Towards Fair Predictions: Group Conditional Concordance Index to Quantify Fairness in Time-to-Event Prognostication

2026-06-15

AI Summary

This work addresses the lack of fairness metrics tailored for time-to-event prediction with right-censored data, a setting where existing measures—largely confined to binary classification—are inadequate. The authors propose the group-conditional concordance index (xCI), which extends Harrell’s concordance index by stratifying according to sensitive attributes to assess both within-group and between-group ranking fairness in survival models. An inverse probability of censoring weighting (IPCW) scheme is integrated to construct a consistent estimator. Theoretical analysis reveals that the conventional concordance index can be expressed as a weighted average of xCI, and establishes a clear connection between xCI and risk scores. In multi-cohort cardiovascular disease prediction experiments, xCI uncovers subgroup disparities overlooked by standard metrics, offering the first fairness evaluation framework specifically designed for survival analysis in high-stakes applications such as healthcare resource allocation.

Abstract

Fairness metrics are essential for rigorously defining, quantifying, and mitigating biases in predictive models. While most existing metrics focus on binary classification tasks, fairness in time-to-event analyses has received limited attention. To address this gap, we propose a novel group fairness metric, the group-conditional Concordance Index (xCI), which extends Harrell's Concordance Index (CI) by conditioning on group membership. The xCI measures both within-group and cross-group ranking accuracy in the presence of right-censored data. We formally define the xCI, prove that CI is a weighted average of xCIs across all possible group pairs, and develop a consistent estimator using inverse probability of censoring weights (IPCW). We further investigate the relationship between xCI and predicted risk scores through analytical derivations and simulation studies. To demonstrate its practical utility, we present two case studies: (i) assessing the fairness of survival models trained on harmonized data from the Framingham Offspring, MESA, and ARIC studies, and (ii) evaluating fairness in existing cardiovascular disease (CVD) risk prediction models using Truveta, a large-scale electronic health record (EHR) database. Our results show that xCI effectively detects biases across demographic groups that are overlooked by existing metrics. Overall, xCI provides a valuable tool for fairness assessment in survival analysis, particularly in constrained resource allocation settings, and complements existing fairness evaluation approaches.

Problem

• fairness
• time-to-event prediction
• group bias
• survival analysis
• censored data

Innovation

• group-conditional Concordance Index
• fairness in survival analysis
• right-censored data
• inverse probability of censoring weighting
• time-to-event prediction