Optimum designs for non-linear mixed effects models in the presence of covariates

In this article, we present a new method for optimizing designs of experiments for non-linear mixed effects models, where a categorical factor with covariate information is a design variable combined with another design factor. The work is motivated by the need to efficiently design preclinical experiments in enzyme kinetics for a set of Human Liver Microsomes. However, the results are general and can be applied to other experimental situations where the variation in the response due to a categorical factor can be partially accounted for by a covariate. The covariate included in the model explains some systematic variability in a random model parameter. This approach allows better understanding of the population variation as well as estimation of the model parameters with higher precision.

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

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.