IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v72y2014i2p133-151.html
   My bibliography  Save this article

Bayesian-frequentist sample size determination: a game of two priors

Author

Listed:
  • Pierpaolo Brutti
  • Fulvio Santis
  • Stefania Gubbiotti

Abstract

Experimental design represents the typical context in which the interplay between Bayesian and frequentist methodology is natural and useful. Before the data are observed, it is licit and unavoidable even for a Bayesian statistician to take into account sample variability for the evaluation of statistical procedures and for decision making. At the same time, design planning fatally involves a number of pre-experimental choices that even a frequentist statistician is forced to make, preferably by exploiting external sources of knowledge. In this paper we discuss this mutual exchange between Bayesian and frequentist methodology, with specific focus on the primary crucial aspect of experimental designs, that is sample size determination (SSD). We review this topic by highlighting how the interplay between two prior distributions helps in managing the close relationship between the two approaches. Although the distinction between decisional and performance-based methods for Bayesian SSD is discussed, the main interest of this article is on the latter. We propose a general framework that includes several performance-based methods as special cases and thus makes the comparison of their characteristics easier. Finally, we extend the overview to robust methods for Bayesian SSD that allow to deal with the critical issue of sensitivity to prior elicitation. Illustrative examples are provided for normal models. Copyright Sapienza Università di Roma 2014

Suggested Citation

  • Pierpaolo Brutti & Fulvio Santis & Stefania Gubbiotti, 2014. "Bayesian-frequentist sample size determination: a game of two priors," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 133-151, August.
    • Handle: RePEc:spr:metron:v:72:y:2014:i:2:p:133-151
    DOI: 10.1007/s40300-014-0043-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-014-0043-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s40300-014-0043-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. De Santis, Fulvio, 2006. "Sample Size Determination for Robust Bayesian Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 278-291, March.
    2. S. K. Sahu & T. M. F. Smith, 2006. "A Bayesian method of sample size determination with practical applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 235-253, March.
    3. Anthony O’Hagan & John W. Stevens, 2001. "Bayesian Assessment of Sample Size for Clinical Trials of Cost-Effectiveness," Medical Decision Making, , vol. 21(3), pages 219-230, May.
    4. Fulvio De Santis, 2007. "Using historical data for Bayesian sample size determination," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 95-113, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ali Karimnezhad & Ahmad Parsian, 2018. "Most stable sample size determination in clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 437-454, August.
    2. Fulvio De Santis & Stefania Gubbiotti, 2021. "On the predictive performance of a non-optimal action in hypothesis testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 689-709, June.
    3. Fulvio De Santis & Stefania Gubbiotti, 2021. "Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials," IJERPH, MDPI, vol. 18(2), pages 1-11, January.
    4. Armando Turchetta & Erica E. M. Moodie & David A. Stephens & Sylvie D. Lambert, 2023. "Bayesian sample size calculations for comparing two strategies in SMART studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2489-2502, September.
    5. Filip Melinscak & Dominik R Bach, 2020. "Computational optimization of associative learning experiments," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-23, January.

    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. Fulvio De Santis & Stefania Gubbiotti, 2021. "On the predictive performance of a non-optimal action in hypothesis testing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 689-709, June.
    2. Jörg Martin & Clemens Elster, 2021. "The variation of the posterior variance and Bayesian sample size determination," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1135-1155, October.
    3. Bhramar Mukherjee & Jaeil Ahn & Stephen B. Gruber & Malay Ghosh & Nilanjan Chatterjee, 2010. "Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis," Biometrics, The International Biometric Society, vol. 66(3), pages 934-948, September.
    4. Fulvio De Santis & Maria Fasciolo & Stefania Gubbiotti, 2013. "Predictive control of posterior robustness for sample size choice in a Bernoulli model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(3), pages 319-340, August.
    5. Jing Zhang & Yunzhi Kong & A. John Bailer & Zheng Zhu & Byran Smucker, 2022. "Incorporating Historical Data When Determining Sample Size Requirements for Aquatic Toxicity Experiments," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 544-561, September.
    6. Armando Turchetta & Erica E. M. Moodie & David A. Stephens & Sylvie D. Lambert, 2023. "Bayesian sample size calculations for comparing two strategies in SMART studies," Biometrics, The International Biometric Society, vol. 79(3), pages 2489-2502, September.
    7. P. Brutti & F. Santis & S. Gubbiotti, 2013. "Robust Bayesian monitoring of sequential trials," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 81-95, June.
    8. Ali Karimnezhad & Ahmad Parsian, 2018. "Most stable sample size determination in clinical trials," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 437-454, August.
    9. Hui Quan & Xiaofei Chen & Xun Chen & Xiaodong Luo, 2022. "Assessments of Conditional and Unconditional Type I Error Probabilities for Bayesian Hypothesis Testing with Historical Data Borrowing," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(1), pages 139-157, April.
    10. A. Gafni & S. D. Walter & S. Birch & P. Sendi, 2008. "An opportunity cost approach to sample size calculation in cost‐effectiveness analysis," Health Economics, John Wiley & Sons, Ltd., vol. 17(1), pages 99-107, January.
    11. Wenqing Li & Ming-Hui Chen & Xiaojing Wang & Dipak K. Dey, 2018. "Bayesian Design of Non-inferiority Clinical Trials Via the Bayes Factor," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(2), pages 439-459, August.
    12. Boris G. Zaslavsky, 2013. "Bayesian Hypothesis Testing in Two-Arm Trials with Dichotomous Outcomes," Biometrics, The International Biometric Society, vol. 69(1), pages 157-163, March.
    13. Andrew R. Willan & Matthew E. Kowgier, 2008. "Cost‐effectiveness analysis of a multinational RCT with a binary measure of effectiveness and an interacting covariate," Health Economics, John Wiley & Sons, Ltd., vol. 17(7), pages 777-791, July.
    14. Ming-Hui Chen & Joseph G. Ibrahim & Peter Lam & Alan Yu & Yuanye Zhang, 2011. "Bayesian Design of Noninferiority Trials for Medical Devices Using Historical Data," Biometrics, The International Biometric Society, vol. 67(3), pages 1163-1170, September.
    15. Daniel P Beavers & James D Stamey, 2018. "Bayesian sample size determination for cost-effectiveness studies with censored data," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-16, January.
    16. Alan Brennan & Samer A. Kharroubi, 2007. "Expected value of sample information for Weibull survival data," Health Economics, John Wiley & Sons, Ltd., vol. 16(11), pages 1205-1225, November.
    17. Alan Brennan & Samer A. Kharroubi, 2007. "Expected value of sample information for Weibull survival data," Health Economics, John Wiley & Sons, Ltd., vol. 16(11), pages 1205-1225.
    18. Fulvio De Santis, 2007. "Using historical data for Bayesian sample size determination," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 95-113, January.
    19. Danila Azzolina & Giulia Lorenzoni & Silvia Bressan & Liviana Da Dalt & Ileana Baldi & Dario Gregori, 2021. "Handling Poor Accrual in Pediatric Trials: A Simulation Study Using a Bayesian Approach," IJERPH, MDPI, vol. 18(4), pages 1-16, February.
    20. Thompson, Nathanael M. & Brorsen, B. Wade & DeVuyst, Eric A. & Lusk, Jayson L., 2016. "Random Sampling of Beef Cattle for Genetic Testing: Optimal Sample Size Determination," 2016 Annual Meeting, February 6-9, 2016, San Antonio, Texas 229195, Southern Agricultural Economics Association.

    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:spr:metron:v:72:y:2014:i:2:p:133-151. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.