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A Bayesian Sample Size Estimation Procedure Based on a B-Splines Semiparametric Elicitation Method

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  • Danila Azzolina

    (Unit of Biostatistics, Epidemiology and Public Health, Department of Cardiac Thoracic Vascular Sciences and Public Health, University of Padova, 35122 Padua, Italy
    Department of Environmental and Preventive Science, University of Ferrara, 44121 Ferrara, Italy)

  • Paola Berchialla

    (Department of Clinical and Biological Sciences, University of Torino, 10124 Turin, Italy)

  • Silvia Bressan

    (Department of Pediatrics, University of Padova, 35122 Padua, Italy)

  • Liviana Da Dalt

    (Department of Pediatrics, University of Padova, 35122 Padua, Italy)

  • Dario Gregori

    (Unit of Biostatistics, Epidemiology and Public Health, Department of Cardiac Thoracic Vascular Sciences and Public Health, University of Padova, 35122 Padua, Italy)

  • Ileana Baldi

    (Unit of Biostatistics, Epidemiology and Public Health, Department of Cardiac Thoracic Vascular Sciences and Public Health, University of Padova, 35122 Padua, Italy)

Abstract

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines.

Suggested Citation

  • Danila Azzolina & Paola Berchialla & Silvia Bressan & Liviana Da Dalt & Dario Gregori & Ileana Baldi, 2022. "A Bayesian Sample Size Estimation Procedure Based on a B-Splines Semiparametric Elicitation Method," IJERPH, MDPI, vol. 19(21), pages 1-15, October.
    • Handle: RePEc:gam:jijerp:v:19:y:2022:i:21:p:14245-:d:959249
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    References listed on IDEAS

    as
    1. 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.
    2. Jeremy E. Oakley & Anthony O'Hagan, 2007. "Uncertainty in prior elicitations: a nonparametric approach," Biometrika, Biometrika Trust, vol. 94(2), pages 427-441.
    3. Bornkamp, Björn & Ickstadt, Katja, 2009. "A Note on B-Splines for Semiparametric Elicitation," The American Statistician, American Statistical Association, vol. 63(4), pages 373-377.
    4. Beat Neuenschwander & Sebastian Weber & Heinz Schmidli & Anthony O'Hagan, 2020. "Predictively consistent prior effective sample sizes," Biometrics, The International Biometric Society, vol. 76(2), pages 578-587, June.
    5. John Paul Gosling, 2018. "SHELF: The Sheffield Elicitation Framework," International Series in Operations Research & Management Science, in: Luis C. Dias & Alec Morton & John Quigley (ed.), Elicitation, chapter 0, pages 61-93, Springer.
    6. 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.
    7. 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.
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