ENC-ODE: Event-level Neurodegenerative Modeling in Continuous Time with Neural ODEs
Authors: Yujee Song, Seunghun Baek, Guorong Wu, Won Hwa Kim
Organizations: Pohang University of Science and Technology, Pohang, South Korea · University of North Carolina at Chapel Hill, Chapel Hill, USA
Abstract
Accurately predicting the temporal evolution of clinical biomarkers is crucial for the early diagnosis and management of neurodegenerative diseases such as Alzheimer's disease. However, this relies on longitudinal data to capture biomarker changes over time, which is often sparse and irregular due to the high cost, labor-intensive nature, and patient burden. To address these challenges, we propose ENC-ODE, an Event-level Neurodegenerative modeling in Continuous time with neural Ordinary Differential Equations. ENC-ODE predicts future biomarker evolution by modeling clinical events through diagnosis-conditioned continuous dynamics. A target-conditioned attention mechanism weights and aggregates event-level predictions for the target time and modality without history compression. Extensive experiments on Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that ENC-ODE outperforms representative sequence models while offering a scalable and neuroscientifically grounded solution for clinical support. The code is available at https://github.com/JardinDelSol/enc-ode.
Event-Based Models (EBMs) infer biomarker progression from cross-sectional data but typically only as ordinal sequences and rely on rigid model assumptions. We propose \textsc{Tempo}, a Transformer architecture that learns both ordinal and continuous event sequences through simulation-based supervised learning. \textsc{Tempo} uses two Transformer modules: one treats biomarkers as tokens to infer event sequencing; the other treats patients as tokens, representing each by their per-biomarker abnormality profile, to infer patients' disease stages. On synthetic benchmarks, \textsc{Tempo} reduces normalized Kendall's Tau distance by 52.89% and staging MAE by 25.33% compared to state-of-the-art SA-EBM, with larger reductions in high-dimensional settings (58.88% and 61.10%). Applied to ADNI, \textsc{Tempo} recovers a biologically plausible Alzheimer's progression: early medial temporal atrophy, followed by amyloid accumulation and cognitive decline, and late-stage tau pathology with terminal acceleration of global neurodegeneration -- broadly consistent with established disease models. \textsc{Tempo} also eliminates the need to derive custom inference algorithms and enables rapid empirical comparison of generative hypotheses.
Alzheimer's disease (AD) progression is often described through the amyloid-tau-neurodegeneration, or AT(N), cascade. However, most longitudinal models represent this cascade either as a fixed sequence of biomarkers or as a black-box forecasting task. This makes it difficult to determine when biologically guided biomarker relationships influence future regional pathology. In this study, we introduce Bayesian Networks with Latent Time Embedding (BN-LTE), a Bayesian structural framework for stage-aware modeling of AD progression. BN-LTE estimates disease pseudotime from baseline biomarker profiles and constrains directed dependencies according to biologically plausible AT(N) ordering. Posterior spline-varying structural equations are then used to link initial multimodal measurements with future annualized regional tau-PET change. Across repeated subject-disjoint evaluations using ADNI data, BN-LTE shows strong spatial reconstruction of tau progression compared with the included forecasting baselines. Beyond spatial reconstruction, BN-LTE recovers posterior stage-varying AT(N)-constrained effects and identifies a mid-pseudotime window of amyloid sensitivity. This window is supported by model-implied g-formula contrasts, root-adjusted AIPW, mechanism-sensitive ablations, and robustness analyses across spline and prior specifications. Overall, these findings position BN-LTE as a Bayesian structural framework for forecasting tau progression while examining stage-dependent AT(N)-cascade mechanisms in observational longitudinal neuroimaging data. Our code is available at https://github.com/danleneurocom/BN-LTE.
Alzheimer's disease is a progressive neurodegenerative disorder, and its progression varies substantially across patients. Existing work aims to forecast patients' future cognitive state, with minimal focus on reconstructing the state from past visits. Furthermore, in current research, quantifying predictive uncertainty remains underexplored and relies on costly modalities such as MRI, PET, and CSF, limiting their deployment in resource-limited settings. In this research, our primary objectives are: First, bidirectional prediction of cognitive scores from irregular visits to present the complete disease trajectory. Second, to enable interpolation and extrapolation capabilities to assist clinicians in informed prognostic decision making, and third, to provide a well-calibrated uncertainty estimate for all predictions, and finally, to achieve the objectives using the modalities available during routine visits. We propose a unified framework, GNOVA: A GRU-Neural ODE Variational Autoencoder. The architecture combines a Gated Recurrent Unit encoder and a Neural ODE decoder within a variational autoencoder framework. In our work, we forecast the CDR-SB and MMSE Scores. The GRU encoder allows for any number of inputs at any time point. The Neural-ODE decoder performs continuous estimation, allowing interpolation and extrapolation at any desired time point. The Variational autoencoder allows for uncertainty estimation in predictions. We worked with 1,727 patients from the ADNI dataset over 10 years; the model achieved mean absolute errors of 1.35 and 2.28 for CDR-SB and MMSE scores, respectively, without requiring any neuroimaging or biomarker data. Feature-ablation studies revealed that age, BMI, and APOE4 status were strong predictors. The proposed framework enables the reconstruction of incomplete patient histories and the anticipation of future cognitive states.