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Dose-Finding Designs: The Role of Convergence Properties

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  • Oron Assaf P.
  • Azriel David
  • Hoff Peter D.

Abstract

It is common for novel dose-finding designs to be presented without a study of their convergence properties. In this article we suggest that examination of convergence is a necessary quality check for dose-finding designs. We present a new convergence proof for a nonparametric family of methods called “interval designs,” under certain conditions on the toxicity-frequency function F. We compare these conditions with the convergence conditions for the popular CRM one-parameter Phase I cancer design, via an innovative numerical sensitivity study generating a diverse sample of dose-toxicity scenarios. Only a small fraction of scenarios meet the Shen-O'Quigley convergence conditions for CRM. Conditions for “interval design” convergence are met more often, but still less than half the time. In the discussion, we illustrate how convergence properties and limitations help provide insight about small-sample behavior.

Suggested Citation

  • Oron Assaf P. & Azriel David & Hoff Peter D., 2011. "Dose-Finding Designs: The Role of Convergence Properties," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-17, October.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:39
    DOI: 10.2202/1557-4679.1298
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    References listed on IDEAS

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    1. Linda M. Haines & Inna Perevozskaya & William F. Rosenberger, 2003. "Bayesian Optimal Designs for Phase I Clinical Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 591-600, September.
    2. Zacks, S. & Rogatko, A. & Babb, J., 1998. "Optimal Bayesian-feasible dose escalation for cancer phase I trials," Statistics & Probability Letters, Elsevier, vol. 38(3), pages 215-220, June.
    3. Ying Kuen Cheung & Rick Chappell, 2002. "A Simple Technique to Evaluate Model Sensitivity in the Continual Reassessment Method," Biometrics, The International Biometric Society, vol. 58(3), pages 671-674, September.
    4. Paoletti, Xavier & O'Quigley, John & Maccario, Jean, 2004. "Design efficiency in dose finding studies," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 197-214, March.
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    Cited by:

    1. Nancy Flournoy & José Moler & Fernando Plo, 2020. "Performance Measures in Dose‐Finding Experiments," International Statistical Review, International Statistical Institute, vol. 88(3), pages 728-751, December.
    2. Azriel, David, 2014. "Optimal sequential designs in phase I studies," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 288-297.
    3. Azriel, David, 2012. "A note on the robustness of the continual reassessment method," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 902-906.

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