The receiver operating characteristic (ROC) curve is a graphical tool commonly used to assess the discriminatory ability of continuous markers in binary classification problems. Different extensions of the ROC curve have been proposed in the prognosis context, where the characteristics in the study are time-dependent events. Perhaps the most direct generalization is the so-called cumulative/dynamic (C/D) ROC curve. The main particularity when dealing with the C/D ROC curve estimation is the presence of incomplete information. Several approximation methods addressing this censoring problem have been suggested in the statistical literature, most of them focused on the right-censored case. Interval censorship arises naturally from those studies where subjects undergo periodical follow-ups. They may miss a scheduled appointment and the exact event times are only known to fall in a certain range. A new approach for estimating the C/D ROC curve under the particular scheme of interval censorship is presented in this work. Its finite-sample behaviour is studied via Monte Carlo simulations on two different scenarios. Results suggest that the proposed approximation is better than the existing one in terms of absolute error. Its direct application is illustrated in the real-world data set which motivated this research. The uniform strong consistency and a suitable R function for its practical implementation are provided as Appendices.

中文翻译：

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区间审查下的累积/动态 ROC 曲线估计

接收者操作特征 (ROC) 曲线是一种图形工具，通常用于评估连续标记在二元分类问题中的区分能力。已经在预后背景中提出了 ROC 曲线的不同扩展，其中研究中的特征是时间依赖性事件。也许最直接的概括是所谓的累积/动态 (C/D) ROC 曲线。处理 C/D ROC 曲线估计时的主要特殊性是存在不完整信息。统计文献中已经提出了几种解决这个删失问题的近似方法，其中大部分都集中在右删失的情况下。间隔审查自然产生于那些受试者接受定期随访的研究。他们可能会错过预定的约会，确切的活动时间只知道在某个范围内。本文提出了一种在特定区间审查方案下估计 C/D ROC 曲线的新方法。它的有限样本行为是通过蒙特卡罗模拟在两种不同情况下进行研究的。结果表明，就绝对误差而言，所提出的近似值优于现有近似值。它的直接应用在激发这项研究的真实世界数据集中得到了说明。附录中提供了统一的强一致性和适合其实际实现的 R 函数。它的有限样本行为是通过蒙特卡罗模拟在两种不同情况下进行研究的。结果表明，就绝对误差而言，所提出的近似值优于现有近似值。它的直接应用在激发这项研究的真实世界数据集中得到了说明。附录中提供了统一的强一致性和适合其实际实现的 R 函数。它的有限样本行为是通过蒙特卡罗模拟在两种不同情况下进行研究的。结果表明，就绝对误差而言，所提出的近似值优于现有近似值。它的直接应用在激发这项研究的真实世界数据集中得到了说明。附录中提供了统一的强一致性和适合其实际实现的 R 函数。