Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models

2026-05-15

AI Summary

This study addresses the poor calibration of survival probability predictions from deep Cox models, which hinders their clinical utility. The authors propose a post-hoc calibration method based on isotonic regression that substantially improves calibration while preserving the model’s discriminative performance. This work introduces, for the first time, a calibration framework for deep Cox models that offers dual robustness and asymptotic calibration guarantees, enabling reliable calibration of predicted survival distributions. Experimental results on both synthetic and real-world clinical datasets demonstrate that the proposed approach effectively enhances calibration without compromising discrimination, thereby advancing the practical applicability of deep survival models in clinical settings.

Abstract

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.

Problem

• isotonic regression
• survival analysis
• calibration
• Deep Cox models
• censoring

Innovation

• Isotonic Regression
• Deep Cox Models
• Survival Calibration
• Time-to-Event Prediction
• Double Robustness