How to show average bioequivalence of concentrations in a test sample with a reference population pharmacokinetic model?
Marylore Chenel(1), Karl Brendel(1), Emmanuelle Foos-Gilbert(1), Céline M. Laffont(1) and France Mentré(2)
1. Institut de Recherches Internationales Servier, France, (2) INSERM U738 - Université Paris 7, France
Introduction: The case considered here is when a pharmacokinetic (PK) study is performed in a special population (i.e. a specific ethnic group, a high risk population such as renally or hepatically impaired subjects, ...) without a control group. The purpose is to show average bioequivalence of the PK in this specific population to the PK in the reference population using all previous knowledge summarized with a population PK model. Such an approach is an alternative to the classical analyses based on parallel group trials.
Objectives: The objective of the present work was to propose statistical methods to show the absence of difference in PK (average bioequivalence) between the sample obtained from a special population and the reference population PK model. These statistical methods can be applied either to standard PK parameters (AUC and Cmax) or to the whole PK profile. The latter approach is sometimes more relevant.
Methods: The following methods were investigated, using simulations with the reference model: (i) a method based on non-compartmental analysis (NCA) to study standard PK parameters (for rich sampling studies), and (ii) a method based on an extension of visual predictive checks (VPC) for mean concentrations to study the whole PK profile (in rich or sparse sampling studies).
Let's define MR as the reference population PK model already developed, and T the investigated trial in the special population. For both methods, PK parameters or PK profile, the first step is to define the reference means under MR for the parameters or for the concentrations, using the population model. This was done through simulation of K individuals using MR with the design of T, with K being large enough (here, K=1000). For the equivalence limits, the usual values, 0.80 and 1.25, were used for both AUC and Cmax, and by homogeneity, similar limits were used for the whole PK profile.
For the method based on PK parameters, AUC and Cmax were computed by NCA for each subject of T and each of the K simulated individuals using the sampling times of T. Reference mean mR was computed as the exponential of the sample mean of log parameters from the K simulated individuals. For T, sample mean and standard deviation of individual log(AUC) and log(Cmax) were computed. The 90% confidence intervals (CI) for the geometric mean parameters were then derived taking the exponent of the limits of the 90% CI on the log parameters. For each PK parameter, average bioequivalence between T and MR was shown if the 90% CI for the geometric mean parameters on T was included in [mR ´0.8; mR ´1.25].
For the method based on the PK profile, a similar approach was used. At each scheduled time, the reference mean concentration was computed as the exponential of the sample mean of log concentrations from the K simulated individuals. For T, sample mean and standard deviation of individual log concentrations were computed at each scheduled time, and the 90% CI for the geometric mean concentration was derived. In case of average bioequivalence between T and MR, it was expected that the 90% CI of the observed geometric means on T lied within the reference geometric mean times 0.8 and times 1.25. This can be illustrated nicely on a graph of concentrations versus time.
To illustrate those methods, a two-compartment population PK model that had been developed for a compound in development, SX [1], was used as MR. Two datasets were simulated (Nsubjects =100 and nobservations/subject = 16): the first one (Ttrue) was simulated with the parameters values estimated in MR and the other one (Tfalse) was simulated using the same model but with a bioavailability parameter multiplied by 1.5. To perform these methods on PK parameters and on PK profile, K=1000 individuals were simulated.
Results: The proposed methods were successfully illustrated in both simulated trials. As expected, the 90% CI of the mean of each PK parameter, AUC and Cmax, lied within the equivalence limit computed with MR with Ttrue, and were outside with Tfalse.
Moreover, the 90% CI for means of the concentrations lied within the equivalence limit with Ttrue, and were outside the 90% equivalence interval with Tfalse.
References:
[1] Roy P, Lemenuel-Diot A. and Chenel M. Is it possible to perform equivalent simulations with NONMEM and TS2? PAGE 15 (2006) Abstr 1002 [www.page-meeting.org/abstract=1002]
