  The use of massive survival data has become common in survival analysis. In
this study, a subsampling algorithm is proposed for the Cox proportional
hazards model with time-dependent covariates when the sample is extraordinarily
large but computing resources are relatively limited. A subsample estimator is
developed by maximizing the weighted partial likelihood; it is shown to have
consistency and asymptotic normality. By minimizing the asymptotic mean squared
error of the subsample estimator, the optimal subsampling probabilities are
formulated with explicit expressions. Simulation studies show that the proposed
method can satisfactorily approximate the estimator of the full dataset. The
proposed method is then applied to corporate loan and breast cancer datasets,
with different censoring rates, and the outcomes confirm its practical
advantages.
