# The C-index Multiverse

arXiv: https://arxiv.org/abs/2508.14821 · HTML: https://mlsanity.com/paper/2508.14821/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 47 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models](https://mlsanity.com/paper/2203.00144/) (2022)
- [Avoiding C-hacking when evaluating survival distribution predictions with discrimination measures](https://mlsanity.com/paper/2112.04828/) (2021)
- [The risks of risk assessment: causal blind spots when using prediction models for treatment decisions](https://mlsanity.com/paper/2402.17366/) (2024)
- [A new discrimination measure for assessing predictive performance of non-linear survival models](https://mlsanity.com/paper/2504.05630/) (2025)

## Built on by (most cited first, 1 of 1)

- [A reproducible and extensible framework for benchmarking competing risks survival models](https://mlsanity.com/paper/2608.00271/) (2026)

## Abstract (arXiv)

Quantifying out-of-sample discrimination performance for time-to-event outcomes is a fundamental step for model evaluation and selection in the context of predictive modelling. The concordance index, or C-index, is a widely used metric for this purpose, particularly with the growing development of machine learning methods. Beyond differences between proposed C-index estimators (e.g. Harrell's, Uno's and Antolini's), we demonstrate the existence of a C-index multiverse among available R and python software, where seemingly equal implementations can yield different results. This can undermine reproducibility and complicate fair comparisons across models and studies. Key variation sources include tie handling and adjustment to censoring. Additionally, the absence of a standardised approach to summarise risk from survival distributions, result in another source of variation dependent on input types. We demonstrate the consequences of the C-index multiverse when quantifying predictive performance for several survival models (from Cox proportional hazards to recent deep learning approaches) on publicly available breast cancer data, and semi-synthetic examples. Our work emphasises the need for better reporting to improve transparency and reproducibility. This article aims to be a useful guideline, helping analysts when navigating the multiverse, providing unified documentation and highlighting potential pitfalls of existing software. All code is publicly available at: www.github.com/BBolosSierra/CindexMultiverse.