The occurrence of incidents seriously affects the operation of the whole urban railway system and passengers’ travel experience. Accurate delay prediction is important for traffic control and management under incidents. Few studies were reported on incident prediction in urban railway systems because of the unexpected nature of incidents and the lack of comprehensive incident data. Existing models used to predict incident delay can be divided into statistical methods and traditional machine learning methods, as well as ensemble learning methods. This study conducts a methodology review for these models by comparing their performance in predicting incident delays using a large-scale incident dataset collected from an urban railway system in Hong Kong. Three statistical models and six machine/ensemble learning methods are examined: ordinary least squares, accelerated failure time, quantile regression (QR), support vector regression (SVR), K-nearest neighbor, random forest, adaptive boosting, gradient boosting decision tree (GBDT), and extreme gradient boosting (XGBoost) tree. The results indicate that statistical models perform better than machine/ensemble learning models in predicting train delays under incidents. The QR, SVR, and XGBoost tree models outperform other models in incident delay prediction in their respective methodological categories. The factors of the incident type and affected line type present the most significant effects on incident delay prediction in selected models.