Pharmacokinetic Studies Described by Stochastic Differential Equations: Optimal Design for Systems with Positive Trajectories
In compartmental pharmacokinetic (PK) modelling, ordinary differential equations (ODE) are traditionally used with two sources of randomness: measurement error and population variability. In this paper we focus on intrinsic (within-subject) variability modelled with stochastic differential equations (SDE), and consider stochastic systems with positive trajectories which are important from a physiological perspective. We derive mean and covariance functions of solutions of SDE models, and construct optimal designs, i.e. find sampling schemes that provide the most precise estimation of model parameters under cost constraints.
KeywordsOptimal Design Covariance Function Stochastic Differential Equation Stochastic System Ordinary Differential Equation
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- Anisimov, V., V. Fedorov, and S. Leonov (2007). Optimal design of pharmacokinetic studies described by stochastic differential equations. In J. López-Fidalgo, J. Rodriguez-Diaz, and B. Torsney (Eds.), mODa 8 - Advances in Model-Oriented Design and Analysis, pp. 9–16. Physica-Verlag, Heidelberg.CrossRefGoogle Scholar
- Fedorov, V., R. Gagnon, S. Leonov, and Y. Wu (2007). Optimal design of experiments in pharmaceutical applications. In A. Dmitrienko, C. Chuang-Stein, and R. D’Agostino (Eds.), Pharmaceutical Statistics Using SAS. A Practical Guide, pp. 151–195. SAS Press, Cary, NC.Google Scholar
- Gardiner, C. (2003). Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer-Verlag, Berlin.Google Scholar
- López-Fidalgo, J. and W. Wong (2002). Design issues for Michaelis-Menten model. J. Theoretical Biology 215, 1–11.Google Scholar
- Mentré, F., S. Duffull, I. Gueorguieva, A. Hooker, S. Leonov, K. Ogungbenro, and S. Retout (2007). Software for optimal design in population PK/PD: a comparison. In Abstracts of the Annual Meeting of the Population Approach Group in Europe (PAGE). ISSN 1871-6032, http://www.page-meeting.org/?abstract=1179.