Stepwise normal theory multiple test procedures controlling the false discovery rate
Identifieur interne : 001735 ( Istex/Corpus ); précédent : 001734; suivant : 001736Stepwise normal theory multiple test procedures controlling the false discovery rate
Auteurs : James F. TroendleSource :
- Journal of Statistical Planning and Inference [ 0378-3758 ] ; 2000.
Abstract
The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (Benjamini and Hochberg, 1995). In this paper, step-down and step-up procedures are described which asymptotically (as N→∞) control the FDR when the test statistics are the t statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate t distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.
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DOI: 10.1016/S0378-3758(99)00145-7
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Troendle</name><affiliation><mods:affiliation>E-mail: jt3t@nih.gov</mods:affiliation></affiliation><affiliation><mods:affiliation>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75</idno><date when="2000" year="2000">2000</date><idno type="doi">10.1016/S0378-3758(99)00145-7</idno><idno type="url">https://api.istex.fr/document/7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001735</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001735</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Stepwise normal theory multiple test procedures controlling the false discovery rate</title><author><name sortKey="Troendle, James F" sort="Troendle, James F" uniqKey="Troendle J" first="James F." last="Troendle">James F. Troendle</name><affiliation><mods:affiliation>E-mail: jt3t@nih.gov</mods:affiliation></affiliation><affiliation><mods:affiliation>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Journal of Statistical Planning and Inference</title><title level="j" type="abbrev">JSPI</title><idno type="ISSN">0378-3758</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000">2000</date><biblScope unit="volume">84</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="139">139</biblScope><biblScope unit="page" to="158">158</biblScope></imprint><idno type="ISSN">0378-3758</idno></series><idno type="istex">7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75</idno><idno type="DOI">10.1016/S0378-3758(99)00145-7</idno><idno type="PII">S0378-3758(99)00145-7</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0378-3758</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (Benjamini and Hochberg, 1995). In this paper, step-down and step-up procedures are described which asymptotically (as N→∞) control the FDR when the test statistics are the t statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate t distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>James F. Troendle</name><affiliations><json:string>E-mail: jt3t@nih.gov</json:string><json:string>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>62F03</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>False discovery rate</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multiple testing</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-down</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Step-up</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Power</value></json:item></subject><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (Benjamini and Hochberg, 1995). In this paper, step-down and step-up procedures are described which asymptotically (as N→∞) control the FDR when the test statistics are the t statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate t distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.</abstract><qualityIndicators><score>7.28</score><pdfVersion>1.2</pdfVersion><pdfPageSize>408 x 660 pts</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>6</keywordCount><abstractCharCount>1282</abstractCharCount><pdfWordCount>7418</pdfWordCount><pdfCharCount>38519</pdfCharCount><pdfPageCount>20</pdfPageCount><abstractWordCount>190</abstractWordCount></qualityIndicators><title>Stepwise normal theory multiple test procedures controlling the false discovery rate</title><pii><json:string>S0378-3758(99)00145-7</json:string></pii><refBibs><json:item><author><json:item><name>Y. Benjamini</name></json:item><json:item><name>Y. Hochberg</name></json:item></author><host><volume>57</volume><pages><last>300</last><first>289</first></pages><author></author><title>J. Roy. Statist. Soc. B</title></host><title>Controlling the false discovery rate: a practical and powerful approach to multiple testing</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>S.R. Dalal</name></json:item><json:item><name>C.L. Mallows</name></json:item></author><host><volume>2</volume><pages><last>765</last><first>752</first></pages><author></author><title>Ann. Appl. Probab.</title></host><title>Buying with exact confidence</title></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>C.W. Dunnett</name></json:item><json:item><name>A.C. Tamhane</name></json:item></author><host><volume>87</volume><pages><last>170</last><first>162</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>A step-up multiple test procedure</title></json:item><json:item><author><json:item><name>C.W. Dunnett</name></json:item><json:item><name>A.C. Tamhane</name></json:item></author><host><volume>51</volume><pages><last>227</last><first>217</first></pages><author></author><title>Biometrics</title></host><title>Step-up multiple testing of parameters with unequally correlated estimates</title></json:item><json:item><host><author></author></host></json:item><json:item><host><author></author></host></json:item><json:item><author><json:item><name>J.F. Troendle</name></json:item></author><host><volume>52</volume><pages><last>859</last><first>846</first></pages><author></author><title>Biometrics</title></host><title>A permutational step-up method of testing multiple outcomes</title></json:item><json:item><author><json:item><name>P.H. Westfall</name></json:item><json:item><name>S.S. Young</name></json:item></author><host><volume>84</volume><pages><last>786</last><first>780</first></pages><author></author><title>J. Amer. Statist. Assoc.