Beyond Cox Models: Assessing the Performance of Machine-Learning Methods in Non-Proportional Hazards and Non-Linear Survival Analysis

Strategic Insights -

Researchers at the University of Turin have published a new study on machine learning, highlighting the limitations of Cox models in survival analysis and demonstrating the potential of deep learning methods to improve predictive performance. The study, published in the journal Computers in Biology and Medicine, evaluated the performance of eight different models, including six non-linear models, on a benchmark of synthetic and real datasets. The results show that machine and deep learning models can outperform Cox regression under certain conditions, particularly when the proportional hazards assumption does not hold.

Key Takeaways:

  • The study evaluated the performance of eight different models, including six non-linear models, on a benchmark of synthetic and real datasets.
  • Cox regression often yielded satisfactory performance, but machine and deep learning models can perform better under certain conditions, such as non-proportional hazards and non-linearity.
  • The performance of machine and deep learning models has often been underestimated due to the improper use of Harrell's concordance index (C-index) instead of more appropriate scores, such as Antolini's concordance index.
  • Combining Antolini's C-index with Brier's score is useful to assess the overall performance of a survival method.
  • The study demonstrated that survival prediction should be approached by testing different methods to select the most appropriate one according to sample size, non-linearity, and non-PH conditions.

Statistics:

  • Eight different models were tested, including six non-linear models.
  • Three synthetic and three real datasets were used as the benchmark.
  • Cox regression often yielded satisfactory performance, but machine and deep learning models outperformed it under certain conditions.
  • Antolini's concordance index was used to evaluate the performance of the models, which is more appropriate than Harrell's C-index in cases where the PH assumption does not hold.

Sources:

  • Beyond Cox models: Assessing the performance of machine-learning methods in non-proportional hazards and non-linear survival analysis. Computers in Biology and Medicine, 2025;198:111176.
  • Pergamon-elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, England.
  • University of Turin, Department of Medical Sciences, Turin, Italy.
  • Giovanni Birolo, Ivan Rossi, Flavio Sartori, Cesare Rollo, Piero Fariselli, and Tiziana Sanavia.