Synthetic-data augmented calibration for expert-informed rare disease models

Clinical data for rare diseases are sparse, noisy, and heterogeneous, complicating calibration of ordinary differential equation (ODE) models. Thus, we introduce a noise-robust calibration in latent space that combines expertderived ODEs with learned latent representations. Our approach leverages synthetic ODE trajectories, augmenting our scarce observations to train a model-specific autoencoder representation and imputer. During calibration, observed and ODE-generated trajectories are compared in latent space, and ODE parameters are updated by minimizing their latent distance. In a controlled ABCDE simulation model, the imputer outperformed a carry-forward baseline for moderate parameter shifts, parameter recovery remained stable under random missingness, calibration remained robust to additional noise variables despite reduced downstream identifiability, and distinct dynamics formed visually separable latent trajectories. On a custom developed ODE model for real Epidermolysis Bullosa patients, the calibrated phenomenological model reproduced patient-level trajectories from sparse observations. Thus, we conclude that our latent-space calibration approach supports rare-disease modeling.