Multiple test procedures for identifying the maximum safe dose

Ajit C. Tamhane; Charles W. Dunnett; John W. Green; Jeffrey D. Wetherington

doi:10.1198/016214501753208546

Multiple test procedures for identifying the maximum safe dose

Ajit C. Tamhane^*, Charles W. Dunnett, John W. Green, Jeffrey D. Wetherington

^*Corresponding author for this work

Industrial Engineering and Management Sciences

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We consider dose response studies for safety assessment of crop protection compounds and drugs, and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence. The focus is on step-down (SD) multiple test procedures for identifying the maximum safe dose. We propose two classes of contrasts among the dose means as test statistics for these procedures: pairwise contrasts (PC) and Helmert contrasts (HC). The first procedure (SD2PC) consists of a sequence of ordinary t tests and is thus easy to apply, but it can have very low power for certain step response functions. The second procedure (SD1HC) does not suffer from this drawback, but it requires a weak monotonicity assumption for its mathematical validity. The powers of SD2PC and SD1HC are studied via Monte Carlo simulation. We recommend SD2PC for linear response functions and SD1HC for step response functions. The procedures are illustrated by applying them to data from an aquatic toxicity laboratory experiment conducted to assess the safe level of a pesticide.

Original language	English (US)
Pages (from-to)	835-843
Number of pages	9
Journal	Journal of the American Statistical Association
Volume	96
Issue number	455
DOIs	https://doi.org/10.1198/016214501753208546
State	Published - Sep 1 2001

Funding

Ajit C. Tame iPshfraeo,nDspaseortormSf tieacandtsDitset partment of Inustdrial Engineegr&iMnanagement ScienceNorths,western Ursnit, yive Enstovn, IaL6280. 0Charles W. Dunnett is Professor Emeritus, Department of Mathematics & Statistics and Dpartmente of CliniacEpildemiology & Bio- stistics,taMcMaster Urnts, yHamiltoiivn,eOntario L8S 4K1, Canada. John W. Green is Principal Reseh BaorisscttaiDctPniiuSoatna,H,flteehandtay EvironnmentExcellenceCent,eHaskellr LaboratoryforToxicology&Inus-d trial Medicine, Nwre, kDEa19714. JfeyrD.feWeertinghton is Di, Nornector Clinical/Phase I Biometrics, DuPont PhaeticalsrumComa,cWpimlaingtonn, y DE 19880. The authors thank Brent Logan, for suggesting the forumlation of hypotheses given in Section 8, and two editors and the rereffeeomsrany comntsmanseguedsogts. iThnis reasrwascesuphported in part by a grant from the DuPont Agriculturl Proaducts Dvisioni.

Keywords

Dose response
Familywise error rate
Minimum unsafe dose
Multiple comparisons
Multivariate
Step-down multiple testing procedure
T-distribution
Toxicology

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1198/016214501753208546

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@article{d2240c92b6ae444e97fbd99380340409,

title = "Multiple test procedures for identifying the maximum safe dose",

abstract = "We consider dose response studies for safety assessment of crop protection compounds and drugs, and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence. The focus is on step-down (SD) multiple test procedures for identifying the maximum safe dose. We propose two classes of contrasts among the dose means as test statistics for these procedures: pairwise contrasts (PC) and Helmert contrasts (HC). The first procedure (SD2PC) consists of a sequence of ordinary t tests and is thus easy to apply, but it can have very low power for certain step response functions. The second procedure (SD1HC) does not suffer from this drawback, but it requires a weak monotonicity assumption for its mathematical validity. The powers of SD2PC and SD1HC are studied via Monte Carlo simulation. We recommend SD2PC for linear response functions and SD1HC for step response functions. The procedures are illustrated by applying them to data from an aquatic toxicity laboratory experiment conducted to assess the safe level of a pesticide.",

keywords = "Dose response, Familywise error rate, Minimum unsafe dose, Multiple comparisons, Multivariate, Step-down multiple testing procedure, T-distribution, Toxicology",

author = "Tamhane, \{Ajit C.\} and Dunnett, \{Charles W.\} and Green, \{John W.\} and Wetherington, \{Jeffrey D.\}",

