Evidential time-to-event prediction with calibrated uncertainty quantification

TL;DR

This work tackles time-to-event prediction under censoring with a focus on calibrated uncertainty. It introduces an evidential regression framework based on Gaussian random fuzzy numbers within Epistemic Random Fuzzy Sets to jointly model aleatory and epistemic uncertainty without strong distributional assumptions. The ENNreg model uses a radial-basis prototype layer, an evidence-mapping GRFN, and an evidence-fusion rule to produce a log-time prediction with Bel/Pl-based confidence and conservative survival bounds. Across simulated and real-world clinical datasets, the method demonstrates competitive accuracy and superior calibration, supporting uncertainty-aware clinical decision making in survival analysis.

Abstract

Time-to-event analysis provides insights into clinical prognosis and treatment recommendations. However, this task is more challenging than standard regression problems due to the presence of censored observations. Additionally, the lack of confidence assessment, model robustness, and prediction calibration raises concerns about the reliability of predictions. To address these challenges, we propose an evidential regression model specifically designed for time-to-event prediction. The proposed model quantifies both epistemic and aleatory uncertainties using Gaussian Random Fuzzy Numbers and belief functions, providing clinicians with uncertainty-aware survival time predictions. The model is trained by minimizing a generalized negative log-likelihood function accounting for data censoring. Experimental evaluations using simulated datasets with different data distributions and censoring conditions, as well as real-world datasets across diverse clinical applications, demonstrate that our model delivers both accurate and reliable performance, outperforming state-of-the-art methods. These results highlight the potential of our approach for enhancing clinical decision-making in survival analysis.

Figures (9)

• Figure 1: Overview of the study.
• Figure 2: Visualized prediction performance and uncertainty on the illustrative dataset. Figures (a) and (d) show the simulated data, actual regression function (blue broken lines), and predicted function obtained from the trained model (red solid lines) for 0% and 50% censoring rates. Belief prediction intervals (BPIs) at levels $\alpha \in \{0.5, 0.9, 0.99\}$ are represented by shaded areas in blue, green, and orange.
• Figure 3: Calibration plots for the illustrative dataset: belief prediction intervals (red solid lines) and probabilistic prediction intervals (blue broken lines).
• Figure 4: Performance comparison on the simulated data. The left, middle, and right columns correspond to the prediction results of simulated datasets generated under the LPH, NLPH, and NLNPH assumptions, respectively. The four methods are, from left to right in each plot: Cox based on the LPH assumption, DeepSurv based on the NLPH assumption, Cox-Time based on the NLNPH assumption, and our ENNreg model. Larger values of the concordance index $C_{idx}$ (top row) and lower values of integrated Brier score $IBS$ (middle row) as well as integrated binomial log-likelihood $IBLL$ (bottom row) indicate better performance.
• Figure 5: Calibration plots for the simulated data: belief prediction intervals (red solid lines) and probabilistic prediction intervals (blue broken lines).