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Determination of the optimal sample size for a clinical trial accounting for the population size
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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 ISSN 0323-3847.
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Official URL: http://dx.doi.org/10.1002/bimj.201500228
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 | ||||||||||
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Subjects: | Q Science > QA Mathematics R Medicine > R Medicine (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||||||||
Date of first compliant deposit: | 26 August 2016 | ||||||||||
Date of first compliant Open Access: | 26 August 2016 | ||||||||||
Funder: | Seventh Framework Programme (European Commission) (FP7) | ||||||||||
Grant number: | FP HEALTH 2013 – 602144 | ||||||||||
Open Access Version: |
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