# A Statistical Learning Take on the Concordance Index for Survival Analysis

arXiv: https://arxiv.org/abs/2302.12059 · HTML: https://mlsanity.com/paper/2302.12059/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 60 references that are in the map.
- First posted on arXiv 23 Feb 2023.

## Builds on (most cited first, 11 of 11)

- [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)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Survival regression with accelerated failure time model in XGBoost](https://mlsanity.com/paper/2006.04920/) (2020)
- [Learning Groupwise Multivariate Scoring Functions Using Deep Neural Networks](https://mlsanity.com/paper/1811.04415/) (2018)
- [A General Theory for Structured Prediction with Smooth Convex Surrogates](https://mlsanity.com/paper/1902.01958/) (2019)
- [Deep Learning for Survival Outcomes](https://mlsanity.com/paper/1904.10345/) (2019)
- [Ranking Data with Continuous Labels through Oriented Recursive Partitions](https://mlsanity.com/paper/1801.05772/) (2018)
- [Drug Selection via Joint Push and Learning to Rank](https://mlsanity.com/paper/1801.07691/) (2018)
- [Empirical Risk Minimization under Random Censorship: Theory and Practice](https://mlsanity.com/paper/1906.01908/) (2019)

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

- [Value-Monotonicity Matters: A Concordance Loss for Deep Survival Prediction](https://mlsanity.com/paper/2607.16802/) (2026)

## Abstract (arXiv)

The introduction of machine learning (ML) techniques to the field of survival analysis has increased the flexibility of modeling approaches, and ML based models have become state-of-the-art. These models optimize their own cost functions, and their performance is often evaluated using the concordance index (C-index). From a statistical learning perspective, it is therefore an important problem to analyze the relationship between the optimizers of the C-index and those of the ML cost functions. We address this issue by providing C-index Fisher-consistency results and excess risk bounds for several of the commonly used cost functions in survival analysis. We identify conditions under which they are consistent, under the form of three nested families of survival models. We also study the general case where no model assumption is made and present a new, off-the-shelf method that is shown to be consistent with the C-index, although computationally expensive at inference. Finally, we perform limited numerical experiments with simulated data to illustrate our theoretical findings.