LEArning Spatiotemporal Patterns in Python¶
Description¶
Leaspy is a software package for the statistical analysis of longitudinal data, particularly medical data that comes in a form of repeated observations of patients at different time-points.
Figure 1: Illustration of the Disease Progression Model underlying Leaspy. (a) illustrates how sparse individual observations (colored dots) can be recombined into a common population trajectory (in black), while accounting for the fact that each subject may progress earlier/later or faster/slower than the average (the green individual progresses earlier, and the blue one slower than the average). (b) shows the corresponding geometric interpretation: individual data points are mapped onto a shared trajectory on a Riemannian manifold. Individual trajectories are then computed through subject-specific temporal transformations (time-shift \(\tau_i\) and acceleration \(\alpha_i\)), and spatial transformations (\(w_i\)) capturing differences in the ordering and pattern of deterioration across outcomes.¶
Figure 1 provides an intuitive overview of the objective of the software. By estimating the temporal and spatial transformations, Leaspy positions each patient relative to the group-average disease timeline, enabling meaningful comparison across individuals despite heterogeneous follow-ups.
The framework further allows:
Quantifying impact of cofactors (gender, genetic mutation, environmental factors, …) on the evolution of the signal;
Imputing missing values;
Predicting future observations;
Simulating virtual patients to un-bias the initial cohort or mimic its characteristics.
The software package can be used with scalar multivariate data whose progression can be described by a logistic, linear, joint, or mixture model. The simplest type of data handled by the software are scalar data: they correspond to one (univariate) or multiple (multivariate) measurement(s) per patient observation. This includes, for instance, clinical scores, cognitive assessments, physiological measurements (e.g. blood markers, radioactive markers) but also imaging-derived data that are rescaled, for instance, between 0 and 1 to describe a logistic progression.
Getting started¶
Information to install, test, and contribute to the package are available here.
API Documentation¶
The exact API of all functions and classes, as given in the docstrings. The API documents expected types and allowed features for all functions, and all parameters available for the algorithms.
User Guide¶
The main documentation. This contains an in-depth description of all algorithms and how to apply them.
License¶
The package is distributed under the BSD-3-Clause-Clear license.
Further information¶
More detailed explanations about the models themselves and about the estimation procedure can be found in the following articles :
Mathematical framework: A Bayesian mixed-effects model to learn trajectories of changes from repeated manifold-valued observations. Jean-Baptiste Schiratti, Stéphanie Allassonnière, Olivier Colliot, and Stanley Durrleman. The Journal of Machine Learning Research, 18:1–33, December 2017. Open Access
Mixture Model: A mixture model for subtype identification: Application to CADASIL Sofia Kaisaridi, Juliette Ortholand, Caglayan Tuna, Nicolas Gensollen, and Sophie Tezenas Du Montcel ISCB 46-46th Annual Conference of the International Society for Clinical Biostatistics, August 2025. Open Access
Joint Model: Joint model with latent disease age: overcoming the need for reference time Juliette Ortholand, Nicolas Gensollen, Stanley Durrleman, Sophie Tezenas du Montcel. arXiv preprint arXiv:2401.17249. 2024 Open Access
www.digital-brain.org : Website related to the application of the model for Alzheimer’s disease.