Cox proportional hazards (PH) models are commonly used in medical research to investigate the associations between covariates and time-to-event outcomes. It is frequently noted that with less than 10 events per covariate, these models produce spurious results and therefore should not be used. Statistical literature contains asymptotic power formulas for the Cox model which can be used to determine the number of events needed to detect an association. Here, we investigate via simulations the performance of these formulas in small sample settings for Cox models with one or two covariates. Our simulations indicate that when the number of events is small, the power estimate based on the asymptotic formula is often inflated. The discrepancy between the asymptotic and empirical power is larger for the dichotomous covariate especially in cases where allocation of sample size to its levels is unequal. When more than one covariate is included in the same model, the discrepancy between the asymptotic power and the empirical power is even larger, especially when a high positive correlation exists between the two covariates.

中文翻译：

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小样本情况下 Cox 模型渐近幂公式的基于仿真的评估

Cox 比例风险 (PH) 模型常用于医学研究，以研究协变量与事件发生时间之间的关联。人们经常注意到，如果每个协变量少于 10 个事件，这些模型会产生虚假结果，因此不应使用。统计文献包含 Cox 模型的渐近幂公式，可用于确定检测关联所需的事件数量。在这里，我们通过模拟研究这些公式在具有一两个协变量的 Cox 模型的小样本设置中的性能。我们的模拟表明，当事件数量很少时，基于渐近公式的功率估计经常被夸大。对于二分协变量，渐近和经验功效之间的差异更大，尤其是在样本大小分配到其水平不相等的情况下。当同一个模型中包含多个协变量时，渐近功效与经验功效之间的差异更大，尤其是当两个协变量之间存在高度正相关时。