Relative survival methodology deals with a competing risks survival model where the cause of death is unknown. This lack of information occurs regularly in population-based cancer studies. Non-parametric estimation of the net survival is possible through the Pohar Perme estimator. Derived similarly to Kaplan-Meier, it nevertheless relies on an untestable independence assumption. We propose here to relax this assumption and provide a generalized non-parametric estimator that works for other dependence structures, by leveraging the underlying stochastic processes and martingales. We formally derive asymptotics of this estimator, providing variance estimation and log-rank-type tests. Our approach provides a new perspective on the Pohar Perme estimator and the acceptability of the underlying independence assumption. We highlight the impact of this dependence structure assumption on simulation studies, and illustrate them through an application on registry data relative to colorectal cancer, before discussing potential extensions of our methodology.

翻译：相对生存率方法处理的是死因未知的竞争风险生存模型。这种信息缺失在基于人群的癌症研究中经常发生。通过Pohar Perme估计量可以实现净生存率的非参数估计。该估计量虽与Kaplan-Meier估计量推导方式类似，却依赖于一个不可检验的独立性假设。本文旨在放宽该假设，通过利用底层随机过程与鞅理论，提出一种适用于其他依赖结构的广义非参数估计量。我们严格推导了该估计量的渐近性质，提供了方差估计及对数秩型检验方法。本研究为Pohar Perme估计量及其底层独立性假设的可接受性提供了新的视角。我们通过模拟研究揭示了这种依赖结构假设的影响，并借助结直肠癌登记数据进行了实例验证，最后讨论了本方法可能的扩展方向。