Sample size calculations for two-arm clinical trials with a time-to-event endpoint have traditionally used the assumption of proportional hazards (PH) or the assumption of exponentially distributed survival times. Available software provides methods for sample size calculation using a nonparametric logrank test, Schoenfeld's formula for Cox PH model, or parametric calculations specific to the exponential distribution. In cases where the PH assumption is not valid, the first-choice method is to compute sample size assuming a piecewise linear survival curve (Lakatos approach) for both the control and treatment arms with judiciously chosen cut-points. Recent advances in literature have used the assumption of Weibull distributed times for single-arm trials, and, newer methods have emerged that allow sample size calculations for two-arm trials using the assumption of proportional time (PT) while considering non-PH. These methods, however, always assume an instantaneous effect of treatment relative to control requiring that the effect size be defined by a single number whose magnitude is preserved throughout the trial duration. Here, we consider the scenarios where the hypothesized benefit of treatment relative to control may not be constant giving rise to the notion of Relative Time (RT). By assuming that survival times for control and treatment arm come from two different Weibull distributions with different location and shape parameters, we develop the methodology for sample size calculation for specific cases of both non-PH and non-PT. Simulations are conducted to assess the operation characteristics of the proposed method and a practical example is discussed.

中文翻译：

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当推断建立在比较威布尔分布的基础上时，使用相对时间的概念，计算具有非比例危险的事件时间终点的双臂试验的样本量

具有事件发生时间终点的双组临床试验的样本量计算传统上使用比例风险 (PH) 假设或指数分布生存时间假设。可用软件提供使用非参数对数秩检验、Cox PH 模型的 Schoenfeld 公式或特定于指数分布的参数计算来计算样本量的方法。在 PH 假设无效的情况下，首选方法是计算样本量，假设对照组和治疗组均采用分段线性生存曲线（拉卡托斯方法），并明智地选择切点。文献中的最新进展使用了单臂试验的威布尔分布时间假设，并且出现了新的方法，允许在考虑非 PH 的同时使用比例时间 (PT) 假设来计算双臂试验的样本量。然而，这些方法总是假设治疗相对于对照具有瞬时效果，要求效果大小由单个数字定义，该数字的大小在整个试验期间保持不变。在这里，我们考虑治疗相对于对照的假设益处可能不是恒定的情况，从而产生相对时间（RT）的概念。通过假设对照组和治疗组的生存时间来自具有不同位置和形状参数的两种不同的威布尔分布，我们开发了针对非 PH 和非 PT 特定病例的样本量计算方法。进行仿真以评估所提出方法的操作特性，并讨论了一个实际示例。