We propose a method for comparing survival data based on the higher criticism of p-values obtained from multiple exact hypergeometric tests. The method accommodates non-informative right-censorship and is sensitive to hazard differences in unknown and relatively rare time intervals. It attains much better power against such differences than the log-rank test and its variants. We demonstrate the usefulness of our method in detecting rare and weak non-proportional hazard differences compared to existing tests, using simulations and actual gene expression data. Additionally, we analyze the asymptotic power of our method and other tests under a theoretical framework describing two groups experiencing failure rates that are usually identical over time, except in a few unknown instances where one group's failure rate is higher. Our test's power undergoes a phase transition across the plane of rarity and intensity parameters that mirrors the phase transition of higher criticism in two-sample settings with rare and weak normal and Poisson means. The region of the plane in which our method has asymptotically full power is larger than the corresponding region for the log-rank test.

翻译：我们提出了一种基于多个精确超几何检验所得p值的高阶批评来比较生存数据的方法。该方法适应非信息性右删失，并对未知且相对罕见时间区间内的风险差异具有敏感性。相较于对数秩检验及其变体，该方法在此类差异的检验功效上表现更优。通过模拟实验和实际基因表达数据，我们证明了该方法在检测罕见且微弱的非比例风险差异方面相较于现有检验方法的实用性。此外，我们在一个理论框架下分析了本方法及其他检验的渐近功效，该框架描述了两组个体的失效率通常随时间相同，仅在少数未知时刻其中一组的失效率更高。我们检验的功效在稀有性与强度参数构成的平面上经历相变，这与两样本设置中针对罕见且微弱的正态均值与泊松均值的高阶批评相变现象相呼应。在该平面上，本方法具有渐近完全功效的区域大于对数秩检验的相应区域。