Delayed treatment effects on time-to-event outcomes have often been observed in randomized controlled studies of cancer immunotherapies. In the case of delayed onset of treatment effect, the conventional test/estimation approach using the log-rank test for between-group comparison and Cox's hazard ratio to estimate the magnitude of treatment effect is not optimal, because the log-rank test is not the most powerful option, and the interpretation of the resulting hazard ratio is not obvious. Recently, alternative test/estimation approaches were proposed to address both the power issue and the interpretation problems of the conventional approach. One is a test/estimation approach based on long-term restricted mean survival time, and the other approach is based on average hazard with survival weight. This paper integrates these two ideas and proposes a novel test/estimation approach based on long-term average hazard (LT-AH) with survival weight. Numerical studies reveal specific scenarios where the proposed LT-AH method provides a higher power than the two alternative approaches. The proposed approach has test/estimation coherency and can provide robust estimates of the magnitude of treatment effect not dependent on study-specific censoring time distribution. Also, the proposed LT-AH approach can summarize the magnitude of the treatment effect in both absolute difference and relative terms using ``hazard'' (i.e., difference in LT-AH and ratio of LT-AH), meeting guideline recommendations and practical needs. This proposed approach can be a useful alternative to the traditional hazard-based test/estimation approach when delayed onset of survival benefit is expected.

翻译：摘要：在癌症免疫疗法的随机对照研究中，常观察到治疗对时间-事件结局存在延迟效应。当治疗效果延迟出现时，传统基于对数秩检验进行组间比较、基于Cox比例风险模型的风险比估计疗效幅度的检验/估计方法并非最优，因为对数秩检验并非最具统计效力的选择，且由此得出的风险比解释意义不明确。近年来，为解决传统方法的检验效能与解释困境，研究者提出了替代性检验/估计方法：其一是基于长期受限平均生存时间的检验/估计方法，另一种则是基于生存权重化平均风险的方法。本文整合两种思路，提出基于生存权重化长期平均风险（LT-AH）的新型检验/估计方法。数值研究表明，在特定场景下，所提出的LT-AH方法比两种替代方法具有更高的统计检验效能。该方法具有检验-估计一致性，可提供不依赖于研究特异性删失时间分布的稳健疗效估计。此外，LT-AH方法可通过"风险"指标（即LT-AH差值及LT-AH比值）同时以绝对差异和相对比率形式概括疗效幅度，既符合指南推荐又满足实践需求。当预期存在延迟性生存获益时，该方法可作为传统基于风险的检验/估计方法的有效替代方案。