Robust C-optimal design for estimating multiple EDp under the 4-parameter logistic model

Anqing Zhang, Seung Won Hyun

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


The four-parameter logistic model is often used to describe dose-response functions in many toxicological studies. In this study, under the four-parameter logistic model, optimal designs to estimate the EDp are studied. The EDp is the dose achieving p% of the expected difference between the maximum and the minimum responses. C-optimal design works the best for estimating the EDp, but the best performance is only guaranteed when the goal is for estimating a single EDp. If the c-optimal design for studying a specific EDp is used for studying different EDp values, it may work poorly. This paper shows that the c-optimal design for estimating the EDp truly depends on the value of p under the 4-parameter logistic model. We present a robust c-optimal design that works well for the change in the value of p, so that the design can be used effectively for studying multiple EDp values. In addition, this paper presents a two-stage robust c-optimal design for estimating multiple EDp that is not substantially affected by the mis-specified nominal parameter values.

Original languageEnglish (US)
Pages (from-to)278-288
Number of pages11
JournalStatistics, Optimization and Information Computing
Issue number4
StatePublished - 2016
Externally publishedYes


  • Compound optimal design
  • Dose-response study
  • Equivalence theorem
  • Robust design

ASJC Scopus subject areas

  • Signal Processing
  • Statistics and Probability
  • Information Systems
  • Computer Vision and Pattern Recognition
  • Statistics, Probability and Uncertainty
  • Control and Optimization
  • Artificial Intelligence


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