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arXiv2026

leaspy: LEArning Spatiotemporal Patterns in PYthon

Longitudinal data are fundamental across scientific disciplines for modeling how complex systems evolve over time. A core challenge in these settings is handling temporal misalignment: different subjects undergo a similar underlying process but at varying speeds and starting times. This difficulty is further compounded when tracking multivariate dynamics, where features interact dynamically rather than following simple, independent pathways. To address these challenges, we present leaspy (LEArning Spatiotemporal patterns in PYthon), an open-source Python library. Built on a mixed effects model, leaspy enables the estimation of population-level trajectories while accounting for subject-specific variability. The library supports multivariate formulation across diverse data types, including continuous, time-to-event (joint), and mixture models-and has been successfully applied to characterize disease heterogeneity, and generate individual predictions We demonstrate its practical utility through an application in neurodegenerative disease progression. Developed following modern software engineering practices, including systematic testing and continuous integration, leaspy facilitates the integration of new models and provides a robust user-friendly library for longitudinal progression modeling.

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arXiv2026

A mixture model for subtype identification in the context of disease progression modeling

The progression of chronic diseases often follows highly variable trajectories, and the underlying factors remain poorly understood. Standard mixed-effects models typically represent inter-patient differences as random deviations around a common reference, which may obscure meaningful subgroups. We propose a probabilistic mixture extension of a mixed effects model, the Disease Course Mapping model, to identify distinct disease progression subtypes within a population. The mixture structure is introduced at the latent individual parameters, enabling clustering based on both temporal and spatial variability in disease trajectories. We evaluated the model through simulation studies to assess classification performance and parameter recovery. Classification accuracy exceeded 90% in simpler scenarios and remained above 80% in the most complex case, with particularly high recall and precision for fast-progressing clusters. Compared to a post hoc classification approach, the proposed model yielded more accurate parameter estimates, smaller biases, lower root mean squared errors, and reduced uncertainty. It also correctly recovered the true three-cluster structure in 93% of the simulations. Finally, we applied the model to a longitudinal cohort of CADASIL patients, identifying two clinically meaningful clusters, differentiating patients with early versus late onset and fast versus slow progression, with clear spatial patterns across motor and memory scores. Overall, this probabilistic mixture framework offers a robust, interpretable approach for clustering patients based on spatiotemporal disease dynamics.

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