Predictive Performance of Statistical and Machine Learning Survival Models with Time-Dependent Covariates: An Evaluation

Time-to-event (TTE) endpoints are widely used in drug development and biomedical research. Traditional statistical models, for example the Cox regression model, have been used to predict TTE outcomes. Recent studies have also employed flexible machine learning (ML) methods, for example, tree models, to obtain superior prediction performance. In addition, post-baseline time-varying predictors have recently been reported to improve prediction using ML methods. In this study, we applied the Cox model and ML methods to predict the onset of TTE with both baseline and post-baseline predictors. We evaluated the predictive performance of these models using various metrics, including the time-dependent area under the receiver operating characteristic curve (AUC), the concordance index (C-index), and integrated Brier scores. We also used these metrics as criteria to guide the selection of predictors in the predictive models. Our findings indicate that the Cox model remains a robust choice, often comparable to ML methods in moderate sample sizes, provided the proportional hazards assumption holds. However, tree-based methods demonstrate superior performance in capturing complex, nonlinear interactions, albeit requiring larger sample sizes to stabilize predictions.