</title></host><title>P-value adjustments for multiple tests in multivariate binomial models</title></json:item><json:item><host><author></author></host></json:item><json:item><host><author></author></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>84</volume><pii><json:string>S0378-3758(00)X0084-5</json:string></pii><pages><last>158</last><first>139</first></pages><issn><json:string>0378-3758</json:string></issn><issue>1–2</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><title>Journal of Statistical Planning and Inference</title><publicationDate>2000</publicationDate></host><categories><wos><json:string>science</json:string><json:string>statistics & probability</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>statistics & probability</json:string></scienceMetrix></categories><publicationDate>2000</publicationDate><copyrightDate>2000</copyrightDate><doi><json:string>10.1016/S0378-3758(99)00145-7</json:string></doi><id>7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75</id><score>0.020148594</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Stepwise normal theory multiple test procedures controlling the false discovery rate</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>ELSEVIER</publisher><availability><p>ELSEVIER</p></availability><date>2000</date></publicationStmt><notesStmt><note type="content">Fig. 1: Critical constants for NSD procedure with ρ=0 and v=20 (one-sided tests).</note><note type="content">Table 1: Critical constants cj for the procedures (one-sided tests)a</note><note type="content">Table 2: Critical constants cj for the procedures (two-sided tests)a</note><note type="content">Table 3: Observed FDR when k=5 (one-sided tests)a</note><note type="content">Table 4: Average power of the procedures (one-sided tests)a</note><note type="content">Table 5: Observed FDR when k>5 (one-sided tests)a</note><note type="content">Table 6: Critical constants cj from simulation with equal correlation (one-sided tests)a</note><note type="content">Table 7: Adjusted FDR-values for example data (one-sided tests)a</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Stepwise normal theory multiple test procedures controlling the false discovery rate</title><author xml:id="author-1"><persName><forename type="first">James F.</forename><surname>Troendle</surname></persName><email>jt3t@nih.gov</email><note type="correspondence"><p>Corresponding author. NIH, Bld. 6100 Rm. 7B13, Bethesda, MD 20892, USA</p></note><affiliation>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</affiliation></author></analytic><monogr><title level="j">Journal of Statistical Planning and Inference</title><title level="j" type="abbrev">JSPI</title><idno type="pISSN">0378-3758</idno><idno type="PII">S0378-3758(00)X0084-5</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="2000"></date><biblScope unit="volume">84</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="139">139</biblScope><biblScope unit="page" to="158">158</biblScope></imprint></monogr><idno type="istex">7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75</idno><idno type="DOI">10.1016/S0378-3758(99)00145-7</idno><idno type="PII">S0378-3758(99)00145-7</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2000</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (Benjamini and Hochberg, 1995). In this paper, step-down and step-up procedures are described which asymptotically (as N→∞) control the FDR when the test statistics are the t statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate t distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.</p></abstract><textClass><keywords scheme="keyword"><list><head>MSC</head><item><term>62F03</term></item></list></keywords></textClass><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>False discovery rate</term></item><item><term>Multiple testing</term></item><item><term>Step-down</term></item><item><term>Step-up</term></item><item><term>Power</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1999-05-20">Modified</change><change when="2000">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: ce:floats; body; tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"><istex:entity SYSTEM="gr1" NDATA="IMAGE" name="gr1"></istex:entity></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>JSPI</jid><aid>1639</aid><ce:pii>S0378-3758(99)00145-7</ce:pii><ce:doi>10.1016/S0378-3758(99)00145-7</ce:doi><ce:copyright type="unknown" year="2000"></ce:copyright></item-info><head><ce:title>Stepwise normal theory multiple test procedures controlling the false discovery rate</ce:title><ce:author-group><ce:author><ce:given-name>James F.