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Testing the Maximum by the Mean in Quantitative Group Tests

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datacite.subject.fosCiências Naturais::Matemáticas
dc.contributor.authorMartins, João Paulo
dc.contributor.authorSantos, Rui
dc.contributor.authorSousa, Ricardo
dc.date.accessioned2025-07-03T14:55:50Z
dc.date.available2025-07-03T14:55:50Z
dc.date.issued2014
dc.descriptionEISBN - 9783319053233
dc.description.abstractGroup testing, introduced by Dorfman in 1943, increases the efficiency of screening individuals for low prevalence diseases. A wider use of this kind of methodology is restricted by the loss of sensitivity inherent to the mixture of samples. Moreover, as this methodology attains greater cost reduction in the cases of lower prevalence (and, consequently, a higher optimal batch size), the phenomenon of rarefaction is crucial to understand that sensitivity reduction. Suppose, with no loss of generality, that an experimental individual test consists in determining if the amount of substance overpasses some prefixed threshold l. For a pooled sample of size n, the amount of substance of interest is represented by (Y1, … , Yn), with mean (Formula Presented) and maximum Mn. The goal is to know if any of the individual samples exceeds the threshold l, that is, Mn > l. It is shown that the dependence between (Formula Presented) and Mn has a crucial role in deciding the use of group testing since a higher dependence corresponds to more information about Mn given by the observed value of (Formula Presented).eng
dc.description.sponsorshipThe authors thank the referees for their very useful comments. Research partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal-FCT under the project PEst-OE/MAT/UI0006/2011.
dc.identifier.citationMartins, J.P., Santos, R., Sousa, R. (2014). Testing the Maximum by the Mean in Quantitative Group Tests. In: Pacheco, A., Santos, R., Oliveira, M., Paulino, C. (eds) New Advances in Statistical Modeling and Applications. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05323-3_5.
dc.identifier.doi10.1007/978-3-319-05323-3_5
dc.identifier.eissn2194-7775
dc.identifier.isbn9783319053226
dc.identifier.isbn9783319053233
dc.identifier.issn2194-7767
dc.identifier.urihttp://hdl.handle.net/10400.8/13517
dc.language.isoeng
dc.peerreviewedyes
dc.publisherSpringer Nature
dc.relationStrategic Project - UI 6 - 2011-2012
dc.relation.hasversionhttps://link.springer.com/chapter/10.1007/978-3-319-05323-3_5
dc.relation.ispartofStudies in Theoretical and Applied Statistics
dc.relation.ispartofNew Advances in Statistical Modeling and Applications
dc.rights.uriN/A
dc.subjectIndividual Test
dc.subjectInfected Individual
dc.subjectPareto Distribution
dc.subjectPool Sample
dc.subjectSample Maximum
dc.titleTesting the Maximum by the Mean in Quantitative Group Testseng
dc.typebook part
dspace.entity.typePublication
oaire.awardTitleStrategic Project - UI 6 - 2011-2012
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/PEst-OE%2FMAT%2FUI0006%2F2011/PT
oaire.citation.endPage63
oaire.citation.startPage55
oaire.citation.titleStudies in Theoretical and Applied Statistics, Selected Papers of the Statistical Societies
oaire.fundingStream6817 - DCRRNI ID
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
person.familyNameOliveira Martins
person.familyNameSantos
person.givenNameJoão Paulo
person.givenNameRui
person.identifier1051057
person.identifier.ciencia-id7610-8B27-8044
person.identifier.orcid0000-0002-0474-1397
person.identifier.orcid0000-0002-7371-363X
person.identifier.ridC-1873-2015
person.identifier.scopus-author-id56979441000
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
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Group testing, introduced by Dorfman in 1943, increases the efficiency of screening individuals for low prevalence diseases. A wider use of this kind of methodology is restricted by the loss of sensitivity inherent to the mixture of samples. Moreover, as this methodology attains greater cost reduction in the cases of lower prevalence (and, consequently, a higher optimal batch size), the phenomenon of rarefaction is crucial to understand that sensitivity reduction. Suppose, with no loss of generality, that an experimental individual test consists in determining if the amount of substance overpasses some prefixed threshold l. For a pooled sample of size n, the amount of substance of interest is represented by (Y1, … , Yn), with mean (Formula Presented) and maximum Mn. The goal is to know if any of the individual samples exceeds the threshold l, that is, Mn > l. It is shown that the dependence between (Formula Presented) and Mn has a crucial role in deciding the use of group testing since a higher dependence corresponds to more information about Mn given by the observed value of (Formula Presented).
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