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Prognostic prediction is important in medical domain, because it can be used to select an appropriate treatment for a patient by predicting the patient's clinical outcomes. For high-dimensional data, a normal prognostic method undergoes two steps: feature selection and prognosis analysis. Recently, the L1-L2-norm Support Vector Machine (L1-L2 SVM) has been developed as an effective classification technique and shown good classification performance with automatic feature selection. In this paper, we extend L1-L2 SVM for regression analysis with automatic feature selection. We further improve the L1-L2 SVM for prognostic prediction by utilizing the information of censored data as constraints. We design an efficient solution to the new optimization problem. The proposed method is compared with other seven prognostic prediction methods on three real-world data sets. The experimental results show that the proposed method performs consistently better than the medium performance. It is more efficient than other algorithms with the similar performance.