Survival prediction on time-to-event data associated with patients is crucial in clinical research. Cox-type regression models are widely used for such prediction, but their performance for practical survival prediction suffers due to their use of a maximum partial likelihood estimator, which undermines the effectiveness and robustness of such models. To address this problem, we propose to maximize a new full likelihood that fits the model to all of the data for both failed and censored patients. We also represent time-to-event data by a new sequencing structure, which allows the proposed likelihood to be estimated by predicting event occurrence across the unit time intervals in practice. Furthermore, the likelihood is regularized to prevent overfitting from arising in the model learning step. We investigate the new approach via experimental studies on real-life clinical data and its superior performance compared to other popular state-of-the-art models reveals the great promise of our approach for clinical prediction.