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PA - C8 - MAP667C : Modèles à effets mixtes et approches de population en sciences de la vie

Domaine > Mathématiques appliquées.


This course introduces methods for analyzing longitudinal repeated data characteristic in biomedical sciences. Mixed-effects models are the statistical tool of choice for modeling inter-individual variability in the evolution of longitudinal markers. In other words, the parameters of the model are considered to be random and to take a different value between the different individuals of a study. Furthermore, in life science, there is often a knowledge of the biological mechanism of a phenomenon. The latter can be described using behavioral models generally described by systems of ordinary differential equations (ODE). In this course we propose to develop mechanistic dynamic models where the trajectories are described by ODEs with mixed effects models on the parameters (a particular type of non-linear mixed effects model).  Pharmacokinetic-pharmacodynamic (PKPD) models are an example of mechanistic models that are extremely useful and used to study the effect of a drug among individuals in the same population. PK models describe how a drug is absorbed into the body, distributed and then eliminated, whereas PD models describe the course of the disease and the effect of the drug on the body. However, we will see that this type of approach has applications in other fields such as toxicology, agronomy, virology, immunology or cell biology.



The objective of this course is to understand how to define and use a mechanistic model. Through examples (PKPD, viral dynamics,...) we will study the methods and algorithms used for mixed-effects models: methods of parameter estimation, model construction, validation and selection.


R and the Monolix software (http://lixoft.com/products/monolix/) will be (widely) used in the course



It will be an in class examination which will consist in theoretical questions ⅓ and computer experiments ⅔. 



  • Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 963-974.
  • Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer.
  • Commenges, D., & Jacqmin-Gadda, H. (2015). Dynamical biostatistical models (Vol. 86). CRC Press.
  • Lavielle, M. (2014). Mixed effects models for the population approach: models, tasks, methods and tools. CRC press.


Format des notes

Numérique sur 20

Littérale/grade réduit

Pour les étudiants du diplôme M2 MSV - Mathématiques pour les Sciences du Vivant

Pour les étudiants du diplôme Master 2 Mathématiques et Applications - Mathématiques pour les Sciences du Vivant

Le rattrapage est autorisé (Max entre les deux notes)
    L'UE est acquise si Note finale >= 10
    • Crédits ECTS acquis : 4 ECTS

    Pour les étudiants du diplôme Echanges PEI

    Pour les étudiants du diplôme Data Sciences

    Le rattrapage est autorisé (Max entre les deux notes)
      L'UE est acquise si Note finale >= 10
      • Crédits ECTS acquis : 3 ECTS
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