Optimal designs for response functions with a downturn

Seung Won Hyun, Min Yang, Nancy Flournoy

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for this situation. A growth model is combined with a death model to allow for the downturn in mean doses. Several different objective functions are studied. When the number of treatments equals the number of parameters, Fisher information is found to be independent of the model of the treatment means and on the magnitudes of the treatments. In general, A- and DA-optimal weights for estimating adjacent mean differences are found analytically for a simple model and numerically for a biologically motivated model. Results on c-optimality are also obtained for estimating the peak dose and the EC50 (the treatment with response half way between the control and the peak response on the increasing portion of the response function). Finally, when interest lies only in the increasing portion of the response function, we propose composite D-optimal designs.

Original languageEnglish (US)
Pages (from-to)559-575
Number of pages17
JournalJournal of Statistical Planning and Inference
Issue number1
StatePublished - Jan 2011
Externally publishedYes


  • A-optimality
  • D-optimality
  • D-optimality
  • Dose-response
  • EC
  • Endocrine-disrupting chemicals
  • Experimental design
  • Laboratory studies
  • Nonlinear response function
  • Optimal weights
  • Peak dose
  • Successive mean differences
  • Toxicological assays

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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