Optimizing a Unimodal Response Function for Binary Variables

  • Janis Hardwick
  • Quentin F. Stout
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)


Several allocation rules are examined for the problem of optimizing a response function for a set of Bernoulli populations, where the population means are assumed to have a strict unimodal structure. This problem arises in dose response settings in clinical trials. The designs are evaluated both on their efficiency in identifying a good population at the end of the experiment, and in their efficiency in sampling from good populations during the trial. A new design, that adapts multi-arm bandit strategies to this unimodal structure, is shown to be superior to the designs previously proposed. The bandit design utilizes approximate Gittin’s indices and shape constrained regression.


adaptive clinical trial dose-response experimental design multi-arm bandit nonparametric Polya urn random walk sequential sampling stochastic approximation unimodal regression up and down 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Janis Hardwick
    • 1
  • Quentin F. Stout
    • 2
  1. 1.Purdue UniversityWest LafayetteUSA
  2. 2.University of MichiganAnn ArborUSA

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