# Confidence intervals for the Cox model test error from cross-validation

arXiv: https://arxiv.org/abs/2201.10770 · HTML: https://mlsanity.com/paper/2201.10770/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 3 of 3)

- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Cross-validation Confidence Intervals for Test Error](https://mlsanity.com/paper/2007.12671/) (2020)
- [Survival stacking: casting survival analysis as a classification problem](https://mlsanity.com/paper/2107.13480/) (2021)

## Abstract (arXiv)

Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test error using estimates from CV may have coverage below nominal levels. This phenomenon occurs because each sample is used in both the training and testing procedures during CV and as a result, the CV estimates of the errors become correlated. Without accounting for this correlation, the estimate of the variance is smaller than it should be. One way to mitigate this issue is by estimating the mean squared error of the prediction error instead using nested CV. This approach has been shown to achieve superior coverage compared to intervals derived from standard CV. In this work, we generalize the nested CV idea to the Cox proportional hazards model and explore various choices of test error for this setting.