Abstract Crossover designs are an extremely useful tool to investigators, and group sequential methods have proven highly proficient at improving the efficiency of parallel group trials. Yet, group sequential methods and crossover designs have rarely been paired together. One possible explanation for this could be the absence of a formal proof of how to strongly control the familywise error rate in the case when multiple comparisons will be made. Here, we provide this proof, valid for any number of initial experimental treatments and any number of stages, when results are analyzed using a linear mixed model. We then establish formulae for the expected sample size and expected number of observations of such a trial, given any choice of stopping boundaries. Finally, utilizing the four-treatment, four-period TOMADO trial as an example, we demonstrate that group sequential methods in this setting could have reduced the trials expected number of observations under the global null hypothesis by over 33%.

中文翻译：

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具有强大的家庭错误率控制的组序贯交叉试验设计

摘要 交叉设计对研究人员来说是一种非常有用的工具，并且组序贯方法已被证明非常擅长提高平行组试验的效率。然而，组序列方法和交叉设计很少结合在一起。对此的一种可能解释可能是，在进行多重比较的情况下，缺乏如何强有力地控制家庭错误率的正式证明。在这里，我们提供了此证明，当使用线性混合模型分析结果时，该证明适用于任意数量的初始实验处理和任意数量的阶段。然后，我们为这种试验的预期样本大小和预期观察次数建立公式，给出任何停止边界的选择。最后以四次治疗四期TOMADO试验为例，