# A personalized Uncertainty Quantification framework for patient survival models: estimating individual uncertainty of patients with metastatic brain tumors in the absence of ground truth

arXiv: https://arxiv.org/abs/2311.17173 · HTML: https://mlsanity.com/paper/2311.17173/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Deep Neural Networks for Survival Analysis Based on a Multi-Task Framework](https://mlsanity.com/paper/1801.05512/) (2018)
- [Unbiased split variable selection for random survival forests using maximally selected rank statistics](https://mlsanity.com/paper/1605.03391/) (2016)
- [Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey](https://mlsanity.com/paper/2011.00680/) (2020)
- [Simultaneous Prediction Intervals for Patient-Specific Survival Curves](https://mlsanity.com/paper/1906.10780/) (2019)

## Abstract (arXiv)

TodevelopanovelUncertaintyQuantification (UQ) framework to estimate the uncertainty of patient survival models in the absence of ground truth, we developed and evaluated our approach based on a dataset of 1383 patients treated with stereotactic radiosurgery (SRS) for brain metastases between January 2015 and December 2020. Our motivating hypothesis is that a time-to-event prediction of a test patient on inference is more certain given a higher feature-space-similarity to patients in the training set. Therefore, the uncertainty for a particular patient-of-interest is represented by the concordance index between a patient similarity rank and a prediction similarity rank. Model uncertainty was defined as the increased percentage of the max uncertainty-constrained-AUC compared to the model AUC. We evaluated our method on multiple clinically-relevant endpoints, including time to intracranial progression (ICP), progression-free survival (PFS) after SRS, overall survival (OS), and time to ICP and/or death (ICPD), on a variety of both statistical and non-statistical models, including CoxPH, conditional survival forest (CSF), and neural multi-task linear regression (NMTLR). Our results show that all models had the lowest uncertainty on ICP (2.21%) and the highest uncertainty (17.28%) on ICPD. OS models demonstrated high variation in uncertainty performance, where NMTLR had the lowest uncertainty(1.96%)and CSF had the highest uncertainty (14.29%). In conclusion, our method can estimate the uncertainty of individual patient survival modeling results. As expected, our data empirically demonstrate that as model uncertainty measured via our technique increases, the similarity between a feature-space and its predicted outcome decreases.