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.

翻译：公平性指标对于严谨定义、量化及缓解预测模型中的偏见至关重要。尽管现有指标多聚焦于二分类任务，但时间至事件分析中的公平性问题仍鲜少被关注。为填补这一空白，我们提出新的群体公平性指标——组条件一致性指数（xCI），该指标通过引入组别条件扩展了Harrell一致性指数（CI）。xCI能在右删失数据情境下同时衡量组内与跨组的排序准确性。我们正式定义了xCI，证明CI是所有可能组对间xCI的加权平均，并基于逆删失权重（IPCW）推导出一致性估计量。此外，通过解析推导与模拟研究，我们探究了xCI与预测风险评分之间的关联。为展示其实用价值，我们呈现两项案例研究：（i）评估基于Framingham后代研究、MESA及ARIC数据训练的生存模型的公平性；（ii）利用Truveta大规模电子健康记录（EHR）数据库，评估现有心血管疾病（CVD）风险预测模型的公平性。结果表明，xCI能有效检测现有指标忽视的跨人口统计群体偏见。总体而言，xCI为生存分析中的公平性评估（尤其在资源受限的分配场景中）提供了有力工具，并补充了现有公平性评价方法体系。