u2013300.","journal-title":"J R Stat Soc Ser B (Methodol)"},{"issue":"4","key":"5678_CR3","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/j.ygeno.2005.06.007","volume":"86","author":"H-R Qian","year":"2005","unstructured":"Qian H-R, Huang S. Comparison of false discovery rate methods in identifying genes with differential expression. Genomics. 2005;86(4):495\u2013503.","journal-title":"Genomics"},{"issue":"4","key":"5678_CR4","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1214\/aos\/1013699998","volume":"29","author":"Y Benjamini","year":"2001","unstructured":"Benjamini Y, Yekutieli D. The control of the false discovery rate in multiple testing under dependency. Ann Stat. 2001;29(4):1165\u201388.","journal-title":"Ann Stat"},{"issue":"499","key":"5678_CR5","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1080\/01621459.2012.720478","volume":"107","author":"J Fan","year":"2012","unstructured":"Fan J, Han X, Gu W. Estimating false discovery proportion under arbitrary covariance dependence. J Am Stat Assoc. 2012;107(499):1019\u201335.","journal-title":"J Am Stat Assoc"},{"issue":"4","key":"5678_CR6","doi-asserted-by":"publisher","first-page":"1143","DOI":"10.1111\/rssb.12204","volume":"79","author":"J Fan","year":"2017","unstructured":"Fan J, Han X. Estimation of the false discovery proportion with unknown dependence. J R Stat Soc Ser B (Stat Methodol). 2017;79(4):1143\u201364.","journal-title":"J R Stat Soc Ser B (Stat Methodol)"},{"issue":"13","key":"5678_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-13-S13-S1","volume":"13","author":"J Zhang","year":"2012","unstructured":"Zhang J, Coombes KR. Sources of variation in false discovery rate estimation include sample size, correlation, and inherent differences between groups. BMC Bioinf. 2012;13(13):1\u201311.","journal-title":"BMC Bioinf"},{"issue":"1","key":"5678_CR8","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1093\/biomet\/asq075","volume":"98","author":"A Schwartzman","year":"2011","unstructured":"Schwartzman A, Lin X. The effect of correlation in false discovery rate estimation. Biometrika. 2011;98(1):199\u2013214.","journal-title":"Biometrika"},{"key":"5678_CR9","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.csda.2019.01.009","volume":"136","author":"X Wang","year":"2019","unstructured":"Wang X, Shojaie A, Zou J. Bayesian hidden Markov models for dependent large-scale multiple testing. Comput Stat Data Anal. 2019;136:123\u201336.","journal-title":"Comput Stat Data Anal"},{"issue":"2","key":"5678_CR10","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1111\/j.1467-9868.2008.00694.x","volume":"71","author":"W Sun","year":"2009","unstructured":"Sun W, Tony Cai T. Large-scale multiple testing under dependence. J R Stat Soc Ser B. 2009;71(2):393\u2013424.","journal-title":"J R Stat Soc Ser B"},{"issue":"477","key":"5678_CR11","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1198\/016214506000001211","volume":"102","author":"B Efron","year":"2007","unstructured":"Efron B. Correlation and large-scale simultaneous significance testing. J Am Stat Assoc. 2007;102(477):93\u2013103.","journal-title":"J Am Stat Assoc"},{"issue":"3","key":"5678_CR12","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/j.1467-9868.2005.00509.x","volume":"67","author":"AB Owen","year":"2005","unstructured":"Owen AB. Variance of the number of false discoveries. J R Stat Soc B. 2005;67(3):411\u201326.","journal-title":"J R Stat Soc B"},{"issue":"05","key":"5678_CR13","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1142\/S0219720006002338","volume":"4","author":"X Qiu","year":"2006","unstructured":"Qiu X, Yakovlev A. Some comments on instability of false discovery rate estimation. J Bioinf Comput Biol. 2006;4(05):1057\u201368.","journal-title":"J Bioinf Comput Biol"},{"issue":"1","key":"5678_CR14","first-page":"1","volume":"4","author":"X Qiu","year":"2005","unstructured":"Qiu X, Klebanov L, Yakovlev A. Correlation between gene expression levels and limitations of the empirical Bayes methodology for finding differentially expressed genes. J Bioinf Mol Biol. 2005;4(1):1.","journal-title":"J Bioinf Mol Biol"},{"issue":"1","key":"5678_CR15","doi-asserted-by":"publisher","first-page":"332","DOI":"10.1214\/07-AOS557","volume":"37","author":"S Clarke","year":"2009","unstructured":"Clarke S, Hall P. Robustness of multiple testing procedures against dependence. Ann Stat. 2009;37(1):332\u201358.","journal-title":"Ann Stat"},{"issue":"1","key":"5678_CR16","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1214\/009053607000000730","volume":"36","author":"WB Wu","year":"2008","unstructured":"Wu WB. On false discovery control under dependence. Ann Stat. 2008;36(1):364\u201380.","journal-title":"Ann Stat"},{"issue":"4","key":"5678_CR17","first-page":"1432","volume":"35","author":"H Finner","year":"2007","unstructured":"Finner H, Dickhaus T, Roters M. Dependency and false discovery rate: asymptotics. J Ann Stat. 2007;35(4):1432\u201355.","journal-title":"J Ann Stat"},{"issue":"2","key":"5678_CR18","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1214\/16-AOS1459","volume":"45","author":"J Li","year":"2017","unstructured":"Li J, Zhong P-S. A rate optimal procedure for recovering sparse differences between high-dimensional means under dependence. Ann Stat. 2017;45(2):557\u201390.","journal-title":"Ann Stat"},{"issue":"493","key":"5678_CR19","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1198\/jasa.2011.ap09587","volume":"106","author":"W Sun","year":"2011","unstructured":"Sun W, Wei Z. Multiple testing for pattern identification, with applications to microarray time-course experiments. J Am Stat Assoc. 