note = "Funding Information: Ajit C. Tame iPshfraeo,nDspaseortormSf tieacandtsDitset partment of Inustdrial Engineegr\&iMnanagement ScienceNorths,western Ursnit, yive Enstovn, IaL6280. 0Charles W. Dunnett is Professor Emeritus, Department of Mathematics \& Statistics and Dpartmente of CliniacEpildemiology \& Bio- stistics,taMcMaster Urnts, yHamiltoiivn,eOntario L8S 4K1, Canada. John W. Green is Principal Reseh BaorisscttaiDctPniiuSoatna,H,flteehandtay EvironnmentExcellenceCent,eHaskellr LaboratoryforToxicology\&Inus-d trial Medicine, Nwre, kDEa19714. JfeyrD.feWeertinghton is Di, Nornector Clinical/Phase I Biometrics, DuPont PhaeticalsrumComa,cWpimlaingtonn, y DE 19880. The authors thank Brent Logan, for suggesting the forumlation of hypotheses given in Section 8, and two editors and the rereffeeomsrany comntsmanseguedsogts. iThnis reasrwascesuphported in part by a grant from the DuPont Agriculturl Proaducts Dvisioni.",

year = "2001",

month = sep,

day = "1",

doi = "10.1198/016214501753208546",

language = "English (US)",

volume = "96",

pages = "835--843",

journal = "Journal of the American Statistical Association",

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T1 - Multiple test procedures for identifying the maximum safe dose

AU - Tamhane, Ajit C.

AU - Dunnett, Charles W.

AU - Green, John W.

AU - Wetherington, Jeffrey D.

N1 - Funding Information: Ajit C. Tame iPshfraeo,nDspaseortormSf tieacandtsDitset partment of Inustdrial Engineegr&iMnanagement ScienceNorths,western Ursnit, yive Enstovn, IaL6280. 0Charles W. Dunnett is Professor Emeritus, Department of Mathematics & Statistics and Dpartmente of CliniacEpildemiology & Bio- stistics,taMcMaster Urnts, yHamiltoiivn,eOntario L8S 4K1, Canada. John W. Green is Principal Reseh BaorisscttaiDctPniiuSoatna,H,flteehandtay EvironnmentExcellenceCent,eHaskellr LaboratoryforToxicology&Inus-d trial Medicine, Nwre, kDEa19714. JfeyrD.feWeertinghton is Di, Nornector Clinical/Phase I Biometrics, DuPont PhaeticalsrumComa,cWpimlaingtonn, y DE 19880. The authors thank Brent Logan, for suggesting the forumlation of hypotheses given in Section 8, and two editors and the rereffeeomsrany comntsmanseguedsogts. iThnis reasrwascesuphported in part by a grant from the DuPont Agriculturl Proaducts Dvisioni.

PY - 2001/9/1

Y1 - 2001/9/1

N2 - We consider dose response studies for safety assessment of crop protection compounds and drugs, and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence. The focus is on step-down (SD) multiple test procedures for identifying the maximum safe dose. We propose two classes of contrasts among the dose means as test statistics for these procedures: pairwise contrasts (PC) and Helmert contrasts (HC). The first procedure (SD2PC) consists of a sequence of ordinary t tests and is thus easy to apply, but it can have very low power for certain step response functions. The second procedure (SD1HC) does not suffer from this drawback, but it requires a weak monotonicity assumption for its mathematical validity. The powers of SD2PC and SD1HC are studied via Monte Carlo simulation. We recommend SD2PC for linear response functions and SD1HC for step response functions. The procedures are illustrated by applying them to data from an aquatic toxicity laboratory experiment conducted to assess the safe level of a pesticide.

AB - We consider dose response studies for safety assessment of crop protection compounds and drugs, and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence. The focus is on step-down (SD) multiple test procedures for identifying the maximum safe dose. We propose two classes of contrasts among the dose means as test statistics for these procedures: pairwise contrasts (PC) and Helmert contrasts (HC). The first procedure (SD2PC) consists of a sequence of ordinary t tests and is thus easy to apply, but it can have very low power for certain step response functions. The second procedure (SD1HC) does not suffer from this drawback, but it requires a weak monotonicity assumption for its mathematical validity. The powers of SD2PC and SD1HC are studied via Monte Carlo simulation. We recommend SD2PC for linear response functions and SD1HC for step response functions. The procedures are illustrated by applying them to data from an aquatic toxicity laboratory experiment conducted to assess the safe level of a pesticide.

KW - Dose response

KW - Familywise error rate

KW - Minimum unsafe dose

KW - Multiple comparisons

KW - Multivariate

KW - Step-down multiple testing procedure

KW - T-distribution

KW - Toxicology

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JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

IS - 455

ER -

Multiple test procedures for identifying the maximum safe dose

Abstract

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Keywords

ASJC Scopus subject areas

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