Uncertainty quantification for intervals

Authors: Carlos García Meixide, Michael R. Kosorok, Marcos Matabuena

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Overview

uncervals introduces a novel uncertainty quantification algorithm specifically designed for interval-censored data — a common but challenging data structure in modern healthcare, digital health, and biomedical research.

The Problem

In many clinical settings, exact event times are unknown:

• Digital Health: Events occur between device measurements or when wearables are removed
• Electronic Health Records: Clinical events happen between medical visits
• Sleep Studies: The exact moment of falling asleep occurs within a known time window
• Chronic Disease Monitoring: Diabetes onset, cardiovascular events detected between checkups

Traditional survival analysis focuses on right-censored data, but interval-censored outcomes require fundamentally different approaches.

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Key Contributions

Practical Impact

A comprehensive uncertainty quantification algorithm compatible with off-the-shelf regression models for interval-censored data, providing:

• Valid prediction intervals for outcomes bounded by observation windows
• Up to 60% improvement in conditional coverage over naive approaches
• Distribution-free guarantees without strong parametric assumptions

Theoretical Foundations

• Novel class of functions specifically designed for interval data structures
• Rigorous empirical process theory establishing consistency and convergence rates
• Proof that 𝒢 is a universal Donsker class, guaranteeing asymptotic properties
• Bootstrap consistency results for interval-censored scenarios

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Algorithm

uncervals operates in two modes:

• Mode e=0: Conservative approach with finite-sample validity guarantees (generalization of conformal prediction to interval-censoring)
• Mode e=*: Bootstrap-enhanced version with improved conditional coverage

Both modes integrate seamlessly with any interval-censored regression estimator.

Key Features

Non-asymptotic coverage guarantees for exchangeable data
Model-agnostic: Works with any conditional survival function estimator
Handles: interval, left, and right censoring
Minimal assumptions: No parametric distributional requirements

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Installation & Usage

All code and data to reproduce the analyses are available in this repository:

git clone https://github.com/meixide/uncervals
cd uncervals

Basic Example

Try main.R

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Mathematical Framework

The algorithm constructs lower predictive bounds (LPBs) satisfying:

$$\mathbb{P}(T_{N+1} \in \widehat{\mathcal{C}}_{1-\alpha}(X_{N+1})) \geq 1-\alpha$$

Key innovation: The Interval Process $\mathbb{H}_n$ derived from the function class 𝒢, which:

• Captures information from observed interval boundaries $(L_i, U_i)$
• Extends the empirical CDF to interval-censored settings
• Enables rigorous theoretical analysis via VC theory

Citation

If you use this code or methodology in your research, please cite:

@article{meixide2025uncervals,
  title={Uncertainty Quantification for Intervals},
  author={Meixide, Carlos García and Kosorok, Michael R. and Matabuena, Marcos},
  journal={arXiv},
  year={2025}
}

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Unlike existing methods that focus exclusively on right-censoring, uncervals addresses the fundamental challenge that survival times are never observed under interval-censoring.