</ce:given-name><ce:surname>Troendle</ce:surname><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref><ce:cross-ref refid="CORR1">*</ce:cross-ref><ce:e-address>jt3t@nih.gov</ce:e-address></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>NIH, Bld. 6100 Rm. 7B13, Bethesda, MD 20892, USA</ce:textfn></ce:affiliation><ce:correspondence id="CORR1"><ce:label>*</ce:label><ce:text>Corresponding author. NIH, Bld. 6100 Rm. 7B13, Bethesda, MD 20892, USA</ce:text></ce:correspondence></ce:author-group><ce:date-received day="1" month="9" year="1998"></ce:date-received><ce:date-revised day="20" month="5" year="1999"></ce:date-revised><ce:date-accepted day="28" month="6" year="1999"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (<ce:cross-ref refid="BIB1">Benjamini and Hochberg, 1995</ce:cross-ref>). In this paper, step-down and step-up procedures are described which asymptotically (as <ce:italic>N</ce:italic>→∞) control the FDR when the test statistics are the <ce:italic>t</ce:italic> statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate <ce:italic>t</ce:italic> distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.</ce:simple-para></ce:abstract-sec></ce:abstract><ce:keywords class="msc"><ce:section-title>MSC</ce:section-title><ce:keyword><ce:text>62F03</ce:text></ce:keyword></ce:keywords><ce:keywords class="keyword"><ce:section-title>Keywords</ce:section-title><ce:keyword><ce:text>False discovery rate</ce:text></ce:keyword><ce:keyword><ce:text>Multiple testing</ce:text></ce:keyword><ce:keyword><ce:text>Step-down</ce:text></ce:keyword><ce:keyword><ce:text>Step-up</ce:text></ce:keyword><ce:keyword><ce:text>Power</ce:text></ce:keyword></ce:keywords></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Stepwise normal theory multiple test procedures controlling the false discovery rate</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Stepwise normal theory multiple test procedures controlling the false discovery rate</title></titleInfo><name type="personal"><namePart type="given">James F.</namePart><namePart type="family">Troendle</namePart><affiliation>E-mail: jt3t@nih.gov</affiliation><affiliation>Biometry and Mathematical Statistics Branch, Division of Epidemiology, Statistics, and Prevention Research, National Institute of Child Health and Human Development, USA</affiliation><description>Corresponding author. NIH, Bld. 6100 Rm. 7B13, Bethesda, MD 20892, USA</description><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">2000</dateIssued><dateModified encoding="w3cdtf">1999-05-20</dateModified><copyrightDate encoding="w3cdtf">2000</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">The false discovery rate (FDR), or the expected proportion of falsely rejected null hypotheses to rejected null hypotheses, has recently been proposed as an error rate that multiple testing procedures should in certain circumstances control. So far, only a step-up procedure for independent test statistics has been created explicitly to control the FDR (Benjamini and Hochberg, 1995). In this paper, step-down and step-up procedures are described which asymptotically (as N→∞) control the FDR when the test statistics are the t statistics from consistent multivariate normal estimators of the tested parameters. Determination of the necessary critical constants for the normal theory procedures is achieved using numerical integration when the correlations are equal, or through simulation using the multivariate t distribution when the correlations are arbitrary. The critical constants of the normal theory procedures are compared to those of the Benjamini and Hochberg procedure under the normal assumption, and a large potential power increase is found. Simulation strongly supports the use of critical constants, obtained by an asymptotic argument, in small samples for as many as 30 tests. Adjusted FDR values can be found to quantify the evidence against a given hypothesis.</abstract><note type="content">Fig. 1: Critical constants for NSD procedure with ρ=0 and v=20 (one-sided tests).</note><note type="content">Table 1: Critical constants cj for the procedures (one-sided tests)a</note><note type="content">Table 2: Critical constants cj for the procedures (two-sided tests)a</note><note type="content">Table 3: Observed FDR when k=5 (one-sided tests)a</note><note type="content">Table 4: Average power of the procedures (one-sided tests)a</note><note type="content">Table 5: Observed FDR when k>5 (one-sided tests)a</note><note type="content">Table 6: Critical constants cj from simulation with equal correlation (one-sided tests)a</note><note type="content">Table 7: Adjusted FDR-values for example data (one-sided tests)a</note><subject><genre>MSC</genre><topic>62F03</topic></subject><subject><genre>Keywords</genre><topic>False discovery rate</topic><topic>Multiple testing</topic><topic>Step-down</topic><topic>Step-up</topic><topic>Power</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Statistical Planning and Inference</title></titleInfo><titleInfo type="abbreviated"><title>JSPI</title></titleInfo><genre type="journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">200003</dateIssued></originInfo><identifier type="ISSN">0378-3758</identifier><identifier type="PII">S0378-3758(00)X0084-5</identifier><part><date>200003</date><detail type="volume"><number>84</number><caption>vol.</caption></detail><detail type="issue"><number>1–2</number><caption>no.</caption></detail><extent unit="issue pages"><start>1</start><end>354</end></extent><extent unit="pages"><start>139</start><end>158</end></extent></part></relatedItem><identifier type="istex">7F8B833D2A8D553DBCE8C9C7C0617D52BE46FD75</identifier><identifier type="DOI">10.1016/S0378-3758(99)00145-7</identifier><identifier type="PII">S0378-3758(99)00145-7</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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