A time-dependent divergence measure is proposed to compare the survival functions of two lifetime random variables. It is shown that the proposed measure ranges between and for the proportional hazards case has the metric properties. Several properties of the divergence measure are investigated, among others, it is shown that the divergence between two survival functions does not depend on time if and only if they follow the proportional hazards model. The measure is also examined for various other well-known survival models such as the proportional odds model. The estimation of the suggested divergence measure for survival data is also discussed, and the asymptotic normal distribution of the resulting estimator is established. The proposed estimation is evaluated via simulation and further employed to compare the effects of two treatment groups on the overall survival times of kidney cancer patients.

中文翻译：

---

将 Cox-Czanner 散度度量扩展到具有应用的剩余寿命分布

提出了一种时间相关的散度度量来比较两个生命周期随机变量的生存函数。结果表明，在比例风险案例之间和之间的建议度量范围具有度量属性。研究了散度度量的几个属性，其中表明两个生存函数之间的散度不依赖于时间，当且仅当它们遵循比例风险模型时。还针对各种其他众所周知的生存模型（例如比例优势模型）检查了该度量。还讨论了对生存数据的建议散度度量的估计，并建立了所得估计量的渐近正态分布。