Scalable Sparse Cox's Regression for Large-Scale Survival Data via Broken Adaptive Ridge

This paper develops a new sparse Cox regression method for high-dimensional massive sample size survival data. Our method is an L 0 -based iteratively reweighted L 2 penalized Cox regression, which inherits some appealing properties of both L 0 and L 2 -penalized Cox regression while overcoming their limitations. We establish that it has an oracle property for selection and estimation and a grouping property for highly correlated covariates. We develop an efficient implementation for high-dimensional massive sample size survival data, which exhibits up to a 20-fold speedup over a competing method in our numerical studies. We also adapt our method to high-dimensional small sample size data. The performance of our method is illustrated using simulations and real data examples.

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