# The Concordance Index decomposition: A measure for a deeper understanding of survival prediction models

arXiv: https://arxiv.org/abs/2203.00144 · HTML: https://mlsanity.com/paper/2203.00144/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 6 of 6)

- [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)
- [Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data with Competing Risks](https://mlsanity.com/paper/2003.01176/) (2020)
- [Deep Survival Analysis](https://mlsanity.com/paper/1608.02158/) (2016)
- [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018)
- [Variational Learning of Individual Survival Distributions](https://mlsanity.com/paper/2003.04430/) (2020)

## Built on by (most cited first, 8 of 8)

- [Colorectal cancer survival prediction using deep distribution based multiple-instance learning](https://mlsanity.com/paper/2204.11294/) (2022)
- [CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis](https://mlsanity.com/paper/2407.13849/) (2024)
- [Tackling Small Sample Survival Analysis via Transfer Learning: A Study of Colorectal Cancer Prognosis](https://mlsanity.com/paper/2501.12421/) (2025)
- [The C-index Multiverse](https://mlsanity.com/paper/2508.14821/) (2025)
- [Multimodal Feature Prototype Learning for Interpretable and Discriminative Cancer Survival Prediction](https://mlsanity.com/paper/2510.06113/) (2025)
- [Synergy vs. Noise: Performance-Guided Multimodal Fusion For Biochemical Recurrence-Free Survival in Prostate Cancer](https://mlsanity.com/paper/2511.11452/) (2025)
- [K-Survival Means](https://mlsanity.com/paper/2607.24405/) (2026)
- [Nonparametric Distribution Matching for Self-Supervised Whole-Slide Image Condensation](https://mlsanity.com/paper/2610.00678/) (2026)

## Abstract (arXiv)

The Concordance Index (C-index) is a commonly used metric in Survival Analysis for evaluating the performance of a prediction model. In this paper, we propose a decomposition of the C-index into a weighted harmonic mean of two quantities: one for ranking observed events versus other observed events, and the other for ranking observed events versus censored cases. This decomposition enables a finer-grained analysis of the relative strengths and weaknesses between different survival prediction methods. The usefulness of this decomposition is demonstrated through benchmark comparisons against classical models and state-of-the-art methods, together with the new variational generative neural-network-based method (SurVED) proposed in this paper. The performance of the models is assessed using four publicly available datasets with varying levels of censoring. Using the C-index decomposition and synthetic censoring, the analysis shows that deep learning models utilize the observed events more effectively than other models. This allows them to keep a stable C-index in different censoring levels. In contrast to such deep learning methods, classical machine learning models deteriorate when the censoring level decreases due to their inability to improve on ranking the events versus other events.