Introduction: The SAEM (Stochastic Approximation Expectation Maximisation) algorithm [1], implemented in the Monolix software [2], is an exact maximum likelihood estimation method with good statistical properties. However, the current version of SAEM does not allow the estimation of Inter-Occasion Variability (IOV).
Objectives: To extend the SAEM algorithm in order to enable the estimation of IOV when analysing data measured at several occasions, to evaluate it by simulation and to apply it to the simultaneous population PK of nelfinavir (NFV), an HIV-1 protease inhibitor, and its metabolite M8 in HIV-infected patients.
Methods: We proposed and implemented a hybrid Gibbs sampling algorithm for the simulation of the random effects describing inter-individual variability (IIV) and IOV in the S step of SAEM. We derived the sufficient statistics for the estimation of IOV. We evaluated the properties of this extension of SAEM on 1000 simulated datasets based on theophylline PK with 12 patients and 10 samples per patient. We compared the results obtained with SAEM and the FOCE algorithm implemented in nlme, respectively. We applied this extended algorithm to the simultaneous population PK of NFV and M8 using concentration data measured in the Cophar1 – ANRS 102 study. A previous analysis was performed using nlme [3].
Results: The bias and RMSE obtained with SAEM on the 1000 simulated datasets were satisfactory for all parameters. The RMSE obtained for IIV, IOV and residual variability were greatly improved compared to those obtained with nlme. The analysis of the PK of NFV/M8 with SAEM enabled the estimation of IIV and IOV on the 5 PK parameters of the model, whereas IIV and IOV could be estimated on only 3 and 1 parameters, respectively, using nlme. Goodness-of-fit plots were also improved compared to the analysis with nlme.
Conclusion: This extension of the SAEM algorithm allows the estimation of IOV even when classical algorithms such as FOCE fail to converge. It can also be used to handle concentration data from interaction and bioequivalence cross-over PK studies.
References
[1] Kuhn and Lavielle. Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis, 49 (2005), 1020-1038.
[2] Monolix software. http://www.math.u-psud.fr/~lavielle/monolix.
[3] Panhard et al. Population pharmacokinetic analysis for nelfinavir and its metabolite M8 in virologically controlled HIV-infected patients on HAART. British Journal of Clinical Pharmacology, 60 (2005), 390-403.
Acknowledgements
Cophar1 - ANRS 102 study team (investigator: Dr Goujard, pharmacology: Dr Taburet, methodology: Pr Mentré) | 
