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A Stochastic Compartmental Model with Long Lasting Infusion
Author(s) -
Ferrante L.,
Bompadre S.,
Leone L.
Publication year - 2003
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200390004
Subject(s) - mathematics , estimator , covariance , stochastic differential equation , stochastic modelling , linear model , function (biology) , stochastic process , probabilistic logic , likelihood function , statistics , mathematical optimization , estimation theory , evolutionary biology , biology
Most of the compartmental models in current use to model pharmacokinetic systems are deterministic. Stochastic formulations of pharmacokinetic compartmental models introduce stochasticity through either a probabilistic transfer mechanism or the randomization of the transfer rate constants. In this paper we consider a linear stochastic differential equation (LSDE) which represents a stochastic version of a one‐compartment linear model when input function undergoes random fluctuations. The solution of the LSDE, its mean value and covariance structure are derived. An explicit likelihood function is obtained either when the process is observed continuously over a period of time or when sampled data are available, as it is generally feasible. We discuss some asymptotic properties of the maximum likelihood estimators for the model parameters. Furthermore we develop expressions for two random variables of interest in pharmacokinetics: the area under the time‐concentration curve, M 0 ( T ), and the plateau concentration, x ss . Finally the estimation procedure is illustrated by an application to real data.