Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients.

• MeSH
• Algorithms MeSH
• Bayes Theorem MeSH
• HIV Infections drug therapy   MeSH
• Carbamates pharmacokinetics   MeSH
• Clinical Trials as Topic MeSH
• Anti-HIV Agents pharmacokinetics   MeSH
• Humans MeSH
• Drug Monitoring instrumentation   methods   MeSH
• Likelihood Functions MeSH
• Reproducibility of Results MeSH
• Software * MeSH
• Models, Statistical MeSH
• Sulfonamides pharmacokinetics   MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH

For most patients, the HIV viral load can be made undetectable by highly active antiretroviral treatments highly active antiretroviral therapy: the virus, however, cannot be eradicated. Thus, the major problem is to try to reduce the side effects of the treatment that patients have to take during their life time. We tackle the problem of monitoring the treatment dose, with the aim of giving the minimum dose that yields an undetectable viral load. The approach is based on mechanistic models of the interaction between virus and the immune system. It is shown that the "activated cells model," allows making good predictions of the effect of dose changes and, thus, could be a good basis for treatment monitoring. Then, we use the fact that in dynamical models, there is a nontrivial equilibrium point, that is with a virus load larger than zero, only if the reproductive number R(0) is larger than one. For reducing side effects, we may give a dose just above the critical dose corresponding to R(0) equal to 1. A prior distribution of the parameters of the model can be taken as the posterior arising from the analysis of previous clinical trials. Then the observations for a given patient can be used to dynamically tune the dose so that there is a high probability that the reproductive number is below one. The advantage of the approach is that it does not depend on a cost function, weighing side effects and efficiency of the drug. It is shown that it is possible to approach the critical dose if the model is correct. A sensitivity analysis assesses the robustness of the approach.

• MeSH
• Algorithms MeSH
• Models, Biological MeSH
• Biometry MeSH
• CD4-Positive T-Lymphocytes drug effects   immunology   virology   MeSH
• HIV Infections drug therapy   immunology   virology   MeSH
• Clinical Trials as Topic statistics & numerical data   MeSH
• Anti-HIV Agents administration & dosage   adverse effects   MeSH
• Humans MeSH
• Models, Immunological MeSH
• Drug Monitoring statistics & numerical data   MeSH
• Models, Statistical * MeSH
• Viral Load drug effects   MeSH
• Antiretroviral Therapy, Highly Active * adverse effects   MeSH
• Dose-Response Relationship, Drug MeSH
• Check Tag
• Humans MeSH
• Publication type
• Journal Article MeSH