Cette thèse est consacrée au développement de nouvelles méthodologies pour l'analyse des modèles non-linéaires à effets mixtes, à leur implémentation dans un logiciel accessible et leur application à des problèmes réels. Nous considérons particulièrement des extensions des modèles non-linéaires à effets mixtes aux modèles de mélange et aux modèles conjoints. Dans la première partie, nous proposons, dans le but d'avoir une meilleure maîtrise de l'hétérogénéité liée aux données sur des patients issus de plusieurs clusters, des extensions des MNLEM aux modèles de mélange. Nous proposons ensuite de combiner l'algorithme EM, utilisé traditionnellement pour les modèles de mélanges lorsque les variables étudiées sont observées, et l'algorithme SAEM, utilisé pour l'estimation de paramètres par maximum de vraisemblance lorsque ces variables ne sont pas observées. La procédure résultante, dénommée MSAEM, permet ainsi d'éviter l'introduction d'une étape de simulation des covariables catégorielles latentes dans l'algorithme d'estimation. Cet algorithme est extrêmement rapide, très peu sensible à l'initialisation des paramètres, converge vers un maximum (local) de la vraisemblance et est implémenté dans le logiciel Monolix.La seconde partie de cette Thèse traite de la modélisation conjointe de l'évolution d'un marqueur biologique au cours du temps et les délais entre les apparitions successives censurées d'un évènement d'intérêt. Nous considérons entre autres, les censures à droite, les multiples censures par intervalle d'évènements répétés. Les paramètres du modèle conjoint résultant sont estimés en maximisant la vraisemblance jointe exacte par un algorithme de type MCMC-SAEM. Cette méthodologie est désormais disponible sous Monolix / The main goal of this thesis is to develop new methodologies for the analysis of non linear mixed-effects models, along with their implementation in accessible software and their application to real problems. We consider particularly extensions of non-linear mixed effects model to mixture models and joint models. The study of these two extensions is the essence of the work done in this document, which can be divided into two major parts. In the first part, we propose, in order to have a better control of heterogeneity linked to data of patient issued from several clusters, extensions of NLMEM to mixture models. We suggest in this Thesis to combine the EM algorithm, traditionally used for mixtures models when the variables studied are observed, and the SAEM algorithm, used to estimate the maximum likelihood parameters when these variables are not observed. The resulting procedure, referred MSAEM, allows avoiding the introduction of a simulation step of the latent categorical covariates in the estimation algorithm. This algorithm appears to be extremely fast, very little sensitive to parameters initialization and converges to a (local) maximum of the likelihood. This methodology is now available under the Monolix software. The second part of this thesis deals with the joint modeling of the evolution of a biomarker over time and the time between successive appearances of a possibly censored event of interest. We consider among other, the right censoring and interval censorship of multiple events. The parameters of the resulting joint model are estimated by maximizing the exact joint likelihood by using a MCMC-SAEM algorithm. The proposed methodology is now available under Monolix.

Introduction: Type-2 diabetes is one of the most common metabolic diseases characterized by elevated blood sugar levels in the body. The disease is caused by lost insulin sensitivity and insufficient insulin production, which leads to an increase in sugar levels in the blood. Lifestyle interventions such as physical activity, good eating habits and weight loss are important factors that play a crucial role in the treatment of type 2-diabetes. In most cases, they need medication to lower blood sugar level. Gliclazide is a medicine used in many countries for the treatment of type-2 diabetes if metformin, the first line treatment, do not have a sufficient effect. Gliclazide is available in two formulations: immediate release (IR) and modified release (MR) tablet.  Aim: The aim of this study was to develop a model that describes the pharmacokinetics of a gliclazide (IR) tablet based on prior knowledge of PK in the MR formulation and using data from previous published studies. Method: Modeling software Monolix was used to find the most appropriate model for describing the pharmacokinetics of gliclazide. During the study, the most common absorption models were examined, e.g., first and zero order absorption with and without time delay, transit compartment, zero order first order absorption in succession and zero order first order absorption occurring simultaneously. The best model was chosen by comparing the so-called Akaike information criteria (AIC) and by visual predictive control (VPC) for all absorption models tested. AIC values for all absorption models tested by Monolix were compared and the absorption model that shows the lowest value of AIC was the best model.  Results: For single-IR data, where each profile corresponded to an individual pharmacokinetic profile, the zero- order absorption adaptation with a delay (Tlag) was the best adaptation. For population IR and population MR data, each pharmacokinetic profile represents an average of all individuals' measured concentrations. The fit for these data showed that zero- order kinetics with a delay (Tlag) was the best fit. Conclusion: In summary, this work showed that the best absorption model that is well adapted to both single and population data for the IR formulation, and that well describes the pharmacokinetics of gliclazide, is a single compartment with zero order kinetics and time delay. The results showed that the best absorption model that is well adapted to population data for the MR formulation is also a one-compartment with zero-order kinetics and time delay.