Survival prediction from neural parametrization of diffusive processes.

Area of Science:

• Computational biology
• Statistical modeling
• Machine learning

Background:

• Survival analysis is crucial for predicting time-to-event outcomes.
• Existing methods like Cox regression have limitations in capturing complex, time-varying risk.
• Deep learning offers powerful predictive capabilities but often lacks interpretability.

Purpose of the Study:

• To introduce DeepFHT, a new survival analysis framework.
• To integrate deep neural networks with first hitting time (FHT) distributions from stochastic process theory.
• To provide a physics-based, interpretable model for survival phenomena.

Main Methods:

• Developed DeepFHT, coupling deep neural networks with FHT distributions.
• Represented time-to-event as a latent diffusion process reaching an absorbing boundary.
• Utilized neural networks to map input variables to FHT process parameters (initial condition, drift, diffusion).
• Employed Brownian motion (with and without drift) as an example FHT process.

Main Results:

• DeepFHT achieved predictive accuracy comparable to state-of-the-art methods (Cox regression, DeepHit).
• The framework provides closed-form survival and hazard functions.
• It effectively captures time-varying risk without the proportional hazards assumption.
• The physics-based parametrization offers interpretable insights into feature-risk relationships.

Conclusions:

• DeepFHT offers a principled approach to survival analysis by combining stochastic processes and deep learning.
• The method provides both high predictive accuracy and interpretable, physics-based modeling.
• This framework advances the modeling of survival phenomena in complex systems.