Whitehead John, Valdés-Márquez Elsa, Johnson Patrick, Graham Gordon
Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.
Stat Med. 2008 Jun 15;27(13):2307-27. doi: 10.1002/sim.3140.
This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored.
本文提出了一种用于确定临床试验样本量的简单贝叶斯方法。要求试验规模足够大，以确保所收集的数据能够提供令人信服的证据，证明实验性治疗优于对照治疗，或者证明其未能在临床上有意义的差异方面比对照有所改善。该方法类似于该问题的标准频率论公式，实际上在某些涉及“无信息”先验信息的情况下，它会得出相同的答案。特别是，与许多用于确定样本量的贝叶斯方法不同，该方法使用了一个备择假设，即实验性治疗比对照治疗好一定的幅度。该方法是在检验单个二元观测流是否与给定成功率p(0)一致的背景下引入的。接下来考虑比较两个独立的正态分布响应流的情况，首先假设它们的共同方差已知，然后考虑方差未知的情况。最后，探讨了根据得分统计量的渐近性质收集和分析大样本的更一般情况。
