  We propose a computationally and statistically efficient divide-and-conquer
(DAC) algorithm to fit sparse Cox regression to massive datasets where the
sample size $n_0$ is exceedingly large and the covariate dimension $p$ is not
small but $n_0\gg p$. The proposed algorithm achieves computational efficiency
through a one-step linear approximation followed by a least square
approximation to the partial likelihood (PL). These sequences of linearization
enable us to maximize the PL with only a small subset and perform penalized
estimation via a fast approximation to the PL. The algorithm is applicable for
the analysis of both time-independent and time-dependent survival data.
Simulations suggest that the proposed DAC algorithm substantially outperforms
the full sample-based estimators and the existing DAC algorithm with respect to
the computational speed, while it achieves similar statistical efficiency as
the full sample-based estimators. The proposed algorithm was applied to an
extraordinarily large time-independent survival dataset and an extraordinarily
large time-dependent survival dataset for the prediction of heart
failure-specific readmission within 30 days among Medicare heart failure
patients.
