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An Optimizing Up-and-Down Design

  • Euloge E. Kpamegan
  • Nancy Flournoy
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

Abstract

Assume that the probability of success is unimodal as a function of dose. Take the response to be binary and the possible treatment space to be a lattice. The Optimizing Up-and-Down Design allocates treatments to pairs of subjects in a way that causes the treatment distribution to cluster around the treatment with maximum success probability. This procedure is constructed to use accruing information to limit the number of patients that are exposed to doses with high probabilities of failure. The Optimizing Up-and-Down Design is motivated by Kiefer and Wolfowitz’s stochastic approximation procedure. In this paper, we compare its performance to stochastic approximation. As an estimator of the best dose, simulation studies demonstrate that the mode of the empirical treatment distribution using the Optimizing Up-and-Down Design converges faster than does the usual estimator using stochastic approximation.

Keywords

constant gain stochastic algorithm Markov chains phase I/II clinical trial random walk designs stationary treatment distribution stochastic approximation 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Euloge E. Kpamegan
    • 1
  • Nancy Flournoy
    • 1
  1. 1.Department of Mathematics and StatisticsAmerican UniversityUSA

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