Performance Analysis for Parameter Estimators in Pharmacokinetics

Carolin Malsch

University of Greifswald

"Performance Analysis for Parameter Estimators in Pharmacokinetics"

Classical compartment models of pharmacokinetics are represented by deterministic kinetic equations and embedded in a probability theoretical context in terms of residence time random variables. Several parameter estimation and test methods are available to estimate related model parameters. The aim of this study is to examine the performance of these methods in the context of individual and population pharmacokinetics. A simulation study for four standard compartment models for individual and population pharmacokinetics is conducted assessing the performance of the parameter estimation methods (a) minimum least squares, (b) maximum likelihood, and (c) minimum chi-squared estimation, as well as for the Chi-squared goodness of fit test. Performance measures include bias and standard error for the parameter estimators, and error probabilities for the Chi-squared test. In the simpler compartment models and given an appropriate choice of measurement time points, all three estimators show satisfying results with regard to bias and standard error. Parameter estimates are asymptotically normal distributed. Further, distribution of the Chi-squared test statistic approaches the Chi-squared distribution asymptotically. In case of non-optimal choice of measurement time points, performance is poor for all estimation methods. Maximum likelihood method appears to be most robust for parameter estimation, but subsequent Chi-squared test statistic fails to asymptotically approach the Chi-squared distribution. In the more complex compartment models, minimum Chi-squared estimation appears to be most robust with regard to test errors of subsequent Chi-squared goodness of fit test. For minimum least squares and maximum likelihood parameter estimation, subsequent Chi-squared test statistic shows severely distorted error probabilities, suggesting that the asymptotic distribution of the Chi-squared test statistic is not the Chi-squared distribution. Performance depends on the underlying model and the measurement time points in relation to the speed of elimination and dosage of the pharmakon. A simulation study can help to decide upon which method is most suitable in the application case.
Additional authors: Karl-Ernst Biebler, Institute of Bioinformatics, University Medicine Greifswald, University of Greifswald, Germany

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