The clinical progression of neurodegenerative diseases takes place over several years and involves a complex evolution of patients’ motor and/or cognitive abilities, physiological biomarkers, and brain structure. Longitudinal studies are a key tool for investigating the underlying mechanisms of these disorders. In such studies, biomarkers and clinical scores are repeatedly measured at multiple time points and must be analyzed jointly. Patient-related events (such as diagnosis, surgical interventions, or death) further enrich the clinical dataset. Altogether, these data enable both population-level modeling to characterize the average disease trajectory and individualized prediction to capture inter-patient variability.

Leaspy (LEArning Spatiotemporal Patterns in Python)¹ was developed within our research team to jointly analyze the simultaneous evolution of multiple biomarkers. It is based on a nonlinear mixed-effects model with a time reparameterization. The fixed effects are estimated using an iterative MCMC-SAEM algorithm. Subsequently, the random effects representing inter-subject variability are estimated through various methods. Accurate estimation of individual parameters is a key step, particularly for predicting the progression of new patients.

The proposed research project focuses on the statistical inference of individual random effects in nonlinear mixed-effects models, which is a key component for accurate individualized prediction. In particular, the project will investigate the limitations of empirical Bayes estimators in the presence of shrinkage, which can distort the distribution of individual parameters and impact model diagnostics, uncertainty quantification, and statistical inference². The research will explore alternative statistical methodologies based on sampling from conditional distributions of random effects, allowing a more faithful representation of inter-individual variability and improved inference procedures³.

These methodological developments will contribute to advancing statistical approaches for longitudinal disease modeling and improving patient-specific trajectory estimation in neurodegenerative diseases.

[1] Jean-Baptiste Schiratti, Stéphanie Allassonnière, Olivier Colliot, and Stanley Durrleman.  A Bayesian mixed-effects model to learn trajectories of changes from repeated manifold-valued observations.  The Journal of Machine Learning Research, 18:1–33, December 2017. https://inria.hal.science/hal-01540367

[2] Savic, R. M., Karlsson, M. O. Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions. AAPS J 11, 558–569 (2009). https://doi.org/10.1208/s12248-009-9133-0

[3] Lavielle, M., Ribba, B. Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions. Pharm Res 33, 2979–2988 (2016). https://doi.org/10.1007/s11095-016-2020-3

• Investigating statistical inference methods for individual random effects in nonlinear mixed-effects models
• Studying the impact of shrinkage in empirical Bayes estimates on model diagnostics and uncertainty quantification
• Developing and evaluating alternative inference strategies based on sampling from conditional distributions
• Contributing to methodological advances in statistical modeling for longitudinal disease progression
• Applying and validating these methods on real datasets from neurodegenerative disease studies

• Bibliographic review and analysis of the state of the art in nonlinear mixed-effects modeling
• Development of novel statistical inference methods
• Theoretical and methodological investigation of shrinkage effects and uncertainty quantification
• Design and analysis of simulation studies to evaluate methodological performance
• Application of developed methods to longitudinal biomedical datasets
• Dissemination of research results through scientific publications and international conferences
• Contribution to collaborative research within a multidisciplinary team of statisticians, computer scientists, and clinicians

• Strong background in statistics
• Expertise or interest in mixed-effects models, Bayesian statistics, or longitudinal data analysis
• Experience with Python
• Ability to conduct independent research and publish scientific results
• Experience with collaborative research environments and version control tools (e.g., Git)
• Fluent spoken and written English
• Ability to work in an interdisciplinary research environment

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage