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Most stable sample size determination in clinical trials

Author

Listed:
  • Ali Karimnezhad

    (K. N. Toosi University of Technology)

  • Ahmad Parsian

    (University of Tehran)

Abstract

This paper is devoted to robust Bayes sample size determination under the quadratic loss function. The idea behind the proposed approach is that the smaller a chosen posterior functional, the more robust the posterior inference. Such desired posterior functional has been taken, in the literature, as the range of posterior mean over a class of priors but we show that dealing with the posterior mean is not the only method leading to an optimal sample size. To provide an alternative approach, we propose implementing most stable rules into the context of sample size determination. We discuss properties of the desired most stable estimate and provide some examples in the normal model. We then compare the proposed approach with that of a recent global robustness study from both numerical and theoretical aspects. We illustrate the practical utility of our proposed method by analyzing a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0419-6
    DOI: 10.1007/s10260-017-0419-6
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    References listed on IDEAS

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    1. Ali Karimnezhad & Ahmad Parsian, 2014. "Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 287-303, July.
    2. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    3. 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.
    4. 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.
    5. Leila Golparvar & Ali Karimnezhad & Ahmad Parsian, 2016. "Bayes and robust Bayes predictions in a subfamily of scale parameters under a precautionary loss function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3970-3992, July.
    6. Meczarski, Marek & Zielinski, Ryszard, 1991. "Stability of the Bayesian estimator of the Poisson mean under the inexactly specified gamma prior," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 329-333, October.
    7. 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.
    8. 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.
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