Are the tests overpowered or underpowered? A unified solution to correctly specify type I errors in design of clinical trials for two sample proportions

As one of the most commonly used data types, methods in testing or designing a trial for binary endpoints from two independent populations are still being developed until recently. However, the power and the minimum required sample size comparisons between different tests may not be valid if their t...

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Bibliographic Details
Published in:Statistics in medicine 2024-04, Vol.43 (9), p.1688-1707
Main Authors: Liu, Peiran, Chen, Ming‐Hui, Sinks, Susie, Sun, Peng
Format: Article
Language:English
Subjects:
actual type I error
Algorithms
Bayes Theorem
Bayesian analysis
Clinical outcomes
Clinical trials
decision framework
exact calculations
Humans
noninferiority trial
Probability
Research Design
Sample Size
superiority trial
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Summary:As one of the most commonly used data types, methods in testing or designing a trial for binary endpoints from two independent populations are still being developed until recently. However, the power and the minimum required sample size comparisons between different tests may not be valid if their type I errors are not controlled at the same level. In this article, we unify all related testing procedures into a decision framework, including both frequentist and Bayesian methods. Sufficient conditions of the type I error attained at the boundary of hypotheses are derived, which help reduce the magnitude of the exact calculations and lay out a foundation for developing computational algorithms to correctly specify the actual type I error. The efficient algorithms are thus proposed to calculate the cutoff value in a deterministic decision rule and the probability value in a randomized decision rule, such that the actual type I error is under but closest to, or equal to, the intended level, respectively. The algorithm may also be used to calculate the sample size to achieve the prespecified type I error and power. The usefulness of the proposed methodology is further demonstrated in the power calculation for designing superiority and noninferiority trials.
ISSN:0277-6715
1097-0258
DOI:10.1002/sim.10005