Online Updating of Survival Analysis

When large amounts of survival data arrive in streams, conventional estimation methods become computationally infeasible since they require access to all observations at each accumulation point. We develop online updating methods for carrying out survival analysis under the Cox proportional hazards model in an online-update framework. Our methods are also applicable with time-dependent covariates. Specifically, we propose online-updating estimators as well as their standard errors for both the regression coefficients and the baseline hazard function. Extensive simulation studies are conducted to investigate the empirical performance of the proposed estimators. A large colon cancer dataset from the Surveillance, Epidemiology, and End Results program and a large venture capital dataset with time-dependent covariates are analyzed to demonstrate the utility of the proposed methodologies. Supplemental files for this article are available online.

当海量生存数据以流的形式持续传入时，传统估计方法因需在每一次累计更新节点调取全部观测数据，导致计算上不可行。本文针对在线更新框架下的考克斯比例风险模型（Cox proportional hazards model）生存分析问题，提出了在线更新方法，该方法同样适用于含时变协变量（time-dependent covariates）的场景。具体而言，本文针对回归系数（regression coefficients）与基准风险函数（baseline hazard function），分别提出了在线更新估计量及其标准误（standard errors）。本文开展了大量仿真实验，以考察所提估计量的实证表现。本文采用来自监测、流行病学与最终结果（Surveillance, Epidemiology, and End Results, SEER）项目的大型结直肠癌数据集，以及一款含时变协变量的大型风险投资数据集，对所提方法的实用性进行了展示与验证。本文的补充材料可在线获取。