Shun Z, Yuan W, Brady W E, Hsu H
Bristol-Myers Squibb, Organon Inc. and ACRO Inc. 2902 Johnson Cricle, Bridgewater, NJ 08807, USA.
Stat Med. 2001 Feb 28;20(4):497-513. doi: 10.1002/sim.531.
Sample size re-estimation based on an observed difference can ensure an adequate power and potentially save a large amount of time and resources in clinical trials. One of the concerns for such an approach is that it may inflate the type I error. However, such a possible inflation has not been mathematically quantified. In this paper the mathematical mechanism of this inflation is explored for two-sample normal tests. A (conditional) type I error function based on normal data is derived. This function not only provides the quantification but also gives mathematical mechanisms of possible inflation in the type I error due to the sample size re-estimation. Theoretically, based on their decision rules (certain upper and lower bounds), people can calculate this function and exactly visualize the changes in type I error. Computer simulations are performed to ensure the results. If there are no bounds for the adjustment, the inflation is evident. If proper adjusting rules are used, the inflation can be well controlled. In some cases the type I error can even be reduced. The trade-off is to give up some 'unrealistic power'. We investigated several scenarios in which the mechanisms to change the type I error are different. Our simulations show that similar results may apply to other distributions.
基于观察到的差异进行样本量重新估计，可以确保在临床试验中有足够的检验效能，并有可能节省大量时间和资源。这种方法的一个问题是，它可能会增大I型错误。然而，这种可能的增大尚未在数学上进行量化。本文针对双样本正态检验探讨了这种增大的数学机制。推导了基于正态数据的（条件）I型错误函数。该函数不仅提供了量化，还给出了由于样本量重新估计导致I型错误可能增大的数学机制。从理论上讲，人们可以根据其决策规则（某些上下界）来计算这个函数，并准确地直观呈现I型错误的变化。进行了计算机模拟以确保结果。如果调整没有界限，增大是明显的。如果使用适当的调整规则，增大可以得到很好的控制。在某些情况下，I型错误甚至可以降低。权衡之处在于要放弃一些“不切实际的检验效能”。我们研究了几种I型错误变化机制不同的情况。我们的模拟表明，类似的结果可能适用于其他分布。
