Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials
Identifieur interne : 000397 ( Istex/Corpus ); précédent : 000396; suivant : 000398Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials
Auteurs : Peter B. Gilbert ; Xuesong Yu ; Andrea RotnitzkySource :
- Statistics in Medicine [ 0277-6715 ] ; 2014-03-15.
Abstract
To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. Copyright © 2013 John Wiley & Sons, Ltd.
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DOI: 10.1002/sim.6006
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Gilbert, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave North, PO Box 19024, Seattle, WA 98109, U.S.A.E‐mail:</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pgilbert@scharp.org</mods:affiliation></affiliation></author><author><name sortKey="Yu, Xuesong" sort="Yu, Xuesong" uniqKey="Yu X" first="Xuesong" last="Yu">Xuesong Yu</name><affiliation><mods:affiliation>Vaccine Infectious Disease Division, Fred Hutchinson Cancer Research Center, WA 98109, Seattle, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Rotnitzky, Andrea" sort="Rotnitzky, Andrea" uniqKey="Rotnitzky A" first="Andrea" last="Rotnitzky">Andrea Rotnitzky</name><affiliation><mods:affiliation>Department of Economics, Universidad Di Tella, Buenos Aires, Argentina</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Biostatistics, Harvard School of Public Health, MA 02115, Boston, U.S.A.</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:6E8E781B3B546224CA95768C6C749694D6028AFF</idno><date when="2014" year="2014">2014</date><idno type="doi">10.1002/sim.6006</idno><idno type="url">https://api.istex.fr/ark:/67375/WNG-XG36Q0KP-B/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">000397</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000397</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main">Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials</title><author><name sortKey="Gilbert, Peter B" sort="Gilbert, Peter B" uniqKey="Gilbert P" first="Peter B." last="Gilbert">Peter B. 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Gilbert, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave North, PO Box 19024, Seattle, WA 98109, U.S.A.E‐mail:</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pgilbert@scharp.org</mods:affiliation></affiliation></author><author><name sortKey="Yu, Xuesong" sort="Yu, Xuesong" uniqKey="Yu X" first="Xuesong" last="Yu">Xuesong Yu</name><affiliation><mods:affiliation>Vaccine Infectious Disease Division, Fred Hutchinson Cancer Research Center, WA 98109, Seattle, U.S.A.</mods:affiliation></affiliation></author><author><name sortKey="Rotnitzky, Andrea" sort="Rotnitzky, Andrea" uniqKey="Rotnitzky A" first="Andrea" last="Rotnitzky">Andrea Rotnitzky</name><affiliation><mods:affiliation>Department of Economics, Universidad Di Tella, Buenos Aires, Argentina</mods:affiliation></affiliation><affiliation><mods:affiliation>Department of Biostatistics, Harvard School of Public Health, MA 02115, Boston, U.S.A.</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j" type="main">Statistics in Medicine</title><title level="j" type="alt">STATISTICS IN MEDICINE</title><idno type="ISSN">0277-6715</idno><idno type="eISSN">1097-0258</idno><imprint><biblScope unit="vol">33</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="901">901</biblScope><biblScope unit="page" to="917">917</biblScope><biblScope unit="page-count">17</biblScope><date type="published" when="2014-03-15">2014-03-15</date></imprint><idno type="ISSN">0277-6715</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0277-6715</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract">To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. Copyright © 2013 John Wiley & Sons, Ltd.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Peter B. Gilbert</name><affiliations><json:string>Vaccine Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, U.S.A.</json:string><json:string>Department of Biostatistics, University of Washington, WA 98105, Seattle, U.S.A.</json:string><json:string>Correspondence to: Peter B. 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This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. 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<lineatedText xml:id="sim6006-lntext-0001"><line>Correspondence to: Peter B. Gilbert, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave North, PO Box 19024, Seattle, WA 98109, U.S.A.</line><line>E‐mail: <email>pgilbert@scharp.org</email></line></lineatedText> </correspondenceTo><objectNameGroup><objectName elementName="mathStatement">Result</objectName></objectNameGroup><linkGroup><link type="toTypesetVersion" href="file:SIM.SIM6006.pdf"></link></linkGroup></publicationMeta><contentMeta><titleGroup><title type="main">Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials</title><title type="shortAuthors">P. B. GILBERT, X. YU AND A. ROTNITZKY</title></titleGroup><creators><creator xml:id="sim6006-cr-0001" creatorRole="author" affiliationRef="#sim6006-aff-0001 #sim6006-aff-0002" corresponding="yes"><personName><givenNames>Peter B.</givenNames><familyName>Gilbert</familyName></personName></creator><creator xml:id="sim6006-cr-0002" creatorRole="author" affiliationRef="#sim6006-aff-0001"><personName><givenNames>Xuesong</givenNames><familyName>Yu</familyName></personName></creator><creator xml:id="sim6006-cr-0003" creatorRole="author" affiliationRef="#sim6006-aff-0003 #sim6006-aff-0004"><personName><givenNames>Andrea</givenNames><familyName>Rotnitzky</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="sim6006-aff-0001" countryCode="US" type="organization"><orgDiv>Vaccine Infectious Disease Division</orgDiv><orgName>Fred Hutchinson Cancer Research Center</orgName><address><city>Seattle</city><countryPart>WA 98109</countryPart><country>U.S.A.