Continuous and discrete-time survival prediction with neural networks

Area of Science:

• Machine Learning
• Survival Analysis
• Biostatistics

Background:

• Recent advancements in machine learning, especially neural networks, have spurred novel time-to-event prediction techniques.
• Parametric survival models are more readily integrated into neural networks than semi-parametric Cox models.
• Discrete-time survival models are well-suited for neural network extensions due to their fully parametric nature.

Purpose of the Study:

• To review and compare neural network-based discrete-time survival models.
• To demonstrate the application of discrete-time methods as approximations for continuous-time data.
• To introduce and evaluate a novel continuous-time survival prediction method.

Main Methods:

• Comparison of neural network approaches using probability mass function (PMF) and discrete hazard rate parametrizations.
• Development of discretization schemes (equidistant times/survival probabilities) and interpolation methods (piecewise constant density/hazard rates) for continuous-time approximation.
• Proposal and evaluation of a continuous-time method (PC-Hazard) with a piecewise constant hazard rate assumption.

Main Results:

• Methods utilizing hazard rate parametrization slightly outperformed those using PMF parametrization in simulations and real-world data analysis.
• Discrete-time methods effectively approximate continuous-time survival data.
• The proposed PC-Hazard method demonstrates high competitiveness against existing survival prediction techniques.

Conclusions:

• Neural network-based discrete-time survival models, particularly hazard rate formulations, offer robust performance for time-to-event predictions.
• The developed methods provide viable approximations for continuous-time survival data.
• The PC-Hazard method represents a significant advancement in continuous-time survival analysis.