Massive sized survival datasets are becoming increasingly prevalent with the development of the healthcare industry. Such datasets pose computational challenges unprecedented in traditional survival analysis use-cases. A popular way for coping with massive datasets is downsampling them to a more manageable size, such that the computational resources can be afforded by the researcher. Cox proportional hazards regression has remained one of the most popular statistical models for the analysis of survival data to-date. This work addresses the settings of right censored and possibly left truncated data with rare events, such that the observed failure times constitute only a small portion of the overall sample. We propose Cox regression subsampling-based estimators that approximate their full-data partial-likelihood-based counterparts, by assigning optimal sampling probabilities to censored observations, and including all observed failures in the analysis. Asymptotic properties of the proposed estimators are established under suitable regularity conditions, and simulation studies are carried out to evaluate the finite sample performance of the estimators. We further apply our procedure on UK-biobank colorectal cancer genetic and environmental risk factors.

翻译：随着保健行业的发展,大规模生存数据集日益普遍。这类数据集在传统生存分析使用案例中构成前所未有的计算挑战。处理大规模数据集的流行方式是将它们降格到更易于管理的规模,这样研究人员就可以提供计算资源。考克斯比例危害回归仍然是迄今分析生存数据最受欢迎的统计模型之一。这项工作处理的是受右侧审查的、可能左侧截断的数据,并有罕见事件,因此观察到的失败时间只占总样本的一小部分。我们提议使用基于考克斯回归的子抽样估计器,以近似于其全数据半类似对应数据,方法是为经过审查的观察确定最佳采样概率,并将所有观察到的失败情况纳入分析中。拟议估算器的随机特性是在适当的正常条件下建立的,并进行模拟研究,以评价估算器的有限样品性能。我们进一步对英国生物银行的红外癌和环境风险因素适用了我们的程序。