{"id":"https://openalex.org/W2090626261","doi":"https://doi.org/10.3109/1354750x.2013.868516","title":"Sorting multiple classes in multi-dimensional ROC analysis: parametric and nonparametric approaches","display_name":"Sorting multiple classes in multi-dimensional ROC analysis: parametric and nonparametric approaches","publication_year":2013,"publication_date":"2013-12-16","ids":{"openalex":"https://openalex.org/W2090626261","doi":"https://doi.org/10.3109/1354750x.2013.868516","mag":"2090626261","pmid":"https://pubmed.ncbi.nlm.nih.gov/24329017"},"language":"en","primary_location":{"id":"doi:10.3109/1354750x.2013.868516","doi":"https://doi.org/10.3109/1354750x.2013.868516","is_oa":false,"landing_page_url":"https://doi.org/10.3109/1354750x.2013.868516","pdf_url":null,"source":{"id":"https://openalex.org/S7166883","display_name":"Biomarkers","issn_l":"1354-750X","issn":["1354-750X","1366-5804"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biomarkers","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100358351","display_name":"Jialiang Li","orcid":"https://orcid.org/0000-0002-9704-4135","observed_orcids":["https://orcid.org/0000-0002-9704-4135"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I4210116917","display_name":"Singapore Eye Research Institute","ror":"https://ror.org/02crz6e12","country_code":"SG","type":"facility","lineage":["https://openalex.org/I4210116917"]},{"id":"https://openalex.org/I4210126319","display_name":"Duke-NUS Medical School","ror":"https://ror.org/02j1m6098","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596","https://openalex.org/I170897317","https://openalex.org/I4210126319"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Jialiang Li","raw_affiliation_strings":["Department of Statistics and Applied Probability, National University of SingaporeSingapore","Centre for Quantitative Medicine, Duke-NUS Graduate Medical SchoolSingapore","Singapore Eye Research InstituteSingapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Applied Probability, National University of SingaporeSingapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Centre for Quantitative Medicine, Duke-NUS Graduate Medical SchoolSingapore","institution_ids":["https://openalex.org/I165932596","https://openalex.org/I4210126319"]},{"raw_affiliation_string":"Singapore Eye Research InstituteSingapore","institution_ids":["https://openalex.org/I4210116917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045490225","display_name":"Yanyu Chow","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yanyu Chow","raw_affiliation_strings":["Department of Statistics and Applied Probability, National University of SingaporeSingapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Applied Probability, National University of SingaporeSingapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050143476","display_name":"Weng Kee Wong","orcid":"https://orcid.org/0000-0001-5568-3054","observed_orcids":["https://orcid.org/0000-0001-5568-3054"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weng Kee Wong","raw_affiliation_strings":["Department of Biostatistics, University of California at Los Angeles, CAUSA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics, University of California at Los Angeles, CAUSA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072258594","display_name":"Tien Yin Wong","orcid":"https://orcid.org/0000-0002-8448-1264","observed_orcids":["https://orcid.org/0000-0002-8448-1264"]},"institutions":[{"id":"https://openalex.org/I4210116917","display_name":"Singapore Eye Research Institute","ror":"https://ror.org/02crz6e12","country_code":"SG","type":"facility","lineage":["https://openalex.org/I4210116917"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Tien Yin Wong","raw_affiliation_strings":["Singapore Eye Research InstituteSingapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Singapore Eye Research InstituteSingapore","institution_ids":["https://openalex.org/I4210116917"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100358351"],"corresponding_institution_ids":["https://openalex.org/I165932596","https://openalex.org/I4210116917","https://openalex.org/I4210126319"],"apc_list":null,"apc_paid":null,"fwci":0.8954,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.73633918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"1","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.4683000147342682,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10885","display_name":"Gene expression and cancer classification","score":0.4683000147342682,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.43309998512268066,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.009200000204145908,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/receiver-operating-characteristic","display_name":"receiver operating characteristic","score":0.7009999752044678},{"id":"https://openalex.org/keywords/diagnostic-accuracy","display_name":"diagnostic accuracy","score":0.4480000138282776},{"id":"https://openalex.org/keywords/microarray-data","display_name":"microarray data","score":0.5199999809265137},{"id":"https://openalex.org/keywords/differentially-expressed-genes","display_name":"differentially expressed genes","score":0.9100000262260437},{"id":"https://openalex.org/keywords/high-dimensional-data-classification","display_name":"high-dimensional classification","score":0.5550000071525574},{"id":"https://openalex.org/keywords/leukemia","display_name":"leukemia","score":0.4350000023841858},{"id":"https://openalex.org/keywords/liver-cancer","display_name":"liver cancer","score":0.9539999961853027}],"concepts":[{"id":"https://openalex.org/C58471807","wikidata":"https://www.wikidata.org/wiki/Q327120","display_name":"Receiver operating