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Zbl 1137.62078
Salway, Ruth; Wakefield, Jon
Gamma generalized linear models for pharmacokinetic data. (English)
[J] Biometrics 64, No. 2, 620-626 (2008). ISSN 0006-341X; ISSN 1541-0420/e

Summary: This article considers the modeling of single-dose pharmacokinetic data. Traditionally, so-called compartmental models have been used to analyze such data. Unfortunately, the mean function of such models are sums of exponentials for which inference and computation may not be straightforward. We present an alternative to these models based on generalized linear models, for which desirable statistical properties exist, with a logarithmic link and gamma distribution. The latter has a constant coefficient of variation, which is often appropriate for pharmacokinetic data. Inference is convenient from either a likelihood or a Bayesian perspective. We consider models for both single and multiple individuals, the latter via generalized linear mixed models. For single individuals, Bayesian computation may be carried out with recourse to simulation. We describe a rejection algorithm that, unlike Markov chain Monte Carlo, produces independent samples from the posterior and allows straightforward calculation of Bayes factors for model comparison. We also illustrate how prior distributions may be specified in terms of model-free pharmacokinetic parameters of interest. The methods are applied to data from 12 individuals following administration of the antiasthmatic agent theophylline.

MSC 2000:: *62P10 Appl. of statistics to biology
92C45 Kinetics in biochemical problems
62J12 Generalized linear models
62F15 Bayesian inference

Keywords: rejection algorithm; Bayes factors; clearance; nonlinear mixed effects models

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Zentralblatt MATH Berlin [Germany]