标题： 时间依赖性伪$\boldsymbol{R^2}$用于评估竞争风险数据中的预测性能 显示英文标题

标题： Time-Dependent Pseudo $\boldsymbol{R^2}$ for Assessing Predictive Performance in Competing Risks Data

摘要： 评估和验证预测模型的性能是统计学、机器学习及其各种应用中的基本任务。 然而，为竞争风险的时间至事件数据开发稳健的性能指标面临独特的挑战。 我们首先强调某些传统的预测性能指标，如C指数、Brier分数和时间依赖的AUC，在比较不同预测模型的预测性能时可能会产生不理想的结果。 为解决这一研究空白，我们引入了一种新的时间依赖性伪$R^2$指标，在右删失竞争风险时间至事件数据下，用于评估预测累积发生函数在受限时间域内的预测性能。 具体而言，我们首先提出了针对感兴趣的竞争风险事件的总体水平时间依赖性伪$R^2$指标，然后根据右删失竞争风险时间至事件数据定义了其相应的样本版本。 我们研究了所提出指标的渐近性质，并通过全面的模拟研究和实际数据应用展示了其相对于传统指标的优势。 显示英文摘要

摘要： Evaluating and validating the performance of prediction models is a fundamental task in statistics, machine learning, and their diverse applications. However, developing robust performance metrics for competing risks time-to-event data poses unique challenges. We first highlight how certain conventional predictive performance metrics, such as the C-index, Brier score, and time-dependent AUC, can yield undesirable results when comparing predictive performance between different prediction models. To address this research gap, we introduce a novel time-dependent pseudo $R^2$ measure to evaluate the predictive performance of a predictive cumulative incidence function over a restricted time domain under right-censored competing risks time-to-event data. Specifically, we first propose a population-level time-dependent pseudo $R^2$ measures for the competing risk event of interest and then define their corresponding sample versions based on right-censored competing risks time-to-event data. We investigate the asymptotic properties of the proposed measure and demonstrate its advantages over conventional metrics through comprehensive simulation studies and real data applications.