characteristic","level":2,"score":0.6776127815246582},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5837336778640747},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.549008846282959},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5425409078598022},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.46361738443374634},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.4553873538970947},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.45503494143486023},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4544660151004791},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45088303089141846},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4388011693954468},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.42401576042175293},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.41528505086898804},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4046418368816376},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35133564472198486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19408631324768066},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003627","descriptor_name":"Data Interpretation, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007938","descriptor_name":"Leukemia","qualifier_ui":"Q000145","qualifier_name":"classification","is_major_topic":false},{"descriptor_ui":"D007938","descriptor_name":"Leukemia","qualifier_ui":"Q000378","qualifier_name":"metabolism","is_major_topic":false},{"descriptor_ui":"D008113","descriptor_name":"Liver Neoplasms","qualifier_ui":"Q000145","qualifier_name":"classification","is_major_topic":false},{"descriptor_ui":"D008113","descriptor_name":"Liver Neoplasms","qualifier_ui":"Q000378","qualifier_name":"metabolism","is_major_topic":false},{"descriptor_ui":"D012372","descriptor_name":"ROC Curve","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D018709","descriptor_name":"Statistics, Nonparametric","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D020869","descriptor_name":"Gene Expression Profiling","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059467","descriptor_name":"Transcriptome","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.3109/1354750x.2013.868516","doi":"https://doi.org/10.3109/1354750x.2013.868516","is_oa":false,"landing_page_url":"https://doi.org/10.3109/1354750x.2013.868516","pdf_url":null,"source":{"id":"https://openalex.org/S7166883","display_name":"Biomarkers","issn_l":"1354-750X","issn":["1354-750X","1366-5804"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","doyens","jufo-1","ki-jl-1","medline","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biomarkers","raw_type":"journal-article"},{"id":"pmid:24329017","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/24329017","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Biomarkers : biochemical indicators of exposure, response, and susceptibility to chemicals","raw_type":"Journal Article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/105504","doi":null,"is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/105504","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Review"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313284","display_name":"Isaac Newton Institute for Mathematical Sciences","ror":null},{"id":"https://openalex.org/F4320334737","display_name":"National Medical Research Council","ror":"https://ror.org/04x3cxs03"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W370143576","https://openalex.org/W1483433863","https://openalex.org/W1509445416","https://openalex.org/W1510867316","https://openalex.org/W1977679444","https://openalex.org/W1981428755","https://openalex.org/W1981744949","https://openalex.org/W1985967126","https://openalex.org/W1988964524","https://openalex.org/W1990449924","https://openalex.org/W1998669587","https://openalex.org/W1999668242","https://openalex.org/W2002185523","https://openalex.org/W2008752680","https://openalex.org/W2017727332","https://openalex.org/W2041282815","https://openalex.org/W2048537487","https://openalex.org/W2050241533","https://openalex.org/W2058201002","https://openalex.org/W2066016240","https://openalex.org/W2066215616","https://openalex.org/W2108728387","https://openalex.org/W2109363337","https://openalex.org/W2115823897","https://openalex.org/W2124216274","https://openalex.org/W2129321896","https://openalex.org/W2139405211","https://openalex.org/W2143225045","https://openalex.org/W2143426320","https://openalex.org/W2152431559","https://openalex.org/W2165416472","https://openalex.org/W3143261911","https://openalex.org/W4206021986","https://openalex.org/W4232875550","https://openalex.org/W4237518394"],"related_works":["https://openalex.org/W4313488284","https://openalex.org/W2143225045","https://openalex.org/W2124216274","https://openalex.org/W2103844659","https://openalex.org/W2078663343","https://openalex.org/W2974801075","https://openalex.org/W2464967658","https://openalex.org/W1483433863","https://openalex.org/W2215549086","https://openalex.org/W6917543215"],"abstract_inverted_index":{"In":[0],"large-scale":[1],"data":[2,128,134],"analysis,":[3,72],"such":[4,89],"as":[5,90],"in":[6,119],"a":[7,48,57,66,120,126,131,148],"microarray":[8],"study":[9],"to":[10,22,79],"identify":[11],"the":[12,43,53,82,97,100,107,110,114],"most":[13],"differentially":[14],"expressed":[15],"genes,":[16],"diagnostic":[17],"tests":[18],"are":[19],"frequently":[20],"used":[21],"classify":[23],"and":[24,76,92,113,130],"predict":[25],"subjects":[26],"into":[27],"their":[28],"different":[29],"categories.":[30],"Frequently,":[31],"these":[32],"categories":[33,84],"do":[34],"not":[35],"have":[36,47,147],"an":[37],"intrinsic":[38],"natural":[39],"order":[40,55,108],"even":[41],"though":[42],"quantitative":[44],"test":[45,111],"results":[46,112,144],"relative":[49,93],"order.":[50],"As":[51],"identifying":[52],"correct":[54],"for":[56,65],"proper":[58],"definition":[59],"of":[60,109,151],"accuracy":[61],"measures":[62],"is":[63],"important":[64],"high-dimensional":[67],"receiver":[68],"operating":[69],"characteristic":[70],"(ROC)":[71],"we":[73,136,146],"propose":[74],"rigorous":[75],"automated":[77],"approaches":[78,140],"sort":[80],"out":[81],"multiple":[83],"using":[85],"simple":[86],"summary":[87],"statistics":[88],"means":[91],"effects.":[94],"We":[95],"discuss":[96],"hypervolume":[98],"under":[99],"ROC":[101],"manifold":[102],"(HUM),":[103],"its":[104],"dependence":[105],"on":[106],"minimum":[115],"acceptable":[116],"HUM":[117],"values":[118],"general":[121],"multi-category":[122],"classification":[123],"problem.":[124],"Using":[125],"leukemia":[127],"set":[129],"liver":[132],"cancer":[133],"set,":[135],"show":[137],"how":[138],"our":[139],"provide":[141],"accurate":[142],"screening":[143],"when":[145],"large":[149],"number":[150],"tests.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2016-06-24T00:00:00"}
