Uncovering disease progression trajectories across multiple timescales with hybrid ODE-mixture models

Biological systems are capable of evolving across multiple timescales, yet most modeling approaches capture either short-term physiological responses or long-term disease progression. Additionally, methods that combine these time scales either struggle with inter-individual variation, or require large volumes of data to work. We present Latent Class Parameter Trajectory Analysis (LCPTA), a hybrid framework that combines mechanistic ordinary differential equation (ODE) modeling of short-term dynamics with latent class trajectory modeling of long-term parameter evolution. To support this approach, we developed TemporalMixtureModels.jl, a Julia package for univariate and multivariate temporal mixture modeling. We evaluated LCPTA in two synthetic longitudinal studies, covering a simulation of a heterogeneous population developing hypertension, as well as a synthetic longitudinal study of 75 virtual individuals followed over 30 years, representing muscle insulin resistance, liver insulin resistance, and healthy trajectories. We compared LCPTA with a conditional neural ODE and a conditional neural network for reconstruction of long-term parameter trajectories and subgroup separation. In both studies LCPTA recovered relevant subgroup structure and trajectory patterns. In the cardiovascular study, the neural approaches were able to distinguish inter-individual differences, but in the insulin sensitivity study, neural approaches failed to represent parameter trajectories faithfully, primarily separating individuals along a single dominant parameter and showing weaker multivariate trajectory reconstruction. In additional experiments with sparse and irregularly sampled unseen individuals, LCPTA maintained strong classification performance. We show that LCPTA is an efficient and interpretable strategy for multiscale modeling of heterogeneous metabolic disease progression, with potential utility for data-efficient digital twin applications.