Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach.

Abstract

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 This paper reproduces some unpublished work from my PhD thesis.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. Cet article a reçu le Prix Marie-Jeanne Laurent-Duhamel 2015.