Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating outcomes with a range format. As interest in automating healthcare decisions grows, uncertainty quantification via predictive regions becomes essential for developing reliable and trustworthy predictive algorithms. However, the statistical literature currently lacks a general methodology for interval targets, especially when these outcomes are incomplete due to censoring. We propose an uncertainty quantification algorithm for interval responses and establish its theoretical properties using empirical process arguments based on a newly developed class of functions specifically designed for these interval data structures. Although this paper primarily focuses on deriving predictive regions for interval-censored data, the approach can also be applied to other statistical modeling tasks, such as goodness-of-fit assessments. Finally, the applicability of the method is demonstrated through simulations, showing up to a 60\% improvement in conditional coverage. Our new algorithm is also applied to various biomedical contexts, including two clinical examples: i) sleep duration and its association with cardiovascular diseases, and ii) survival time in relation to physical activity levels.

翻译：在许多科学应用中，遵循区间结构的数据日益普遍。在医学领域，临床事件通常是在两次临床访视之间进行监测的，这使得事件的确切时间未知，并生成了具有区间格式的结果。随着对医疗决策自动化兴趣的增长，通过预测区域进行不确定性量化对于开发可靠且值得信赖的预测算法变得至关重要。然而，目前的统计学文献缺乏针对区间目标的通用方法，特别是当这些结果因删失而不完整时。我们提出了一种针对区间响应的不确定性量化算法，并基于专门为这些区间数据结构新开发的一类函数，利用经验过程论证建立了其理论性质。尽管本文主要侧重于推导区间删失数据的预测区域，但该方法也可应用于其他统计建模任务，例如拟合优度评估。最后，通过模拟证明了该方法的适用性，显示条件覆盖率可提高高达60%。我们的新算法还应用于各种生物医学背景，包括两个临床实例：i) 睡眠时长及其与心血管疾病的关联，以及ii) 与身体活动水平相关的生存时间。