We discuss the multivariate (2L-variate) correlation structure and the asymptotic distribution for the group-sequential weighted logrank statistics formulated when monitoring two correlated event-time outcomes in clinical trials. The asymptotic distribution and the variance–covariance for the 2L-variate weighted logrank statistic are derived as available in various group-sequential trial designs. These methods are used to determine a group-sequential testing procedure based on calendar times or information fractions. We apply the theoretical results to a group-sequential method for monitoring a clinical trial with early stopping for efficacy when the trial is designed to evaluate the joint effect on two correlated event-time outcomes. We illustrate the method with application to a clinical trial and describe how to calculate the required sample sizes and numbers of events.

中文翻译：

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使用双变量非竞争事件时间结果进行试验设计的组顺序对数秩方法。

我们讨论了在监测临床试验中两个相关的事件时间结局时制定的多序列（2 L变量）相关结构和组顺序加权对数秩统计的渐近分布。2 L的渐近分布和方差-协方差得出各组顺序试验设计中可用的变量加权对数秩统计。这些方法用于根据日历时间或信息分数确定组顺序测试程序。当将临床试验设计为评估对两个相关事件时间结局的联合影响时，我们将理论结果应用于组序贯方法来监测临床试验并尽早停止疗效。我们说明了该方法在临床试验中的应用，并描述了如何计算所需的样本量和事件数。