The C-index Multiverse

TL;DR

This paper investigates the variability in C-index calculations across different software implementations, highlighting how this multiverse affects reproducibility and model comparison in survival analysis.

Contribution

It identifies sources of variation in C-index estimation, demonstrates their impact on survival model evaluation, and provides guidelines and tools for more transparent and consistent reporting.

Findings

Different software yield varying C-index results due to tie handling and censoring adjustments.

The C-index multiverse affects model performance comparisons across methods.

Guidelines and code are provided to improve reproducibility and transparency.

Abstract

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.