Type I error in sample size re‐estimations based on observed treatment difference
Type I error in sample size re‐estimations based on observed treatment difference
复制标题
基于观察到的治疗差异的样本量重新估计中的 I 类错误
作者：
Z. Shun;William Yuan;W. E. Brady;Huang Hsu
基于观察到的差异重新估计样本量可以确保足够的把握度，并可能在临床试验中节省大量时间和资源。对这种方法的一个担忧是，它可能会夸大第一类错误。然而，这种可能的通货膨胀还没有在数学上量化。在本文中，这种膨胀的数学机制是探索两个样本的正态检验。一个（条件）I型误差函数的基础上正常的数据。该函数不仅提供了量化，还提供了由于样本量重新估计而导致的I类错误中可能膨胀的数学机制。从理论上讲，人们可以根据自己的决策规则（一定的上界和下界）计算这个函数，并准确地可视化I类错误的变化。计算机模拟进行，以确保结果。如果没有调整的界限，通货膨胀是显而易见的。如果使用适当的调节规则，通货膨胀可以得到很好的控制。在某些情况下，I类错误甚至可以减少。交易是放弃一些“不切实际的权力”。我们研究了几种情况下，改变第一类错误的机制是不同的。我们的模拟表明，类似的结果可能适用于其他分布。版权所有© 2001约翰威利父子有限公司。
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. Copyright © 2001 John Wiley & Sons, Ltd.