We propose a new method to compare survival data based on Higher Criticism (HC) of P-values obtained from many exact hypergeometric tests. The method can accommodate censorship and is sensitive to moderate differences in some unknown and relatively few time intervals, attaining much better power against such differences than the log-rank test and other tests that are popular under non-proportional hazard alternatives. We demonstrate the usefulness of the HC-based test in detecting rare differences compared to existing tests using simulated data and using actual gene expression data. Additionally, we analyze the asymptotic power of our method under a piece-wise homogeneous exponential decay model with rare and weak departures, describing two groups experiencing failure rates that are usually identical over time except in a few unknown instances in which the second group's failure rate is higher. Under an asymptotic calibration of the model's parameters, the HC-based test's power experiences a phase transition across the plane involving the rarity and intensity parameters that mirrors the phase transition in a two-sample rare and weak normal means setting. In particular, the phase transition curve of our test indicates a larger region in which it is fully powered than the corresponding region of the log-rank test. %The latter attains a phase transition curve that is analogous to a test based on Fisher's combination statistic of the hypergeometric P-values. %To our knowledge, this is the first analysis of a rare and weak signal detection model that involves individually dependent effects in a non-Gaussian setting.

翻译：本文提出一种基于高阶批评（Higher Criticism, HC）的新方法，通过从大量精确超几何检验获得的p值比较生存数据。该方法能够处理删失数据，并对某些未知且数量较少的时间区间内的适度差异敏感，在应对此类差异时，其统计功效显著优于对数秩检验及其他在非比例风险备择假设下常用的检验方法。我们通过模拟数据和实际基因表达数据，展示了基于HC的检验在检测稀差异方面相对于现有检验的有效性。此外，我们在分段齐次指数衰减模型下分析了方法的渐近功效，该模型描述了两组通常具有相同失效率的情况，但存在少数未知时刻第二组的失效率更高。在模型参数的渐近标定下，基于HC检验的功效在涉及稀强度和强度的参数平面上经历相变，该相变与双样本稀弱正态均值设定中的相变相似。特别地，本检验的相变曲线表明，其完全具有统计功效的区域大于对数秩检验的对应区域。%后者对应的相变曲线与基于超几何p值Fisher组合统计量的检验类似。%据我们所知，这是首个在非高斯设定中涉及个体相依效应的稀弱信号检测模型分析。