In a clinical trial with a survival outcome, an interim analysis is often performed to allow for early stopping for efficacy. If the interim analysis is early in the trial, one might conclude that a new treatment is more effective (compared to e.g.\ a placebo) and stop the trial, whereas the survival curves in the trial arms are not mature for the research question under investigation, for example because the curves are still close to 1 at that time. This means that the decision is based on a small percentage of the events in the long run only; possibly the events of the more frail patients in the trial who may not be representative for the whole group of patients. It may not be sensible to conclude effectiveness based on so little information. Criteria to determine the moment the interim analysis will be performed, should be chosen with care, and include the maturity of the data at the time of the interim analysis. Here, the expected survival rates at the interim analysis play a role. In this paper we will derive the asymptotic distribution of the Kaplan-Meier curves at the (random) moment the interim analysis will be performed for a one and two arm clinical trial. Based on this distribution, an interval in which the Kaplan Meier curves will fall into (with probability 95\%) is derived and could be used to plan the moment of the interim analysis in the design stage of the trial, so before the trial starts.

翻译：在以生存结局为终点的临床试验中，常开展期中分析以允许因疗效显著而提前终止试验。若期中分析在试验早期进行，可能得出新疗法（如相较于安慰剂）更有效的结论并终止试验，但此时试验组生存曲线尚未成熟以回答所研究的问题——例如，两组的生存曲线仍接近于1。这意味着该决策仅基于长期事件中的一小部分；可能仅涉及试验中较为虚弱的患者发生事件，而这类患者未必能代表整体患者群体。基于如此有限的信息推断疗效可能并不合理。确定期中分析时机的标准需谨慎选择，并考虑该时间点的数据成熟度。其中，期中分析时的预期生存率起关键作用。本文将推导单组及两组临床试验中，在（随机）期中分析时刻Kaplan-Meier曲线的渐近分布。基于该分布，可计算出Kaplan-Meier曲线以95%概率落入的区间，并用于在试验设计阶段（即试验启动前）规划期中分析的时机。