</country></address></affiliation><affiliation xml:id="sim6006-aff-0002" countryCode="US" type="organization"><orgDiv>Department of Biostatistics</orgDiv><orgName>University of Washington</orgName><address><city>Seattle</city><countryPart>WA 98105</countryPart><country>U.S.A.</country></address></affiliation><affiliation xml:id="sim6006-aff-0003" countryCode="AR" type="organization"><orgDiv>Department of Economics</orgDiv><orgName>Universidad Di Tella</orgName><address><city>Buenos Aires</city><country>Argentina</country></address></affiliation><affiliation xml:id="sim6006-aff-0004" countryCode="US" type="organization"><orgDiv>Department of Biostatistics</orgDiv><orgName>Harvard School of Public Health</orgName><address><city>Boston</city><countryPart>MA 02115</countryPart><country>U.S.A.</country></address></affiliation></affiliationGroup><keywordGroup type="author"><keyword xml:id="sim6006-kwd-0001">augmented inverse probability weighting</keyword><keyword xml:id="sim6006-kwd-0002">efficient estimation</keyword><keyword xml:id="sim6006-kwd-0003">efficient sampling</keyword><keyword xml:id="sim6006-kwd-0004">missing data</keyword><keyword xml:id="sim6006-kwd-0005">semiparametric model</keyword><keyword xml:id="sim6006-kwd-0006">two‐phase sampling</keyword></keywordGroup><supportingInformation xml:id="sim6006-supinf-0001"><supportingInfoItem xml:id="sim6006-supitem-0001"><mediaResource alt="supplementary data" mimeType="application/x-zip-compressed" rendition="webOriginal" href="urn-x:wiley:02776715:media:sim6006:sim6006-sup-0001-web"></mediaResource><caption>Supporting info item</caption></supportingInfoItem></supportingInformation><abstractGroup><abstract type="main" xml:id="sim6006-abs-0001"><p xml:id="sim6006-para-0001">To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint <i>Y</i>, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables <i>W</i> predictive of <i>Y</i> are measured in everyone, <i>Y</i> is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (<i>Y</i>) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (<i>W</i>) highly predictive of <i>Y</i> and measures <i>Y</i> in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 <i>%</i> in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of <i>Y</i> given <i>W</i> yields greater efficiency gains. Accurate estimation of <i>E</i>[<i>Y</i> | <i>W</i>] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. Copyright © 2013 John Wiley & Sons, Ltd.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Optimal auxiliary‐covariate‐based two‐phase sampling design for semiparametric efficient estimation of a mean or mean difference, with application to clinical trials</title></titleInfo><name type="personal"><namePart type="given">Peter B.</namePart><namePart type="family">Gilbert</namePart><affiliation>Vaccine Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, U.S.A.</affiliation><affiliation>Department of Biostatistics, University of Washington, WA 98105, Seattle, U.S.A.</affiliation><affiliation>Correspondence to: Peter B. Gilbert, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave North, PO Box 19024, Seattle, WA 98109, U.S.A.E‐mail:</affiliation><affiliation>E-mail: pgilbert@scharp.org</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Xuesong</namePart><namePart type="family">Yu</namePart><affiliation>Vaccine Infectious Disease Division, Fred Hutchinson Cancer Research Center, WA 98109, Seattle, U.S.A.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Andrea</namePart><namePart type="family">Rotnitzky</namePart><affiliation>Department of Economics, Universidad Di Tella, Buenos Aires, Argentina</affiliation><affiliation>Department of Biostatistics, Harvard School of Public Health, MA 02115, Boston, U.S.A.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><dateIssued encoding="w3cdtf">2014-03-15</dateIssued><dateCreated encoding="w3cdtf">2013-10</dateCreated><dateCaptured encoding="w3cdtf">2012-02-22</dateCaptured><dateValid encoding="w3cdtf">2013-09-19</dateValid><copyrightDate encoding="w3cdtf">2014</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract>To address the objective in a clinical trial to estimate the mean or mean difference of an expensive endpoint Y, one approach employs a two‐phase sampling design, wherein inexpensive auxiliary variables W predictive of Y are measured in everyone, Y is measured in a random sample, and the semiparametric efficient estimator is applied. This approach is made efficient by specifying the phase two selection probabilities as optimal functions of the auxiliary variables and measurement costs. While this approach is familiar to survey samplers, it apparently has seldom been used in clinical trials, and several novel results practicable for clinical trials are developed. We perform simulations to identify settings where the optimal approach significantly improves efficiency compared to approaches in current practice. We provide proofs and R code. The optimality results are developed to design an HIV vaccine trial, with objective to compare the mean ‘importance‐weighted’ breadth (Y) of the T‐cell response between randomized vaccine groups. The trial collects an auxiliary response (W) highly predictive of Y and measures Y in the optimal subset. We show that the optimal design‐estimation approach can confer anywhere between absent and large efficiency gain (up to 24 % in the examples) compared to the approach with the same efficient estimator but simple random sampling, where greater variability in the cost‐standardized conditional variance of Y given W yields greater efficiency gains. Accurate estimation of E[Y | W] is important for realizing the efficiency gain, which is aided by an ample phase two sample and by using a robust fitting method. 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