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A Review of Bayesian Perspectives on Sample Size Derivation for Confirmatory Trials

Lookup NU author(s): Dr Michael GraylingORCiD, Professor James WasonORCiD



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


© 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.Sample size derivation is a crucial element of planning any confirmatory trial. The required sample size is typically derived based on constraints on the maximal acceptable Type I error rate and minimal desired power. Power depends on the unknown true effect and tends to be calculated either for the smallest relevant effect or a likely point alternative. The former might be problematic if the minimal relevant effect is close to the null, thus requiring an excessively large sample size, while the latter is dubious since it does not account for the a priori uncertainty about the likely alternative effect. A Bayesian perspective on sample size derivation for a frequentist trial can reconcile arguments about the relative a priori plausibility of alternative effects with ideas based on the relevance of effect sizes. Many suggestions as to how such “hybrid” approaches could be implemented in practice have been put forward. However, key quantities are often defined in subtly different ways in the literature. Starting from the traditional entirely frequentist approach to sample size derivation, we derive consistent definitions for the most commonly used hybrid quantities and highlight connections, before discussing and demonstrating their use in sample size derivation for clinical trials.

Publication metadata

Author(s): Kunzmann K, Grayling MJ, Lee KM, Robertson DS, Rufibach K, Wason JMS

Publication type: Article

Publication status: Published

Journal: American Statistician

Year: 2021

Volume: 75

Issue: 4

Pages: 424-432

Online publication date: 22/04/2021

Acceptance date: 01/03/2021

Date deposited: 07/06/2021

ISSN (print): 0003-1305

ISSN (electronic): 1537-2731

Publisher: American Statistical Association


DOI: 10.1080/00031305.2021.1901782


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