Salway, Ruth; Wakefield, Jon Gamma generalized linear models for pharmacokinetic data. (English) Zbl 1137.62078 Biometrics 64, No. 2, 620-626 (2008). 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. Cited in 4 Documents MSC: 62P10 Applications of statistics to biology and medical sciences; meta analysis 92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) 62J12 Generalized linear models (logistic models) 62F15 Bayesian inference Keywords:rejection algorithm; Bayes factors; clearance; nonlinear mixed effects models PDFBibTeX XMLCite \textit{R. Salway} and \textit{J. Wakefield}, Biometrics 64, No. 2, 620--626 (2008; Zbl 1137.62078) Full Text: DOI Link References: [1] Bates, Non-Linear Regression Analysis and Its Applications (1988) [2] Davidian, Nonlinear Models for Repeated Measurement Data (1995) [3] Gibaldi, Drugs and the Pharmaceutical Sciences, Volume 15: Pharmacokinetics (1982) [4] Godfrey, Compartmental Models and Their Applications (1983) [5] Kass, Bayes factors, Journal of the American Statistical Association 90 pp 773– (1995) · Zbl 0846.62028 [6] Lindsey, Generalized nonlinear models for pharmacokinetic data, Biometrics 56 pp 81– (2000) · Zbl 1060.62637 [7] Pauler, Bayes factors for variance component models, Journal of the American Statistical Association 94 pp 1242– (1999) · Zbl 0998.62017 [8] Rowland, Clinical Pharmacokinetics (1995) [9] Spiegalhalter, WinBUGS User Manual (2003) [10] Upton, Intraindividual variability in theophylline pharmacokinetics: Statistical verification in 39 of 60 healthy young adults, Journal of Pharmacokinetics and Biopharmaceutics 10 pp 123– (1982) [11] Wakefield, An expected loss approach to the design of dosage regimens via sampling-based methods, The Statistician 43 pp 13– (1994) [12] Wakefield, Bayesian individualization via sampling-based methods, Journal of Pharmacokinetics and Biopharmaceutics 24 pp 103– (1996) [13] Wakefield, Methods and Models in Statistics pp 119– (2004) · Zbl 1314.62150 [14] Wakefield, Bayesian analysis of linear and non-linear population models using the Gibbs sampler, Applied Statistics 43 pp 201– (1994) · Zbl 0825.62410 [15] Weiss, Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. I. Log-convex drug disposition curves, Journal of Pharmacokinetics and Biopharmaceutics 14 pp 635– (1986) [16] Weiss, Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. II. Log-concave concentration-time curves following oral administration, Journal of Pharmacokinetics and Biopharmaceutics 15 pp 57– (1987) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.