Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: CausalityConstraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
A new discrimination measure for assessing predictive performance of non-linear survival models
🤖 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
Application Category
📝 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
Research questions and friction points this paper is trying to address.
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
Methods, ideas, or system contributions that make the work stand out.
Introduces time-dependent Uno's C-index
Unbiased version of Antolini's concordance
Proves convergence using U-statistics theory
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2024-09-20arXiv.orgCitations: 0
