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

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 languageEnglish (US)
Pages (from-to)835-843
Number of pages9
JournalJournal of the American Statistical Association
Issue number455
StatePublished - Sep 1 2001


  • 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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