Kim K, Boucher H, Tsiatis A A
Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts, USA.
Biometrics. 1995 Sep;51(3):988-1000.
When monitoring a clinical trial with failure time data using the logrank test and the type I error spending function approach, the information time has to be estimated as a fraction of the maximum number of failures. In maximum duration trials, the denominator of this fraction is a random quantity and has to be estimated; besides, there are two candidates for the denominator, one under the null hypothesis of no treatment difference and the other under the specified alternative hypothesis. Either way, some adjustments are necessary in determining group sequential boundaries in order to maintain type I error at a desired significance level. As a consequence, the type I error spending function will be altered from the one chosen for the design, thus affecting the operating characteristics of the subsequent group sequential logrank tests. In maximum information trials, however, the maximum amount of information is fixed, and thus the estimate of the information time is always unbiased. The net effect is that computation of group sequential boundaries becomes straightforward, with a potential saving in study durations as compared to maximum duration trials. We will illustrate how adjustments are made in maximum duration trials to maintain type I error when the information times are estimated with the information horizons under the null and alternative hypotheses and present numerical explorations to compare robustness of two different estimates of the information times. We then propose a design procedure for maximum information trials and investigate the properties of maximum information trials for different group sequential boundaries. We also compare maximum information trials and maximum duration trials based on an example.
当使用对数秩检验和I型错误消耗函数方法监测具有失效时间数据的临床试验时，信息时间必须估计为最大失效数的一部分。在最大持续时间试验中，该分数的分母是一个随机量，必须进行估计；此外，分母有两个候选值，一个在无治疗差异的原假设下，另一个在指定的备择假设下。无论哪种方式，在确定组序贯边界时都需要进行一些调整，以将I型错误维持在期望的显著性水平。因此，I型错误消耗函数将与设计时选择的函数不同，从而影响后续组序贯对数秩检验的操作特性。然而，在最大信息试验中，最大信息量是固定的，因此信息时间的估计始终是无偏的。其净效应是组序贯边界的计算变得直接，与最大持续时间试验相比，有可能节省研究持续时间。我们将说明在最大持续时间试验中，当根据原假设和备择假设下的信息范围估计信息时间时，如何进行调整以维持I型错误，并进行数值探索以比较信息时间的两种不同估计的稳健性。然后，我们提出一种最大信息试验的设计程序，并研究不同组序贯边界的最大信息试验的性质。我们还基于一个例子比较最大信息试验和最大持续时间试验。
