Design Evaluation and Optimization for models of Hepatitis C viral dynamics
J. Guedj (1), C. Bazzoli (2), A.U. Neumann (3), F. Mentre (2)
(1)Los Alamos National Laboratory, New Mexico, USA ;(2) INSERM, UMR 738, 146 rue Henri Huchard 75018 Paris, France ; (3)Bar-Ilan University, Ramat-Gan, Israel;
Objectives: The Neumann’s model of viral dynamics is the standard explanation for the biphasic decline of Hepatitis C virus (HCV) during frequent administration of Interferon (IFN) and has brought important insights for understanding HCV pathogenesis [1]. This model can be extended to account for pharmacokinetics variation, when drug is administered on a weekly basis [2]. Since this model is based on a complex system of non-linear Ordinary Differential Equations (ODE), the parameter estimation is challenging and requires a rich data set if individual estimation is performed. By borrowing strength from the between-patients variability, nonlinear mixed effect models (NLMEM) allow sparser design within each patient to analyze the observations of the whole sample. Yet, the accuracy of the viral parameters that can be expected using NLMEM has not been investigated so far.
Methods: : In the context of non-linear dynamics without a closed-form solution, the computation of the exact FIM in NLMEM involves heavy computation [3]. Here we use an approximation of the FIM based on the first-order linearization around the mode of the random effects that allows to avoid most of the computation burden [4,5].
We show that this approximation, implemented in the software PFIM, provides a good estimation of the FIM. We compare the ability of different popular designs in HCV clinical trials to estimate the parameters of viral dynamics. Furthermore, we propose different optimal designs according to the maximal number of sampling measurements that is allowed for each patient. We show how an appropriate choice for the sampling measurements can dramatically improve the identifiability of the most critical viral parameters for the prediction of the treatment outcome.
Conclusions: The results can be used for both clinical and methodological purposes.
References:
[1] Neumann et al. Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-alpha therapy. Science 1998; 282:103–107.
[2] Talal et al. Pharmacodynamics of PEG-IFN Differentiate HIV/HCV Coinfected Sustained Virological Responders From Nonresponders. Hepatology 2006; 43:943–953.
[3] Guedj et al. Practical Identifiability of HIV Dynamics Models. Bulletin of Mathematical Biology 2007; 69(8):2493–2513.
[4] Mentre et al. Optimal design in random-effects regression models. Biometrika 1997; 84:429–442.
[5] Bazzoli et al. Fisher information matrix for nonlinear mixed effects multiple response models: evaluation and comparison by simulation to results from FO, FOCE and SAEM algorithms. Statistics in Medicine 2009; 28(14):1940–1956
