Model Simplification
Klaus Lindauer, Thomas Frank, Heiner Speth
Sanofi-Aventis Deutschland GmbH, R\&D TMED Frankfurt, Germany
Objectives: In the course of the development of population pharmacokinetics and - dynamics models often multiple structural different models are able to describe and predict the experimental data nearly equally well. Often the obtained models can be distinguished only by their differences in the respective objective function value (OFV). Even though a more complex model might be favourable based on a lower objective function value compared to a structurally more simple model, the reproducibility of the complex model might be questionable. Therefore we developed a fast and elegant method to evaluate the robustness of the obtained model in varying the initial parameter set. We applied our newly developed method to a one - and two-compartment population pharmacokinetic model of a Glp1 agonist analog.
Methods: The results of the fitting procedure are often dependent on setting of initial values. Therefore the successful NONMEM (version 7.3) [1] run of the one- & two-compartment model was used as a reference of a successful path for the identification of the model parameter respectively. Along this path the model that resulted previously in an OFV with at least 10 points larger than the one of the successful fitting, is used as a starting model for re-fitting purposes. The identified parameter values were modified based on a multivariate normal distribution $\cal N(\theta,\sigma \textrm{= 0.01})$ and used as an initial parameter sets for the re-fitting approach. The procedure was repeated 25 times. Therefore we obtained 25 models (NONMEM runs) and respective parameter sets.
Results: Our newly developed method for evaluating the robustness and validity of the model parameter obtained, was applied to a Glp1 receptor agonist analog. For the one-compartment model all 25 fitting attemps converged into the same parameter set, whereas less than 1/2 (12) of the 25 re-fitting runs converged in case of the two-compartment model. Although the OFV was significantly lower for the two-compartment model, due to the lower robustness of the model, the simplier PK model was selected for our further analysis.
Conclusions: Even though a more complex model seems to be favourable based on its OFV, the one-compartment model resulted in more robust parameter sets.
References:
[1] Nonlinear mixed effects model program (NONMEM) version 7.3.0, originally developed by Stuart Beal, Lewis Sheiner and Alison Boeckmann, current developers are Robert Bauer, Icon Development Solutions, and Alison Boeckmann. Implementation, efficiency and Standardization performed by nous Infosystems.
