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Sample Size Requirements for Calibrated Approximate Credible Intervals for Proportions in Clinical Trials

Author

Listed:
  • Fulvio De Santis

    (Dipartimento di Scienze Statistiche, Sapienza University of Rome, Piazzale Aldo Moro n. 5, 00185 Rome, Italy
    These authors contributed equally to this work.)

  • Stefania Gubbiotti

    (Dipartimento di Scienze Statistiche, Sapienza University of Rome, Piazzale Aldo Moro n. 5, 00185 Rome, Italy
    These authors contributed equally to this work.)

Abstract

In Bayesian analysis of clinical trials data, credible intervals are widely used for inference on unknown parameters of interest, such as treatment effects or differences in treatments effects. Highest Posterior Density (HPD) sets are often used because they guarantee the shortest length. In most of standard problems, closed-form expressions for exact HPD intervals do not exist, but they are available for intervals based on the normal approximation of the posterior distribution. For small sample sizes, approximate intervals may be not calibrated in terms of posterior probability, but for increasing sample sizes their posterior probability tends to the correct credible level and they become closer and closer to exact sets. The article proposes a predictive analysis to select appropriate sample sizes needed to have approximate intervals calibrated at a pre-specified level. Examples are given for interval estimation of proportions and log-odds.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jijerp:v:18:y:2021:i:2:p:595-:d:478998
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    References listed on IDEAS

    as
    1. Fulvio De Santis & Marco Perone Pacifico & Valeria Sambucini, 2004. "Optimal predictive sample size for case–control studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 427-441, August.
    2. Sambucini, Valeria, 2019. "Bayesian predictive monitoring with bivariate binary outcomes in phase II clinical trials," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 18-30.
    3. M'Lan, Cyr Emile & Joseph, Lawrence & Wolfson, David B., 2006. "Bayesian Sample Size Determination for Case-Control Studies," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 760-772, June.
    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. 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. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
    7. Fulvio De Santis & Stefania Gubbiotti, 2017. "A decision‐theoretic approach to sample size determination under several priors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(3), pages 282-295, May.
    8. repec:dau:papers:123456789/1908 is not listed on IDEAS
    9. 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.
    Full references (including those not matched with items on IDEAS)

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