2011;106(493):73\u201388.","journal-title":"J Am Stat Assoc"},{"key":"5678_CR20","first-page":"1","volume":"118","author":"L Du","year":"2021","unstructured":"Du L, et al. False discovery rate control under general dependence by symmetrized data aggregation. J Am Stat Assoc. 2021;118:1\u201334.","journal-title":"J Am Stat Assoc"},{"issue":"525","key":"5678_CR21","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1080\/01621459.2018.1451335","volume":"114","author":"MD Risser","year":"2019","unstructured":"Risser MD, Paciorek CJ, Stone DA. Spatially dependent multiple testing under model misspecification, with application to detection of anthropogenic influence on extreme climate events. J Am Stat Assoc. 2019;114(525):61\u201378.","journal-title":"J Am Stat Assoc"},{"issue":"480","key":"5678_CR22","doi-asserted-by":"publisher","first-page":"1272","DOI":"10.1198\/016214507000000941","volume":"102","author":"Y Benjamini","year":"2007","unstructured":"Benjamini Y, Heller R. False discovery rates for spatial signals. J Am Stat Assoc. 2007;102(480):1272\u201381.","journal-title":"J Am Stat Assoc"},{"issue":"48","key":"5678_CR23","doi-asserted-by":"publisher","first-page":"18718","DOI":"10.1073\/pnas.0808709105","volume":"105","author":"JT Leek","year":"2008","unstructured":"Leek JT, Storey JD. A general framework for multiple testing dependence. Proc Natl Acad Sci. 2008;105(48):18718\u201323.","journal-title":"Proc Natl Acad Sci"},{"issue":"488","key":"5678_CR24","doi-asserted-by":"publisher","first-page":"1406","DOI":"10.1198\/jasa.2009.tm08332","volume":"104","author":"C Friguet","year":"2009","unstructured":"Friguet C, Kloareg M, Causeur D. A factor model approach to multiple testing under dependence. J Am Stat Assoc. 2009;104(488):1406\u201315.","journal-title":"J Am Stat Assoc"},{"issue":"3","key":"5678_CR25","doi-asserted-by":"publisher","first-page":"1686","DOI":"10.1214\/09-AOS764","volume":"38","author":"P Hall","year":"2010","unstructured":"Hall P, Jin J. Innovated higher criticism for detecting sparse signals in correlated noise. Ann Stat. 2010;38(3):1686\u2013732.","journal-title":"Ann Stat"},{"issue":"4","key":"5678_CR26","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1177\/0962280206079046","volume":"17","author":"A Farcomeni","year":"2008","unstructured":"Farcomeni A. A review of modern multiple hypothesis testing, with particular attention to the false discovery proportion. J Stat Methods Med Res. 2008;17(4):347\u201388.","journal-title":"J Stat Methods Med Res"},{"key":"5678_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.genrep.2021.101419","volume":"25","author":"E Nazari","year":"2021","unstructured":"Nazari E, et al. Machine learning approaches for classification of colorectal cancer with and without feature selection method on microarray data. Gene Rep. 2021;25: 101419.","journal-title":"Gene Rep"},{"key":"5678_CR28","first-page":"1","volume":"1","author":"BW Zhao","year":"2023","unstructured":"Zhao BW, et al. Fusing higher and lower-order biological information for drug repositioning via graph representation learning. IEEE Trans Emerg Top Comput. 2023;1:1.","journal-title":"IEEE Trans Emerg Top Comput"},{"issue":"8","key":"5678_CR29","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1093\/bioinformatics\/btad451","volume":"39","author":"BW Zhao","year":"2023","unstructured":"Zhao BW, et al. GRLDTI: an improved graph representation learning method for predicting drug\u2013target interactions over heterogeneous biological information network. Bioinformatics. 2023;39(8):451.","journal-title":"Bioinformatics"}],"updated-by":[{"DOI":"10.1186\/s12859-024-05696-8","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2024,2,23]],"date-time":"2024-02-23T00:00:00Z","timestamp":1708646400000}}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-024-05678-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-024-05678-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-024-05678-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T10:01:57Z","timestamp":1716285717000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/s12859-024-05678-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,5]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["5678"],"URL":"https:\/\/doi.org\/10.1186\/s12859-024-05678-w","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,5]]},"assertion":[{"value":"20 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2024","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1186\/s12859-024-05696-8","URL":"https:\/\/doi.org\/10.1186\/s12859-024-05696-8","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"All data were used in this study are from an open access and open sources; the <u>GSE44861 data<\/u> set of colorectal cancer, this data set was attached at Additional file\n                      \n                      : S3. The R-codes written for this study are available in suppleAdditional file\n                      \n                      S4.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Availability of data and materials"}},{"value":"The authors declare no competing interests.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"57"}}