Sparse Laplacian shrinkage for nonparametric transformation survival model

The rank estimation is an effective inference method for the nonparametric transformation model. This approach avoids any nonparametric estimation about the transformation function and can be applied to the high-dimensional censored data. However, most existing methods do not utilize the potential correlation structures among predictors. In order to incorporate such priori information, we propose a penalized smoothed partial rank with sparse Laplacian shrinkage (PSPRL) method and develop a forward and backward stagewise with sparse Laplacian shrinkage (LFabs) algorithm to compute the estimator. The non-asymptotic bound and algorithm properties are established. Simulation results show that the proposed method outperforms the competing alternatives with better variable selection and prediction. We apply our method to a glioblastoma gene expression study to further demonstrate the advantages.