Abstract：
The delayed treatment effect is a common feature of immunotherapy, characterized by a gradual onset of action ranging from no effect to full effect. In this study, we propose a generalized delayed treatment effect function to depict the delayed effective process precisely and flexibly. To reduce potential power loss caused by the delayed treatment effect in a group sequential trial, we employ the maximin efficiency robust test, which enhances power robustness across a range of possible delays. We present novel approaches based on the Markov chain method for determining group sequential boundaries, calculating the power function, and estimating the maximum sample size through iterative regressions between the square root of the maximum sample size and the normal quantile of power. Extensive simulation studies validate the effectiveness of our approaches, particularly in balanced trials, demonstrating the validity of group sequential boundaries and the accuracy of maximum sample size estimations. Additionally, we utilize a real trial as an example to compare our considered trial with group sequential trials using the log-rank and generalized piecewise weighted log-rank tests. The results show significantly reduced maximum sample sizes, highlighting the economic advantage of our approach.
摘要：
延迟治疗效果是免疫治疗的共同特征,其特征是逐渐开始的作用，从没有效果到完全效果。在这项研究中,我们提出了一个广义的延迟治疗效应函数来精确和灵活地描述延迟有效过程。为了减少由一组序贯试验的延迟治疗效果引起的潜在功率损失，我们采用最大效率稳健测试，这增强了在一系列可能的延迟上的功率鲁棒性。我们提出了基于马尔可夫链方法的新方法来确定组顺序边界，计算幂函数，并通过最大样本量的平方根与正态幂分位数之间的迭代回归来估计最大样本量。广泛的仿真研究验证了我们方法的有效性，特别是在平衡试验中，证明组顺序边界的有效性和最大样本量估计的准确性。此外,我们以真实试验为例,使用对数秩和广义分段加权对数秩检验将我们考虑的试验与小组序贯试验进行比较.结果表明，最大样本量显著减少，强调我们方法的经济优势。
