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

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.