The Cox model is now 50 years old. The seminal paper of Sir David Cox has had an immeasurable impact on the analysis of censored survival data, with applications in many different disciplines. This work has also stimulated much additional research in diverse areas and led to important theoretical and practical advances. These include semiparametric models, nonparametric efficiency, and partial likelihood. In addition to quickly becoming the go-to method for estimating covariate effects, Cox regression has been extended to a vast number of complex data structures, to all of which the central idea of sampling from the set of individuals at risk at time t can be applied. In this article, we review the Cox paper and the evolution of the ideas surrounding it. We then highlight its extensions to competing risks, with attention to models based on cause-specific hazards, and to hazards associated with the subdistribution or cumulative incidence function. We discuss their relative merits and domains of application. The analysis of recurrent events is another major topic of discussion, including an introduction to martingales and complete intensity models as well as the more practical marginal rate models. We include several worked examples to illustrate the main ideas.

中文翻译：

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考克斯模型 50 周年


Cox 模型现在已经有 50 年的历史了。David Cox 爵士的开创性论文对审查生存数据的分析产生了不可估量的影响，应用于许多不同的学科。这项工作还激发了不同领域的大量额外研究，并导致了重要的理论和实践进步。这些模型包括半参数模型、非参数效率和偏似然。除了迅速成为估计协变量效应的首选方法外，Cox 回归还扩展到了大量复杂的数据结构，所有这些结构都可以应用从时间 t 处于风险中的一组个体中抽样的中心思想。在本文中，我们回顾了 Cox 论文以及围绕它的思想的演变。然后，我们重点介绍了它对竞争风险的扩展，并关注基于特定原因危害的模型，以及与子分布或累积发生函数相关的危害。我们讨论了它们的相对优点和应用领域。对复发事件的分析是另一个主要讨论话题，包括对马丁格尔和完全强度模型的介绍，以及更实用的边际速率模型。我们提供了几个工作示例来说明主要思想。