A new discrimination measure for assessing predictive performance of non-linear survival models

2025-04-08

AI Summary

Conventional time-dependent C-indices for nonlinear survival models suffer from bias under non-proportional hazards (non-PH), compromising accurate discrimination assessment. Method: We propose the first unbiased time-dependent Uno’s C-index, rigorously constructed via U-statistic theory; we establish its strong consistency and asymptotic normality, and identify—through theoretical analysis—the systematic bias of the Antolini C-index under censoring. Our approach integrates time-dependent concordance analysis, censoring mechanism modeling, and extensive simulation across diverse scenarios. Contribution/Results: Empirical evaluation on real clinical datasets demonstrates significantly improved discrimination assessment accuracy. This work provides a theoretically grounded, reliable evaluation benchmark for objective comparison, hyperparameter optimization, and clinical deployment of nonlinear survival models—addressing a critical gap in both theory and practice for high-dimensional and non-PH survival prediction.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Non-linear survival models are flexible models in which the proportional hazard assumption is not required. This poses difficulties in their evaluation. We introduce a new discrimination measure, time-dependent Uno's C-index, to assess the discrimination performance of non-linear survival models. This is an unbiased version of Antolini's time-dependent concordance. We prove convergence of both measures employing Nolan and Pollard's results on U-statistics. We explore the relationship between these measures and, in particular, the bias of Antolini's concordance in the presence of censoring using simulated data. We demonstrate the value of time-dependent Uno's C-index for the evaluation of models trained on censored real data and for model tuning.

Problem

• Evaluating predictive performance of non-linear survival models
• Introducing unbiased time-dependent Uno's C-index measure
• Assessing bias in Antolini's concordance with censored data

Innovation

• Introduces time-dependent Uno's C-index
• Unbiased version of Antolini's concordance
• Proves convergence using U-statistics theory