🤖 AI Summary
Modeling individualized local dynamics in high-noise, multivariate longitudinal clinical data using ordinary differential equations (ODEs) remains challenging due to poor robustness and identifiability.
Method: We propose a local ODE modeling paradigm that initializes ODE solutions at each observed time point, generating and aggregating multiple local ODE trajectories per observation. The framework jointly learns a low-dimensional dynamic latent space and patient-specific ODE parameters via a variational autoencoder architecture, differentiable programming, and baseline-feature-driven ODE parameterization—enabling end-to-end interpretable modeling.
Contribution/Results: Evaluated on real-world spinal muscular atrophy cohort data and synthetic experiments, our method significantly improves short-term local prediction accuracy of health-state changes over global regression models (p < 0.01) and enhances dynamic interpretability. It establishes a novel paradigm for personalized disease progression modeling grounded in mechanistic, observation-driven ODE learning.
📝 Abstract
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established for statistical modeling of longitudinal cohort data, e.g., in a clinical setting. Yet, modeling of local changes could also be attractive for assessing the trajectory of an individual in a cohort in the immediate future given its current status, where ODE parameters could be informed by further characteristics of the individual. However, several hurdles so far limit such use of ODEs, as compared to regression-based function fitting approaches. The potentially higher level of noise in cohort data might be detrimental to ODEs, as the shape of the ODE solution heavily depends on the initial value. In addition, larger numbers of variables multiply such problems and might be difficult to handle for ODEs. To address this, we propose to use each observation in the course of time as the initial value to obtain multiple local ODE solutions and build a combined estimator of the underlying dynamics. Neural networks are used for obtaining a low-dimensional latent space for dynamic modeling from a potentially large number of variables, and for obtaining patient-specific ODE parameters from baseline variables. Simultaneous identification of dynamic models and of a latent space is enabled by recently developed differentiable programming techniques. We illustrate the proposed approach in an application with spinal muscular atrophy patients and a corresponding simulation study. In particular, modeling of local changes in health status at any point in time is contrasted to the interpretation of functions obtained from a global regression. This more generally highlights how different application settings might demand different modeling strategies.
