Optimal decorrelated score subsampling for Cox regression with massive survival data

This paper investigates optimal subsampling strategies for the preconceived low-dimensional parameters of main interest in the presence of the nuisance parameters for Cox regression with massive survival data. A general subsampling decorrelated score function based on the log-partial likelihood is constructed to reduce the influence of the less accurate nuisance parameter estimation with a possibly slow convergence rate. The consistency and asymptotic normality of the resultant subsample estimators are established. We derive unified optimal subsampling probabilities based on A- and L-optimality criteria. A two-step algorithm is further proposed to implement practically, and the asymptotic properties of the resultant estimators are also given. The satisfactory performance of our proposed subsample estimators is demonstrated by simulation results and an airline dataset.