Abstract: Objective To compare the predictive ability of two extended Cox models in nonlinear survival data analysis. Methods Through Monte Carlo simulation and empirical study and with the conventional Cox Proportional Hazards model and Random Survival Forests as the reference models, we compared restricted cubic spline Cox model (Cox_RCS) and DeepSurv neural network Cox model (Cox_DNN) for their prediction ability in nonlinear survival data analysis. Concordance index was used to evaluate the differentiation of the prediction results (a larger concordance index indicates a better prediction ability of the model). Integrated Brier Score was used to evaluate the calibration degree of the prediction (a smaller index indicates a better prediction ability). Results For data that met requirement of the proportion risk, the Cox_RCS model had the best prediction ability regardless of the sample size or deletion rate. For data that failed to meet the proportion risk, theprediction ability of Cox_DNN was optimal for a large sample size (≥500) with a low deletion (<40%); the prediction ability of Cox_RCS was superior to those of other models in all other scenarios. For example data, the Cox_RCS model showed the best performance. Conclusion In analysis of nonlinear low maintenance data, Cox_RCS and Cox_DNN have their respectiveadvantages and disadvantages in prediction. The conventional survival analysis methods are not inferior to machine learning or deep learning methods under certain conditions.

Key words: survival analysis; nonlinear correlation; Cox model; restricted cubic spline; deep neural network