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A Bayesian method of sample size determination with practical applications

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  • S. K. Sahu
  • T. M. F. Smith

Abstract

Summary. The problem motivating the paper is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation‐based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution that is used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non‐informative prior distributions lead to very small sample sizes. In contrast, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods that are developed are quite general and can be applied to other sample size determination problems. Some numerical illustrations which bring out many other aspects of the optimum sample size are given.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssa:v:169:y:2006:i:2:p:235-253
    DOI: 10.1111/j.1467-985X.2006.00408.x
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    References listed on IDEAS

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    1. David J. Laws & Anthony O'Hagan, 2000. "Bayesian inference for rare errors in populations with unequal unit sizes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(4), pages 577-590.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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