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The distribution of power-related random variables (and their use in clinical trials)

Author

Listed:
  • Francesco Mariani

    (Sapienza University of Rome)

  • Fulvio De Santis

    (Sapienza University of Rome)

  • Stefania Gubbiotti

    (Sapienza University of Rome)

Abstract

In the hybrid Bayesian-frequentist approach to hypotheses tests, the power function, i.e. the probability of rejecting the null hypothesis, is a random variable and a pre-experimental evaluation of the study is commonly carried out through the so-called probability of success (PoS). PoS is usually defined as the expected value of the random power that is not necessarily a well-representative summary of the entire distribution. Here, we consider the main definitions of PoS and investigate the power related random variables that induce them. We provide general expressions for their cumulative distribution and probability density functions, as well as closed-form expressions when the test statistic is, at least asymptotically, normal. The analysis of such distributions highlights discrepancies in the main definitions of PoS, leading us to prefer the one based on the utility function of the test. We illustrate our idea through an example and an application to clinical trials, which is a framework where PoS is commonly employed.

Suggested Citation

  • Francesco Mariani & Fulvio De Santis & Stefania Gubbiotti, 2024. "The distribution of power-related random variables (and their use in clinical trials)," Statistical Papers, Springer, vol. 65(9), pages 5555-5574, December.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:9:d:10.1007_s00362-024-01599-1
    DOI: 10.1007/s00362-024-01599-1
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    References listed on IDEAS

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    1. 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.
    2. Harlan Campbell & Paul Gustafson, 2023. "Bayes Factors and Posterior Estimation: Two Sides of the Very Same Coin," The American Statistician, Taylor & Francis Journals, vol. 77(3), pages 248-258, July.
    3. Kevin Kunzmann & Michael J. Grayling & Kim May Lee & David S. Robertson & Kaspar Rufibach & James M. S. Wason, 2021. "A Review of Bayesian Perspectives on Sample Size Derivation for Confirmatory Trials," The American Statistician, Taylor & Francis Journals, vol. 75(4), pages 424-432, October.
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