Evaluation of direct population PKPD models for truncated concentration-response curves
D. Perizzolo, S. Zamuner, R. Gomeni, I. Poggesi
GlaxoSmithKline, CPK, Modelling & Simulation, Verona, Italy.
Introduction: There are examples where the concentration-response curves cannot be easily characterized using a pharmacologically relevant Emax model (e.g. impossibility to achieve sufficiently high exposures, high variability, etc.). In such cases, linear or truncated Emax models can be used [1]. A single dose crossover study with 20 subjects treated with two different drugs and placebo was considered. Plasma levels of the two compounds and a marker of pharmacological activity, with limited evidence of achievement of maximal response, were measured throughout the experiment.
Objectives:
- To compare linear, full and truncated Emax models for the PK-PD analysis of the two compounds.
- To evaluate the models behaviour using simulated dataset.
- To evaluate the parameters precision improvement using optimal design approaches and to qualify the study design enabling to identify the parameters of Emax models, providing guidance for future experiments.
Methods: PK-PD models were fitted to the data using NONMEM VI. The evaluation of the objective function and standard goodness of fit diagnostics were used for model discrimination. NONMEM was also used for providing simulation-based diagnostics. Design optimization was performed to define the optimal allocation of the PD observations using POPED [2].
Results: The adoption of full and truncated Emax models had no significant advantages compared with the simpler linear model, which was however able to demonstrate a significant difference in potency between the two compounds. Despite the optimization of the trial design was able to improve the CV% of parameters by 20-25%, it was impossible to correctly identify the more complex structural models with the adopted sample size. Scenario analysis indicated that, in the conditions adopted in the study, a substantial increase of the number of subjects (n>100) was required for this aim.
Conclusions: In cases in which the shape of the concentration-response curves cannot be properly characterized using a pharmacologically relevant Emax model, resorting to simpler models (e.g., linear) allows a better identification of the model parameters, making possible to compare the potency of different compounds. In this specific case, the limited dynamic range of the pharmacodynamic endpoint and its high variability, possibly coupled with the pharmacokinetic characteristics of the compounds (long terminal half-life), can explain why the linear model was the preferred option.
References:
[1] Schoemaker RC van Gerven JMA Cohen AF. Estimating potency for the Emax-model without attaining maximal effects J Pharmacokin Biopharm, 1998, 26, 581-93
[2] Foracchia, M., Hooker, A., Vicini, P. and Ruggeri, A., POPED, a software for optimal experiment design in population kinetics. Comput Methods Programs Biomed, 2004. 74(1): p. 29-46.