Transform-both-sides nonlinear models for in vitro pharmacokinetic experiments

TY - JOUR

T1 - Transform-both-sides nonlinear models for in vitro pharmacokinetic experiments

AU - Latif, A. H M Mahbub

AU - Gilmour, Steven G.

PY - 2015/6/4

Y1 - 2015/6/4

N2 - 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.

AB - 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.

KW - nonlinear mixed effects model

KW - pure error and lack of fit

KW - random block effects

UR - http://www.scopus.com/inward/record.url?scp=84930430311&partnerID=8YFLogxK

U2 - 10.1177/0962280214544017

DO - 10.1177/0962280214544017

M3 - Article

AN - SCOPUS:84930430311

SN - 0962-2802

VL - 24

SP - 306

EP - 324

JO - Statistical Methods in Medical Research

JF - Statistical Methods in Medical Research

IS - 3

ER -