SurvUnc: A Meta-Model Based Uncertainty Quantification Framework for Survival Analysis

TL;DR

SurvUnc tackles the lack of reliable uncertainty quantification in survival analysis by introducing a post-hoc, model-agnostic meta-model that estimates prediction uncertainty for any pretrained survival model. It uses an anchor-based concordance strategy to generate a labeled meta-training set, enabling the meta-model to learn ranking-based uncertainty without accessing base model internals. Across four real and one synthetic dataset and five survival models, SurvUnc improves selective prediction, misprediction detection, and out-of-domain detection compared to MC-Dropout, ensembles, and BNNSurv baselines. The framework maintains compatibility with diverse base models, offering a practical, scalable path toward trustworthy, interpretable survival predictions in high-stakes settings.

Abstract

Survival analysis, which estimates the probability of event occurrence over time from censored data, is fundamental in numerous real-world applications, particularly in high-stakes domains such as healthcare and risk assessment. Despite advances in numerous survival models, quantifying the uncertainty of predictions from these models remains underexplored and challenging. The lack of reliable uncertainty quantification limits the interpretability and trustworthiness of survival models, hindering their adoption in clinical decision-making and other sensitive applications. To bridge this gap, in this work, we introduce SurvUnc, a novel meta-model based framework for post-hoc uncertainty quantification for survival models. SurvUnc introduces an anchor-based learning strategy that integrates concordance knowledge into meta-model optimization, leveraging pairwise ranking performance to estimate uncertainty effectively. Notably, our framework is model-agnostic, ensuring compatibility with any survival model without requiring modifications to its architecture or access to its internal parameters. Especially, we design a comprehensive evaluation pipeline tailored to this critical yet overlooked problem. Through extensive experiments on four publicly available benchmarking datasets and five representative survival models, we demonstrate the superiority of SurvUnc across multiple evaluation scenarios, including selective prediction, misprediction detection, and out-of-domain detection. Our results highlight the effectiveness of SurvUnc in enhancing model interpretability and reliability, paving the way for more trustworthy survival predictions in real-world applications.

Figures (10)

• Figure 1: Illustration of our proposed framework SurvUnc. (a) The pipeline of post-hoc meta-model based uncertainty quantification for survival models, and (b) the anchor-based learning strategy for meta-model optimization.
• Figure 2: $C^\text{td}$ of four survival models of (a) DeepSurv, (b) DeepHit, (c) DSM and (d) RSF on SEER-BC dataset with different percentages of samples discarded according to uncertainty scores from different UQ methods. A consistent upward trend is expected as the percentage of discarded samples increases. Error bars are omitted for better visualization.
• Figure 3: Predicted uncertainty scores versus IBSs from DeepSurv quantified by SurvUnc-RF across samples on (a) FLCHAIN, (b) SUPPORT, (c) SEER-BC and (d) SAC3 datasets.
• Figure 4: Survival curve comparison of high-uncertainty and low-uncertainty samples on SAC3 dataset, quantified by SurvUnc-RF on DeepSurv. "GT" (with solid lines) and "P" (with dashed lines) denote "Ground Truth" and "Predicted", respectively, and the values in legend are uncertainty scores.
• Figure 5: Uncertainty score distribution comparison of DeepSurv between IND (BC) and OOD (HD) samples from SEER dataset, with uncertainty scores from (a) SurvUnC-RF, (b) SurvUnc-MLP, (c) MC-Dropout and (d) Ensemble.