Götte Heiko, Hommel Gerhard, Faldum Andreas
Institute of Medical Biostatistics, Epidemiology and Informatics, University of Mainz, 55131 Mainz, Germany.
Stat Med. 2009 May 1;28(10):1429-44. doi: 10.1002/sim.3555.
In clinical trials, the collected observations such as clustered data or repeated measurements are often correlated. As a consequence, test statistics in a multistage design are correlated. Adaptive designs were originally developed for independent test statistics. We present a general framework for two-stage adaptive designs with correlated test statistics. We show that the significance level for the Bauer-Köhne design is inflated for positively correlated test statistics from a bivariate normal distribution. The decision boundary for the second stage can be modified so that type one error is controlled. This general concept is expandable to other adaptive designs. In order to use these designs, the correlation between test statistics has to be estimated. For a known covariance matrix, we show how correlation can be determined within the framework of linear mixed models. A sample size reassessment rule is proposed and evaluated for an unknown covariance matrix by simulation. As Wald test statistics in linear mixed models have independent increments, we use this property to create valid test procedures. We compare these procedures with the proposed design in our simulations.
在临床试验中，收集到的观测数据，如聚类数据或重复测量数据，往往是相关的。因此，多阶段设计中的检验统计量是相关的。自适应设计最初是为独立检验统计量而开发的。我们提出了一个用于具有相关检验统计量的两阶段自适应设计的通用框架。我们表明，对于来自二元正态分布的正相关检验统计量，Bauer-Köhne设计的显著性水平会膨胀。可以修改第二阶段的决策边界，以便控制第一类错误。这个一般概念可以扩展到其他自适应设计。为了使用这些设计，必须估计检验统计量之间的相关性。对于已知的协方差矩阵，我们展示了如何在线性混合模型的框架内确定相关性。针对未知协方差矩阵，通过模拟提出并评估了一个样本量重新评估规则。由于线性混合模型中的Wald检验统计量具有独立增量，我们利用这一特性创建有效的检验程序。在模拟中，我们将这些程序与所提出的设计进行比较。
