A review of Bayesian perspectives on sample size derivation for confirmatory trials

TY - JOUR

T1 - A review of Bayesian perspectives on sample size derivation for confirmatory trials

AU - Kunzmann, null

AU - Grayling, null

AU - Lee, Kim May

AU - Robertson, null

AU - Rufibach, null

AU - Wason, null

N1 - Funding Information: This research was supported by the NIHR Cambridge BRC. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care. We thank the reviewers and the associate editor for their constructive comments. Publisher Copyright: © 2021 The Author(s). Published with license by Taylor & Francis Group, LLC.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85104783142&partnerID=8YFLogxK

U2 - 10.1080/00031305.2021.1901782

DO - 10.1080/00031305.2021.1901782

M3 - Article

SN - 0003-1305

VL - 75

SP - 424

EP - 432

JO - AMERICAN STATISTICIAN

JF - AMERICAN STATISTICIAN

IS - 4

ER -