Extension of the SAEM algorithm for nonlinear mixed models with 2 levels of random effects.Report as inadecuate

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* Corresponding author 1 Modèles et méthodes de l-évaluation thérapeutique des maladies chroniques 2 MAP5 - MAP5 - Mathématiques Appliquées à Paris 5

Abstract : This article focuses on parameter estimation of multilevel nonlinear mixed-effects models MNLMEMs. These models are used to analyze data presenting multiple hierarchical levels of grouping cluster data, clinical trials with several observation periods,

The variability of the individual parameters of the regression function is thus decomposed as a between-subject variability and higher levels of variability e.g. within-subject variability. We propose maximum likelihood estimates of parameters of those MNLMEMs with 2 levels of random effects, using an extension of the stochastic approximation version of expectation-maximization SAEM-Monte Carlo Markov chain algorithm. The extended SAEM algorithm is split into an explicit direct expectation-maximization EM algorithm and a stochastic EM part. Compared to the original algorithm, additional sufficient statistics have to be approximated by relying on the conditional distribution of the second level of random effects. This estimation method is evaluated on pharmacokinetic crossover simulated trials, mimicking theophylline concentration data. Results obtained on those data sets with either the SAEM algorithm or the first-order conditional estimates FOCE algorithm implemented in the nlme function of R software are compared: biases and root mean square errors of almost all the SAEM estimates are smaller than the FOCE ones. Finally, we apply the extended SAEM algorithm to analyze the pharmacokinetic interaction of tenofovir on atazanavir, a novel protease inhibitor, from the Agence Nationale de Recherche sur le Sida 107-Puzzle 2 study. A significant decrease of the area under the curve of atazanavir is found in patients receiving both treatments.

Keywords : Bioequivalence trials Multilevel nonlinear mixed effects models SAEM algorithm Multiple periods Cross-over trial Bioequivalence trials.

Author: Xavière Panhard - Adeline Samson -

Source: https://hal.archives-ouvertes.fr/


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