From Hazard Functions to Language Space: Cox-Supervised Distillation of Survival Risk into a Large Language Model

Abstract:We investigate whether information about time-to-event risk estimated by a Cox proportional hazards model can be transferred into a generative large language model. We propose a text-based survival modelling pipeline in which structured clinical covariates are converted into text prompts and a Qwen-based large language model is fine-tuned to generate patient-specific survival risk using Cox model predictions as a training target. Across GBSG2, ACTG320, and WHAS500, the model achieves competitive held-out discrimination and calibration despite being trained as a text-generation task rather than with a conventional survival-analysis loss. We further analyse the geometry of the model's hidden states, where t-SNE visualisations reveal smooth risk gradients in latent space, suggesting that the model represents survival risk as a continuous structure rather than isolated risk categories. Together, these findings suggest that large language models can internalise survival-risk structure while supporting calibrated prediction, providing a route towards time-to-event reasoning in language models.

Machine Learning (cs.LG)

arXiv:2606.08945 [cs.LG]

(or arXiv:2606.08945v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.08945 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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