Abstract
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.
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Fedorov, V.V., Leonov, S.L., Vasiliev, V.A. (2010). Pharmacokinetic Studies Described by Stochastic Differential Equations: Optimal Design for Systems with Positive Trajectories. In: Giovagnoli, A., Atkinson, A., Torsney, B., May, C. (eds) mODa 9 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2410-0_10
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DOI: https://doi.org/10.1007/978-3-7908-2410-0_10
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