This paper considers the modeling of single dose pharmacoki- netic 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 straightfor- ward. 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 compari- son. 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 anti-asthmatic agent theophylline.
Salway, Ruth and Wakefield, Jon, "Gamma Generalized Linear Models for Pharmacokinetic Data" (May 2007). UW Biostatistics Working Paper Series. Working Paper 309.