The goal of this research is to integrate group structures to the Cox proportional hazards model with ultra highdimensional predictors. By doubly regularizing the partial likelihood based on the Cox model with convex penalties, this method is able to perform group selection and withingroup selection simultaneously. Compared with methods ignoring the structure information, our method yields better variable selection and more accurate prediction. The convexity of our regularized objective function makes the method numerically stable especially when the number of predictors far exceeds the number of the observations. A fast coordinate descent algorithm is exploited to avoid matrix operations and speed up the computation. Numerical experiments on simulated data demonstrate the good performance of our doubly regularized method. We analyze the TCGA ovarian cancer data with this new method.
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