Uncertainty-Aware Survival Distillation for Flexible Continuous-Time Relative Risk Models

Clinical decision-making requires accurate individualized survival predictions and clinically interpretable characterization of their uncertainty. Prominent survival-distillation approaches typically provide only point predictions. Moreover, existing continuous-time distillation methods either rely on classical regression formulations that may not extend naturally to flexible machine-learning models or transfer relative-risk information without directly incorporating external survival probabilities. To address these gaps, we introduce BayCSD (Bayesian Continuous-Time Survival Distillation), an uncertainty-aware survival-distillation framework for flexible continuous-time relative-risk models, including deep neural networks. The framework introduces a censor-aware interval KL distillation criterion that compares teacher and student models, allowing external survival predictions to inform both nonlinear relative-risk functions and cumulative baseline hazards while retaining the original event and censoring times in the target likelihood. A generalized Bayesian update combines target-data fit, a borrowing-weighted distillation discrepancy, and a structural prior, propagating joint posterior uncertainty in the risk function and baseline hazard to individualized survival probabilities and restricted mean survival time. Controlled synthetic experiments characterize the benefits and limitations of borrowing under teacher compatibility and mismatch. Real-data pooled-reference benchmarks and kidney-alone-to-kidney–pancreas transfer demonstrate improved survival prediction relative to matched target-only learning, while pooled-reference analyses yield narrower posterior intervals at matched reference inclusion. BayCSD also compares favorably with existing survival-transfer approaches in the transplant application.