ICODEN: Ordinary Differential Equation Neural Networks for Interval-Censored Data

2026-02-10

AI Summary

This work proposes a neural ordinary differential equation (Neural ODE)-based survival analysis method to address the challenges of modeling interval-censored time-to-event data with high-dimensional covariates. By leveraging deep neural networks to flexibly model the hazard function and integrating it via an ODE solver to obtain the cumulative hazard, the approach eliminates the need for proportional hazards assumptions or prespecified parametric forms, thereby circumventing structural constraints inherent in traditional survival models. The resulting end-to-end trainable framework effectively handles covariates with dimensions reaching into the thousands—such as SNP data—and demonstrates strong predictive performance on both simulated and real-world biomedical datasets (ADNI, AREDS/AREDS2). Furthermore, it enables data-driven identification of distinct risk subgroups associated with disease progression.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Deep Neural Architectures and Foundation Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Security and Privacy: Data transparency and provenance

Abstract

Predicting time-to-event outcomes when event times are interval censored is challenging because the exact event time is unobserved. Many existing survival analysis approaches for interval-censored data rely on strong model assumptions or cannot handle high-dimensional predictors. We develop ICODEN, an ordinary differential equation-based neural network for interval-censored data that models the hazard function through deep neural networks and obtains the cumulative hazard by solving an ordinary differential equation. ICODEN does not require the proportional hazards assumption or a prespecified parametric form for the hazard function, thereby permitting flexible survival modeling. Across simulation settings with proportional or non-proportional hazards and both linear and nonlinear covariate effects, ICODEN consistently achieves satisfactory predictive accuracy and remains stable as the number of predictors increases. Applications to data from multiple phases of the Alzheimer's Disease Neuroimaging Initiative (ADNI) and to two Age-Related Eye Disease Studies (AREDS and AREDS2) for age-related macular degeneration (AMD) demonstrate ICODEN's robust prediction performance. In both applications, predicting time-to-AD or time-to-late AMD, ICODEN effectively uses hundreds to more than 1,000 SNPs and supports data-driven subgroup identification with differential progression risk profiles. These results establish ICODEN as a practical assumption-lean tool for prediction with interval-censored survival data in high-dimensional biomedical settings.

Problem

• interval-censored data
• time-to-event prediction
• high-dimensional predictors
• survival analysis
• hazard function

Innovation

• interval-censored data
• ordinary differential equation
• neural networks
• survival analysis
• high-dimensional predictors