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

Objective: Survival analysis is central to medical prediction, yet large language models (LLMs) are rarely used as end-to-end survival models because censoring prevents straightforward supervised fine-tuning. Here we present LLMSurvival, a framework that enables censoring-aware survival analysis with unmodified LLMs operating directly on tabular clinical data. Materials and Methods: LLMSurvival reformulates time-to-event prediction as pairwise ranking among comparable subjects, and derives test-time risk by aggregating comparisons against anchor individuals from the training cohort. Results: Across two clinical tasks (ICU mortality prediction in MIMIC-IV and fragility fracture prediction in a NewYork-Presbyterian/Weill Cornell Medicine cohort), LLMSurvival improves overall concordance over Cox proportional hazards modeling by 3.1% for ICU mortality and 0.5% for fracture risk, 2.1% on average for ICU mortality and 2.8% for fracture risk over three established deep learning survival models. Discussion: The results show that survival modeling with censoring can be made compatible with LLM fine-tuning through comparison-based reformulation. The framework demonstrates high portability and superior performance over expert curated scores like SAPS-II and FRAX scores across diverse clinical context. Furthermore, the framework supports local deployment, as compact, publicly available base models provide sufficient performance. Conclusion: The LLMSurvival framework serves as a proof of concept for an integrated, censoring-conscious approach to survival analysis via LLMs.

Time-to-event data is widespread across the life sciences and engineering, but it is typically encountered together with censoring, which complicates the application of standard machine learning methods. Deep Cox models have emerged as a popular method for analyzing time-to-event data because they gracefully handle censoring and can be used with unstructured data such as clinical text reports, genomic sequences, and pathology images. However, their predicted survival probabilities are often poorly calibrated, thus limiting their practical utility. In this paper, we propose a novel post hoc calibration method for Deep Cox models that uses isotonic regression to refine predicted survival probabilities without affecting discriminative power. We establish favorable theoretical guarantees, including a double-robustness property and asymptotic calibration. Experiments on synthetic and real-world clinical data demonstrate the empirical effectiveness of our method.

Clinical language models (LMs) are increasingly applied to support clinical risk prediction from free-text notes, yet their uncertainty estimates often remain poorly calibrated and clinically unreliable. In this work, we propose Clinical Uncertainty Risk Alignment (CURA), a framework that aligns clinical LM-based risk estimates and uncertainty with both individual error likelihoods and cohort-level ambiguities. CURA first fine-tunes domain-specific clinical LMs to obtain task-adapted patient embeddings, and then performs uncertainty fine-tuning of a multi-head classifier using a bi-level uncertainty objective. Specifically, an individual-level calibration term aligns predictive uncertainty with each patient's likelihood of error, while a cohort-aware regularizer pulls risk estimates toward event rates in their local neighborhoods in the embedding space and places extra weight on ambiguous cohorts near the decision boundary. We further show that this cohort-aware term can be interpreted as a cross-entropy loss with neighborhood-informed soft labels, providing a label-smoothing view of our method. Extensive experiments on MIMIC-IV clinical risk prediction tasks across various clinical LMs show that CURA consistently improves calibration metrics without substantially compromising discrimination. Further analysis illustrates that CURA reduces overconfident false reassurance and yields more trustworthy uncertainty estimates for downstream clinical decision support.