Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach
[Utilisation de modèles dynamiques pour l’optimisation des traitements des patients infectés par le VIH : une approche par analyse bayésienne séquentielle]
Journal de la société française de statistique, Tome 157 (2016) no. 2, pp. 19-38.

L’utilisation des modèles mécanistes dynamiques basés sur des équations différentielles ordinaires (ODE) a considérablement amélioré les connaissances de la dynamique HIV-système immunitaire. Leur flexibilité á ajuster des données et leur capacité de prédictions en font un bon outil pour l’optimisation du plan d’expérience et de l’analyse d’efficacité d’interventions nouvelle dans le domaine du VIH. Nous traitons des méthodes d’estimation pour les ODEs dont les paramètres sont représentés par des modèles á effet mixtes. Nous proposons une estimation bayésienne par maximisation de la vraisemblance pénalisée et basée sur l’approximation normale des a posteriori, implémentée dans le logiciel NIMROD. Nous discutons l’impact d’une analyse séquentielle bayésienne (SBA) permettant d’analyser plusieurs jeux de données en utilisant comme nouvel loi a priori la loi a posteriori des analyses précédentes. Nous illustrons que l’approximation normale de la loi a posteriori, qui contraint la forme des nouvelles lois a priori, permet un gain en précision de l’estimation et diminue les temps de calculs. Nous illustrons la méthode avec des données issues de deux essais cliniques testant des combinaisons d’antirétroviraux (cART) : ALBI ANRS 070 et PUZZLE ANRS 104. Cet article reproduit des résultats non publiés de mon manuscrit de thèse. C’est une extension de la conférence sur le même sujet que j’ai eu l’honneur de donner lors de la réception du prix Marie-Jeanne Laurent-Duhamel, dans le cadre des 47èmes Journées de Statistique organisées par la Société Française de Statistique á Lille, France, en mai 2015.

The use of dynamic mechanistic models based on ordinary differential equations (ODE) has greatly improved the knowledge of the dynamics of HIV and of the immune system. Their flexibility for fitting data and prediction abilities make them a good tool for optimization of the design delivery and efficacy of new intervention in the HIV field. We present the problem of inference in ODE models with mixed effects on parameters. We introduce a Bayesian estimation procedure based on the maximization of the penalized likelihood and a normal approximation of posteriors, which is implemented in the NIMROD software. We investigate the impact of pooling different data by using a sequential Bayesian analysis (SBA), which uses posteriors of a previous study as new priors. We show that the normal approximation of the posteriors, which constrains the shape of new priors, leads to gains in accuracy of estimation while reducing computation times. The illustration is from two clinical trials of combination of antiretroviral therapies (cART): ALBI ANRS 070 and PUZZLE ANRS 104. This paper reproduces some unpublished work from my PhD thesis. It is an extension of my oral presentation on the same topic at the 47th Journées de Statistique organized by the French Statistical Society (SFdS) in Lille, France, May 2015, when being awarded the Marie-Jeanne Laurent-Duhamel prize.

Mots clés : antirétroviraux, approximation normale de l’a posteriori, approche bayésienne, choix de modèle, équation différentielles ordinaire (ODE), in vitro, in vivo, médecine personnalisée, mutations, modèles causaux, modèles dynamiques, modèles á effets mixtes, optimisation numérique, pharmacologie, prédiction, SIDA, VIH
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Prague, Mélanie. Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach. Journal de la société française de statistique, Tome 157 (2016) no. 2, pp. 19-38. http://www.numdam.org/item/JSFS_2016__157_2_19_0/

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