A Fast Divide-and-Conquer Sparse Cox Regression
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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≫ 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.
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