Sampling-based estimation for massive survival data with additive hazards model

For massive survival data, we propose a subsampling algorithm to efficiently approximate the estimates of regression parameters in the additive hazards model. We establish consistency and asymptotic normality of the subsample-based estimator given the full data. The optimal subsampling probabilities are obtained via minimizing asymptotic variance of the resulting estimator. The subsample-based procedure can largely reduce the computational cost compared with the full data method. In numerical simulations, our method has low bias and satisfactory coverage probabilities. We provide an illustrative example on the survival analysis of patients with lymphoma cancer from the Surveillance, Epidemiology, and End Results Program.