Stallard, Nigel, Miller, Frank, Day, Simon, Hee, Siew Wan, Madan, Jason, Zohar, Sarah and Posch, Martin (2017) Determination of the optimal sample size for a clinical trial accounting for the population size. Biometrical Journal, 59 (4). pp. 609-625. doi:10.1002/bimj.201500228

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Abstract

The problem of choosing a sample size for a clinical trial is a very common one. In some settings, such as rare diseases or other small populations, the large sample sizes usually associated with the standard frequentist approach may be infeasible, suggesting that the sample size chosen should reflect the size of the population under consideration. Incorporation of the population size is possible in a decision-theoretic approach either explicitly by assuming that the population size is fixed and known, or implicitly through geometric discounting of the gain from future patients reflecting the expected population size. This paper develops such approaches. Building on previous work, an asymptotic expression is derived for the sample size for single and two-arm clinical trials in the general case of a clinical trial with a primary endpoint with a distribution of one parameter exponential family form that optimizes a utility function that quantifies the cost and gain per patient as a continuous function of this parameter. It is shown that as the size of the population, N, or expected size, inline image in the case of geometric discounting, becomes large, the optimal trial size is inline image or inline image. The sample size obtained from the asymptotic expression is also compared with the exact optimal sample size in examples with responses with Bernoulli and Poisson distributions, showing that the asymptotic approximations can also be reasonable in relatively small sample sizes.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > R Medicine (General)
Divisions:	Faculty of Medicine > Warwick Medical School
Library of Congress Subject Headings (LCSH):	Clinical trials -- Design -- Research, Bayesian statistical decision theory
Journal or Publication Title:	Biometrical Journal
Publisher:	Wiley-Blackwell Publishing Ltd.
ISSN:	0323-3847
Official Date:	July 2017
Dates:	Date Event July 2017 Published 17 May 2016 Available 9 March 2016 Accepted 28 October 2015 Submitted
Date of first compliant deposit:	26 August 2016
Volume:	59
Number:	4
Page Range:	pp. 609-625
DOI:	10.1002/bimj.201500228
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Seventh Framework Programme (European Commission) (FP7)
Grant number:	FP HEALTH 2013 – 602144
Open Access Version:	Other

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