Comparison of several prediction errors on concentrations for model evaluation
K. Brendel (1), E. Comets (1), C. Laveille (2), R. Jochemsen (2), F. Mentré (1)
(1) INSERM E 0357,Bichat hospital, Paris (2) Servier, Courbevoie
objectives: The aim of this study is to compare criteria for the evaluation of a population pharmacokinetic model built with data from phase II studies. Several types of prediction errors on concentrations are proposed and evaluated on simulated data.
Methods: The model was built from 2 phases II studies of an antidiabetic drug. It was one compartment model with zero order absorption and first order elimination with exponential random effects on the apparent volume of distribution (V/F) and on the apparent clearance (Cl/F) and proportional error model. Two phase I data sets (12 subjects and 16 pharmacokinetic samples) were simulated according to the design of a real phase I study: the first (Vtrue) was simulated with the parameters values estimated previously; the second (Vfalse) was simulated using the same model, but with the mean value for V/F and Cl/F divided by two. We evaluated the following metrics on both datasets: Standardized Prediction Errors for Concentrations (SPEC) (WRES in NONMEM); Standardized Prediction Error for Concentrations with Simulations (SPECS), where simulations are used to estimate the mean and standard deviation of the predicted distribution of concentrations at each sampling time, and Normalized Prediction Distribution Error with Simulations (NPDECS), where the whole distribution of predicted concentrations is taken into account [1, 2]. Under the assumption that the model and parameter estimates are correct, NPDECS should follow a normal distribution N(0, 1). Under the additional approximation of linearity for the model and normality for the parameter distribution, SPEC and SPECS should also follow a normal distribution N(0, 1). For each criteria, we tested normality using the Shapiro-Wilks test. We then performed a Wilcoxon signed-rank test to test whether the mean was significantly different from 0. The pharmacokinetic evaluations and simulations (1000 for SPECS and for PDECS) were performed with NONMEM version V software. Graphics and tests were performed using SAS version 8.2 software.
Results: Even on Vtrue, both SPEC and SPECS were found to differ significantly from a normal distribution. NPDECS followed a normal distribution and the mean was not significantly different from 0 for the 3 statistics. On Vfalse, SPEC, SPECS and NPDECS were not found to follow a normal distribution and showed a mean significantly different from 0. In conclusion, NPDECS was able to validate Vtrue and reject Vfalse, while SPEC and SPECS showed less discrimination.
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