Forward Stagewise Shrinkage and Addition for High Dimensional Censored Regression

Despite enormous development on variable selection approaches in recent years, modeling and selection of high dimensional censored regression remains a challenging question. When the number of predictors p far exceeds the number of observational units n and the outcome is censored, computations of existing solutions often become difficult, or even infeasible in some situations, while performances frequently deteriorate. In this article, we aim at simultaneous model estimation and variable selection for Cox proportional hazards models with high dimensional covariates. We propose a forward stage-wise shrinkage and addition approach for that purpose. Our proposal extends a popular statistical learning technique, the boosting method. It inherits the flexible nature of boosting and is straightforward to extend to nonlinear Cox models. Meanwhile it advances the classical boosting method by adding explicit variable selection and substantially reducing the number of iterations to the algorithm convergence. Our intensive simulations have showed that the new method enjoys a competitive performance in Cox models with both p < n and p ≥ n scenarios. The new method was also illustrated with analysis of two real microarray survival datasets.