title: Transform-both-sides nonlinear models for in vitro pharmacokinetic experiments.
abstract: Transform-both-sides nonlinear models have proved useful in many experimental applications including those in pharmaceutical sciences and biochemistry. The maximum likelihood method is commonly used to fit transform-both-sides nonlinear models, where the regression and transformation parameters are estimated simultaneously. In this paper, an analysis of variance-based method is described in detail for estimating transform-both-sides nonlinear models from randomized experiments. It estimates the transformation parameter from the full treatment model and then the regression parameters are estimated conditionally on this estimate of the transformation parameter. The analysis of variance method is computationally simpler compared with the maximum likelihood method of estimation and allows a more natural separation of different sources of lack of fit. Simulation studies show that the analysis of variance method can provide unbiased estimators of complex transform-both-sides nonlinear models, such as transform-both-sides random coefficient nonlinear regression models and transform-both-sides fixed coefficient nonlinear regression models with random block effects.
authors.affiliation: Institute of Statistical Research and Training (ISRT), University of Dhaka, Dhaka, Bangladesh.
authors.forename: A H M Mahbub
authors.initials: AH
authors.lastname: Latif
authors.affiliation: Southampton Statistical Sciences Research Institute & Institute for Life Sciences, University of Southampton, Highfield, Southampton, UK S.Gilmour@soton.ac.uk.
authors.forename: Steven G
authors.initials: SG
authors.lastname: Gilmour
mesh_terms: D000704:Analysis of Variance; D006801:Humans; D066298:In Vitro Techniques; D016013:Likelihood Functions; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010599:Pharmacokinetics; D012044:Regression Analysis
keywords: nonlinear mixed effects model; pure error and lack of fit; random block effects