leaspy: LEArning Spatiotemporal Patterns in PYthon

Abstract

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.