Department of Oncology and Cancer Epidemiology, Clinical Sciences, Lund University and Skåne University Hospital, 221 85 Lund, Sweden.
BMC Med Res Methodol. 2013 Jul 19;13:94. doi: 10.1186/1471-2288-13-94.
One major concern with adaptive designs, such as the sample size adjustable designs, has been the fear of inflating the type I error rate. In (Stat Med 23:1023-1038, 2004) it is however proven that when observations follow a normal distribution and the interim result show promise, meaning that the conditional power exceeds 50%, type I error rate is protected. This bound and the distributional assumptions may seem to impose undesirable restrictions on the use of these designs. In (Stat Med 30:3267-3284, 2011) the possibility of going below 50% is explored and a region that permits an increased sample size without inflation is defined in terms of the conditional power at the interim.
A criterion which is implicit in (Stat Med 30:3267-3284, 2011) is derived by elementary methods and expressed in terms of the test statistic at the interim to simplify practical use. Mathematical and computational details concerning this criterion are exhibited.
Under very general conditions the type I error rate is preserved under sample size adjustable schemes that permit a raise. The main result states that for normally distributed observations raising the sample size when the result looks promising, where the definition of promising depends on the amount of knowledge gathered so far, guarantees the protection of the type I error rate. Also, in the many situations where the test statistic approximately follows a normal law, the deviation from the main result remains negligible. This article provides details regarding the Weibull and binomial distributions and indicates how one may approach these distributions within the current setting.
There is thus reason to consider such designs more often, since they offer a means of adjusting an important design feature at little or no cost in terms of error rate.
自适应设计（如样本量可调设计）的一个主要问题是担心会使Ⅰ型错误率膨胀。然而，在（Stat Med 23:1023-1038, 2004）中证明，当观测值服从正态分布且中期结果显示有希望时，即条件功效超过 50%，则可以保护Ⅰ型错误率。这个界限和分布假设似乎对这些设计的使用施加了不理想的限制。在（Stat Med 30:3267-3284, 2011）中，探索了低于 50%的可能性，并根据中期的条件功效定义了一个允许增加样本量而不膨胀的区域。
通过基本方法推导出一个（Stat Med 30:3267-3284, 2011）中隐含的标准，并以中期的检验统计量表示，以简化实际使用。展示了关于该标准的数学和计算细节。
在非常一般的条件下，允许增加样本量的样本量可调方案可以保持Ⅰ型错误率。主要结果表明，对于正态分布的观测值，当结果看起来有希望时（有希望的定义取决于迄今为止收集的知识量），增加样本量可以保证Ⅰ型错误率的保护。此外，在检验统计量近似服从正态规律的许多情况下，偏离主要结果仍然可以忽略不计。本文详细介绍了威布尔和二项式分布，并指出如何在当前的设置中接近这些分布。
因此，有理由更多地考虑这种设计，因为它们提供了一种在不增加错误率的情况下调整重要设计特征的方法。
