Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Seung Won Hyun, Weng Kee Wong

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.

Original languageEnglish (US)
Pages (from-to)253-271
Number of pages19
JournalInternational Journal of Biostatistics
Issue number2
StatePublished - Nov 1 2015
Externally publishedYes


  • approximate design
  • c-optimal design
  • compound optimal design
  • constrained optimal design
  • design efficiency
  • dose-finding study

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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