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The use of massive survival data has become common in survival analysis. Inthis study, a subsampling algorithm is proposed for the Cox proportionalhazards model with time-dependent covariates when the sample is extraordinarilylarge but computing resources are relatively limited. A subsample estimator isdeveloped by maximizing the weighted partial likelihood; it is shown to haveconsistency and asymptotic normality. By minimizing the asymptotic mean squarederror of the subsample estimator, the optimal subsampling probabilities areformulated with explicit expressions. Simulation studies show that the proposedmethod can satisfactorily approximate the estimator of the full dataset. Theproposed method is then applied to corporate loan and breast cancer datasets,with different censoring rates, and the outcomes confirm its practicaladvantages.

Optimal subsampling for the Cox proportional hazards model with massive survival data