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

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.

Regression Trees for Cumulative Incidence Functions

The use of cumulative incidence functions for characterizing the risk of one type of event in the presence of others has become increasingly popular over the past decade. The problems of modeling, estimation and inference have been treated using parametric, nonparametric and semi-parametric methods. Efforts to develop suitable extensions of machine learning methods, such as regression trees and related ensemble methods, have begun only recently. In this paper, we develop a novel approach to building regression trees for estimating cumulative incidence curves in a competing risks setting. The proposed methods employ augmented estimators of the Brier score risk as the primary basis for building and pruning trees. The proposed methods are easily implemented using the R statistical software package. Simulation studies demonstrate the utility of our approach in the competing risks setting. Data from the Radiation Therapy Oncology Group (trial 9410) is used to illustrate these new methods.