VNM: An R package for finding multiple-objective optimal designs for the 4-parameter logistic model

Seung Won Hyun, Weng Kee Wong, Yarong Yang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A multiple-objective optimal design is useful for dose-response studies because it can incorporate several objectives at the design stage. Objectives can be of varying interests and a properly constructed multiple-objective optimal design can provide user-specified efficiencies, delivering higher efficiencies for the more important objectives. In this work, we introduce the VNM package written in R for finding 3-objective locally optimal designs for the 4-parameter logistic (4PL) model widely used in education, bioscience and in the manufacturing industry. The package implements the methodology to construct multiple-objective optimal designs in Hyun and Wong (2015). As illustrative examples, we focus on a biomedical application where our objectives are to estimate: (1) the shape of the dose-response curve, (2) the median effective dose level (ED50) and (3) the minimum effective dose level (MED) in the 4PL model. Our VNM package uses a state-of-the-art algorithm to generate multiple-objective optimal designs that meet the user-specified efficiency requirement for each objective, provides tools for calculating the efficiency of the generated design under each objective and also a plot for confirming optimality of the VNM-generated design. The package can also be used to determine an optimal scheme for allocating subjects to the various doses when the number and doses of the drug are fixed in advance.

Original languageEnglish (US)
JournalJournal of Statistical Software
StatePublished - 2018


  • C-optimal design
  • Compound optimal design
  • Dose-response study
  • Equivalence theorem
  • R
  • Target dose

ASJC Scopus subject areas

  • Software
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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