Inverse-Weighted Survival Games.

Area of Science:

• Biostatistics
• Machine Learning
• Medical Informatics

Background:

• Deep learning models trained via maximum likelihood excel in survival analysis.
• Practitioners often evaluate these models using metrics like Brier score (BS) and Bernoulli log likelihood (BLL) at specific time points.
• Maximum likelihood training does not directly optimize BS or BLL, potentially leading to suboptimal performance on these criteria.

Purpose of the Study:

• To develop a method for directly optimizing evaluation criteria like BS and BLL in deep survival models.
• To address the interdependence of failure and censoring distribution estimation required for direct optimization.
• To introduce a novel training framework that resolves this estimation dilemma.

Main Methods:

• Introduction of Inverse-Weighted Survival Games, a novel training paradigm.
• Objectives for each model are constructed using re-weighted estimates from the other model, with one held fixed during training.
• Demonstration of theoretical convergence properties, showing that proper loss functions lead to stationary points at true distributions.

Main Results:

• The Inverse-Weighted Survival Games ensure that models converge to the true failure and censoring distributions.
• A specific case demonstrating a unique stationary point for these games is constructed.
• Simulations confirm that the games effectively optimize the Brier score (BS).

Conclusions:

• Inverse-Weighted Survival Games provide a robust method for training deep survival models to optimize specific evaluation metrics.
• The framework ensures stable convergence to accurate distributional estimates.
• The approach was successfully applied to real-world datasets from cancer and critically-ill patient cohorts, demonstrating practical utility.