IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i3p51-d1685719.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/3/51/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/3/51/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maarten Ijzerman & Lotte Steuten, 2011. "Early assessment of medical technologies to inform product development and market access," Applied Health Economics and Health Policy, Springer, vol. 9(5), pages 331-347, September.
    2. Claire Copeland & Britta Turner & Gareth Powells & Kevin Wilson, 2022. "In Search of Complementarity: Insights from an Exercise in Quantifying Qualitative Energy Futures," Energies, MDPI, vol. 15(15), pages 1-21, July.
    3. Robert Stewart & Marie Urban & Samantha Duchscherer & Jason Kaufman & April Morton & Gautam Thakur & Jesse Piburn & Jessica Moehl, 2016. "A Bayesian machine learning model for estimating building occupancy from open source data," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(3), pages 1929-1956, April.
    4. Nicholas M. Kiefer, 2011. "Default estimation, correlated defaults, and expert information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 173-192, March.
    5. Ross Gruetzemacher & Kang Bok Lee & David Paradice, 2024. "Calibration training for improving probabilistic judgments using an interactive app," Futures & Foresight Science, John Wiley & Sons, vol. 6(2), June.
    6. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "How Experience Confirms the Gambler's Fallacy when Sample Size is Neglected," OSF Preprints m5xsk, Center for Open Science.
    7. Dai, Min & Jia, Yanwei & Kou, Steven, 2021. "The wisdom of the crowd and prediction markets," Journal of Econometrics, Elsevier, vol. 222(1), pages 561-578.
    8. A Zuashkiani & D Banjevic & A K S Jardine, 2009. "Estimating parameters of proportional hazards model based on expert knowledge and statistical data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1621-1636, December.
    9. K J Wilson & M Farrow, 2010. "Bayes linear kinematics in the analysis of failure rates and failure time distributions," Journal of Risk and Reliability, , vol. 224(4), pages 309-321, December.
    10. Ibsen Chivatá Cárdenas & Saad S.H. Al‐Jibouri & Johannes I.M. Halman & Frits A. van Tol, 2014. "Modeling Risk‐Related Knowledge in Tunneling Projects," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 323-339, February.
    11. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
    12. Nicholas M. Kiefer, 2017. "Correlated defaults, temporal correlation, expert information and predictability of default rates," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 699-712, October.
    13. Azamat Abdymomunov & Sharon Blei & Bakhodir Ergashev, 2015. "Integrating Stress Scenarios into Risk Quantification Models," Journal of Financial Services Research, Springer;Western Finance Association, vol. 47(1), pages 57-79, February.
    14. Clancy, Damian & Tanner, Jason E. & McWilliam, Stephen & Spencer, Matthew, 2010. "Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo," Ecological Modelling, Elsevier, vol. 221(10), pages 1337-1347.
    15. Alfredo Bateman y Javier E. Martinez & Javier Esteban Martinez, 2010. "Cuaderno 4: Análisis de las fuentes de oferta y demanda en el mercado de divisas," Cuadernos de Desarrollo Económico 7586, Secretaría Distrital de Desarrollo Económico.
    16. Nicholas Longford, 2014. "Policy-related small-area estimation," Economics Working Papers 1427, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Wilson, Kevin J., 2017. "An investigation of dependence in expert judgement studies with multiple experts," International Journal of Forecasting, Elsevier, vol. 33(1), pages 325-336.
    18. Meng, Xiaochun & Taylor, James W., 2022. "Comparing probabilistic forecasts of the daily minimum and maximum temperature," International Journal of Forecasting, Elsevier, vol. 38(1), pages 267-281.
    19. Fadlalla Elfadaly & Paul Garthwaite, 2013. "Eliciting Dirichlet and Connor–Mosimann prior distributions for multinomial models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(4), pages 628-646, November.
    20. Constantinou Anthony Costa & Fenton Norman Elliott, 2012. "Solving the Problem of Inadequate Scoring Rules for Assessing Probabilistic Football Forecast Models," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(1), pages 1-14, March.

    More about this item

    Keywords

    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:51-:d:1685719. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.