{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T01:13:28Z","timestamp":1768353208997,"version":"3.49.0"},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Molecular diagnostics aims at classifying diseases into clinically relevant sub-entities based on molecular characteristics. Typically, the entities are split into subgroups, which might contain several variants yielding a hierarchical model of the disease. Recent years have introduced a plethora of new molecular screening technologies to molecular diagnostics. As a result molecular profiles of patients became complex and the classification task more difficult.<\/jats:p>\n               <jats:p>Results: We present a novel tool for detecting hierarchical structure in binary datasets. We aim for identifying molecular characteristics, which are stochastically implying other characteristics. The final hierarchical structure is encoded in a directed transitive graph where nodes represent molecular characteristics and a directed edge from a node A to a node B denotes that almost all cases with characteristic B also display characteristic A. Naturally, these graphs need to be transitive. In the core of our modeling approach lies the problem of calculating good transitive approximations of given directed but not necessarily transitive graphs. By good transitive approximation we understand transitive graphs, which differ from the reference graph in only a small number of edges. It is known that the problem of finding optimal transitive approximation is NP-complete. Here we develop an efficient heuristic for generating good transitive approximations. We evaluate the computational efficiency of the algorithm in simulations, and demonstrate its use in the context of a large genome-wide study on mature aggressive lymphomas.<\/jats:p>\n               <jats:p>Availability: The software used in our analysis is freely available from http:\/\/compdiag.uni-regensburg.de\/software\/transApproxs.shtml<\/jats:p>\n               <jats:p>Contact: \u00a0Juby.Jacob@klinik.uni-regensburg.de, Rainer.Spang@klinik.uni-regensburg.de<\/jats:p>\n               <jats:p>Supplementary information: Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btn056","type":"journal-article","created":{"date-parts":[[2008,2,20]],"date-time":"2008-02-20T03:58:37Z","timestamp":1203479917000},"page":"995-1001","source":"Crossref","is-referenced-by-count":8,"title":["Detecting hierarchical structure in molecular characteristics of disease using transitive approximations of directed graphs"],"prefix":"10.1093","volume":"24","author":[{"given":"Juby","family":"Jacob","sequence":"first","affiliation":[{"name":"1 Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnesta\u00dfe 63\/73, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcel","family":"Jentsch","sequence":"additional","affiliation":[{"name":"1 Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnesta\u00dfe 63\/73, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dennis","family":"Kostka","sequence":"additional","affiliation":[{"name":"1 Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnesta\u00dfe 63\/73, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Bentink","sequence":"additional","affiliation":[{"name":"1 Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnesta\u00dfe 63\/73, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rainer","family":"Spang","sequence":"additional","affiliation":[{"name":"1 Computational Diagnostics Group, Institute of Functional Genomics, University of Regensburg, 93053 Regensburg, Germany and 2Max Planck Institute for Molecular Genetics, Ihnesta\u00dfe 63\/73, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2008,2,19]]},"reference":[{"key":"2023020209533598200_B1","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1038\/35000501","article-title":"Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling","volume":"403","author":"Alizadeh","year":"2000","journal-title":"Nature"},{"key":"2023020209533598200_B2","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s11229-004-6219-1","article-title":"Closer","volume":"146","author":"De Clercq","year":"2005","journal-title":"Synthese"},{"key":"2023020209533598200_B3","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1200\/JCO.2006.09.4490","article-title":"Immunohistochemical prognostic markers in diffuse large B-cell lymphoma: validation of tissue microarray as a prerequisite for broad clinical applications \u2013 a study from the Lunenburg Lymphoma Biomarker Consortium","volume":"25","author":"de Jong","year":"2007","journal-title":"J. Clin. Oncol"},{"key":"2023020209533598200_B4","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/s00236-004-0144-0","article-title":"On best transitive approximations to simple graphs","volume":"40","author":"Delvaux","year":"2004","journal-title":"Acta Informatica"},{"key":"2023020209533598200_B5","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1182\/blood-2003-05-1545","article-title":"Confirmation of the molecular classification of diffuse large B-cell lymphoma by immunohistochemistry using a tissue microarray","volume":"103","author":"Hans","year":"2004","journal-title":"Blood"},{"key":"2023020209533598200_B6","doi-asserted-by":"crossref","first-page":"2419","DOI":"10.1056\/NEJMoa055351","article-title":"A biologic definition of Burkitt's lymphoma from transcriptional and genomic profiling","volume":"354","author":"Hummel","year":"2006","journal-title":"N. Engl. J. Med"},{"key":"2023020209533598200_B7","volume-title":"World Health Organization Classification of Tumours. Pathology and Genetics of Tumours of Haematopoietic and Lymphoid Tissues","author":"Jaffe","year":"2001"},{"key":"2023020209533598200_B8","doi-asserted-by":"crossref","first-page":"5730","DOI":"10.1158\/1078-0432.CCR-04-2225","article-title":"Gene signatures of progression and metastasis in renal cell cancer","volume":"11","author":"Jones","year":"2005","journal-title":"Clin. Cancer. Res"},{"key":"2023020209533598200_B9","doi-asserted-by":"crossref","first-page":"i305","DOI":"10.1093\/bioinformatics\/btm178","article-title":"Nested effects models for high-dimensional phenotyping screens","volume":"23","author":"Markowetz","year":"2007","journal-title":"Bioinformatics"},{"key":"2023020209533598200_B10","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/3-540-46784-X_8","article-title":"Complexity classification of some edge modification problems","author":"Natanzon","year":"1999","journal-title":"In Workshop on Graph-Theoretic Concepts in Computer Science, WG '99. Ascona, Switzerland"},{"key":"2023020209533598200_B11","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/2524","article-title":"High resolution analysis of DNA copy number variation using comparative genomic hybridization to microarrays","volume":"20","author":"Pinkel","year":"1998","journal-title":"Nat. Genet"},{"key":"2023020209533598200_B12","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1038\/12640","article-title":"Genome-wide analysis of DNA copy-number changes using cDNA microarrays","volume":"23","author":"Pollack","year":"1999","journal-title":"Nat. Genet"},{"key":"2023020209533598200_B13","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1056\/NEJMoa012914","article-title":"The use of molecular profiling to predict survival after chemotherapy for diffuse large-B-cell lymphoma","volume":"346","author":"Rosenwald","year":"2002","journal-title":"N. Engl. J. Med"},{"key":"2023020209533598200_B14","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1002\/(SICI)1098-2264(199712)20:4<399::AID-GCC12>3.0.CO;2-I","article-title":"Matrix-based comparative genomic hybridization: biochips to screen for genomic imbalances","volume":"20","author":"Solinas-Toldo","year":"1997","journal-title":"Genes Chromosomes Cancer"},{"key":"2023020209533598200_B15","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1056\/NEJMoa021967","article-title":"A gene-expression signature as a predictor of survival in breast cancer","volume":"347","author":"van de Vijver","year":"2002","journal-title":"N. Engl. J. Med"},{"key":"2023020209533598200_B16","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1137\/0112071","article-title":"Approximation symmetric relations by equivalence relations","volume":"12","author":"Zahn","year":"1964","journal-title":"Journal of the Soceity for Industrial and Applied Mathematics"}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/7\/995\/49049203\/bioinformatics_24_7_995.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/24\/7\/995\/49049203\/bioinformatics_24_7_995.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T11:13:50Z","timestamp":1675336430000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/24\/7\/995\/296851"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,2,19]]},"references-count":16,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2008,4,1]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btn056","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2008,4,1]]},"published":{"date-parts":[[2008,2,19]]}}}