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

Author

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  • Hyun Seung Won

    (Department of Statistics, North Dakota State University, Fargo, ND 58102, USA)

  • Wong Weng Kee

    (Department of Biostatistics, University of California, Los Angeles, Los Angeles, CA, USA)

Abstract

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.

Suggested Citation

  • Hyun Seung Won & Wong Weng Kee, 2015. "Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels," The International Journal of Biostatistics, De Gruyter, vol. 11(2), pages 253-271, November.
    • Handle: RePEc:bpj:ijbist:v:11:y:2015:i:2:p:253-271:n:7
    DOI: 10.1515/ijb-2015-0044
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    References listed on IDEAS

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    1. Ritz, Christian & Streibig, Jens C., 2005. "Bioassay Analysis Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i05).
    2. Min Yang & Stefanie Biedermann & Elina Tang, 2013. "On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1411-1420, December.
    3. Miller, Frank & Dette, Holger & Guilbaud, Olivier, 2007. "Optimal designs for estimating the interesting part of a dose-effect curve," Technical Reports 2007,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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