Advanced Methodology and Data Science, Novartis Pharma AG, Basel, Switzerland.
Pharm Stat. 2021 May;20(3):512-527. doi: 10.1002/pst.2091. Epub 2020 Dec 22.
A fundamental concept in two-arm non-parametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the counting-process theory that provides a rigorous basis for methods such as the log-rank test. It is natural, therefore, to maintain this perspective when extending the log-rank test to deal with non-proportional hazards, for example, by considering a weighted sum of the "observed - expected" terms, where larger weights are given to time periods where the hazard ratio is expected to favor the experimental treatment. In doing so, however, one may stumble across some rather subtle issues, related to difficulties in the interpretation of hazard ratios, that may lead to strange conclusions. An alternative approach is to view non-parametric survival comparisons as permutation tests. With this perspective, one can easily improve on the efficiency of the log-rank test, while thoroughly controlling the false positive rate. In particular, for the field of immuno-oncology, where researchers often anticipate a delayed treatment effect, sample sizes could be substantially reduced without loss of power.
在双臂非参数生存分析中，一个基本概念是比较一个治疗臂（任意选择哪个臂）的实际观察到的事件数量与预期数量之间的差异，其中的预期是假设两个臂中的真实生存曲线是相同的。这个概念是计数过程理论的核心，该理论为对数秩检验等方法提供了严格的基础。因此，在将对数秩检验扩展到处理非比例风险时，例如通过考虑“观察到的 - 预期”项的加权和，其中对预计有利于实验治疗的风险比的时间段赋予更大的权重，从保持这种观点是很自然的。然而，这样做可能会遇到一些相当微妙的问题，这些问题与风险比的解释有关，可能会导致奇怪的结论。另一种方法是将非参数生存比较视为置换检验。从这个角度来看，可以轻松地提高对数秩检验的效率，同时彻底控制假阳性率。特别是在免疫肿瘤学领域，研究人员通常预计会有延迟的治疗效果，在不损失效力的情况下，样本量可以大大减少。
