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 data set from the Surveillance, Epidemiology, and End Results (SEER) program and a large venture capital (VC) data set with time-dependent covariates are analyzed to demonstrate the utility of the proposed methodologies.