Survival analysis is applied in a wide range of sectors (medicine, economy, etc.), and its main idea is based on evaluating the time until the occurrence of an event of interest. The effect of some particular covariates on survival time is usually described by the Cox proportional hazards model and the statistical significance of the impact of covariates is verified by the likelihood ratio test, the Wald test, or the score test. In addition to standard tests, appropriate higher-order approximations based on Barndorff-Nielsen and Lugannani-Rice formulas are used for more accurate approximations. In this paper, comparison of these tests’ size and power for small sample sizes is performed on simulated datasets with various proportions of right-censored data, distributions of baseline hazard functions and different types of covariate—continuous or discrete.

中文翻译：

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单参数 Cox 比例风险模型中检验的高阶近似的行为

生存分析应用于广泛的部门（医学、经济等），其主要思想是基于评估感兴趣事件发生之前的时间。某些特定协变量对生存时间的影响通常由 Cox 比例风险模型描述，协变量影响的统计显着性通过似然比检验、Wald 检验或评分检验来验证。除了标准测试之外，还使用基于 Barndorff-Nielsen 和 Lugannani-Rice 公式的适当高阶近似值来获得更准确的近似值。在本文中，在具有各种右删失数据比例的模拟数据集上，对小样本量的这些检验的大小和功效进行了比较，