Uncertainty quantification for intervals

TL;DR

This paper introduces a new method for quantifying uncertainty in interval-censored data, crucial for reliable predictions in healthcare and biomedical research, with proven improvements in coverage and practical applications.

Contribution

It develops a novel uncertainty quantification algorithm tailored for interval responses, with theoretical validation and broad applicability to statistical modeling tasks.

Findings

Up to 60% improvement in conditional coverage.

Effective in biomedical applications like sleep duration and survival analysis.

Validated through simulations and clinical data.

Abstract

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.