Elicitation of Priors for the Weibull Distribution

Purvi Prajapati, James D. Stamey (), David Kahle, John W. Seaman, Zachary M. Thomas and Michael Sonksen
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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

Stats, 2025, vol. 8, issue 3, 1-14

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.

Keywords: Bayesian; time-to-event data (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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