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Elicitation of Priors for the Weibull Distribution

Author

Listed:
  • Purvi Prajapati

    (Eli Lilly & Company, Indianapolis, IN 46285, USA)

  • James D. Stamey

    (Department of Statistical Science, Baylor University, One Bear Place #97140, Waco, TX 76798, USA)

  • David Kahle

    (Department of Statistical Science, Baylor University, One Bear Place #97140, Waco, TX 76798, USA)

  • John W. Seaman

    (Department of Statistical Science, Baylor University, One Bear Place #97140, Waco, TX 76798, USA)

  • Zachary M. Thomas

    (Eli Lilly & Company, Indianapolis, IN 46285, USA)

  • Michael Sonksen

    (Eli Lilly & Company, Indianapolis, IN 46285, USA)

Abstract

Bayesian methods have attracted increasing interest in the design and analysis of clinical trials. Many of these clinical trials investigate time-to-event endpoints. The Weibull distribution is often used in survival and reliability analysis to model time-to-event data. We propose a process to elicit information about the parameters of the Weibull distribution for pharmaceutical applications. Our method is based on an expert’s answers to questions about the median and upper quartile of the distribution. Using the elicited information, a joint prior is constructed for the median and upper quartile of the Weibull distribution, which induces a joint prior distribution on the shape and rate parameters of the Weibull. To illustrate, we apply our elicitation methodology to a pediatric clinical trial, where information is elicited from a subject-matter expert for the control arm.

Suggested Citation

  • Purvi Prajapati & James D. Stamey & David Kahle & John W. Seaman & Zachary M. Thomas & Michael Sonksen, 2025. "Elicitation of Priors for the Weibull Distribution," Stats, MDPI, vol. 8(3), pages 1-14, June.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:51-:d:1685719
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    References listed on IDEAS

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    1. repec:plo:pone00:0120981 is not listed on IDEAS
    2. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
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