Impact of modelling intra‐subject variability on tests based on non‐linear mixed‐effects models in cross‐over pharmacokinetic trials with application to the interaction of tenofovir on atazanavir in HIV patients

Abstract

We evaluated the impact of modelling intra‐subject variability on the likelihood ratio test (LRT) and the Wald test based on non‐linear mixed effects models in pharmacokinetic interaction and bioequivalence cross‐over trials. These tests were previously found to achieve a good power but an inflated type I error when intra‐subject variability was not taken into account. Trials were simulated under H0 and several H1 and analysed with the NLME function. Different configurations of the number of subjects n and of the number of samples per subject J were evaluated for pharmacokinetic interaction and bioequivalence trials. Assuming intra‐subject variability in the model dramatically improved the type I error of both interaction tests. For the Wald test, the type I error decreased from 22, 14 and 7.7 per cent for the original (n = 12, J = 10), intermediate (n = 24, J = 5) and sparse (n = 40, J = 3) designs, respectively, down to 7.5, 6.4 and 3.5 per cent when intra‐subject variability was modelled. The LRT achieved very similar results. This improvement seemed mostly due to a better estimation of the standard error of the treatment effect. For J = 10, the type I error was found to be closer to 5 per cent when n increased when modelling intra‐subject variability. Power was satisfactory for both tests. For bioequivalence trials, the type I error of the Wald test was 6.4, 5.7 and 4.2 per cent for the original, intermediate and sparse designs, respectively, when modelling intra‐subject variability. We applied the Wald test to the pharmacokinetic interaction of tenofovir on atazanavir, a novel protease inhibitor. A significant decrease of the area under the curve of atazanavir was found when patients received tenofovir. Copyright © 2006 John Wiley & Sons, Ltd.

Bioequivalence Tests Based on Individual Estimates Using Non-compartmental or Model-Based Analyses: Evaluation of Estimates of Sample Means and Type I Error for Different Designs

“…In these situations, other tests based on a global analysis of all data should be considered. Panhard et al already developed a global bioequivalence Wald test based on NLMEM (14,25). This test is directly performed on the treatment effect parameter after fitting together the data of both treatment groups with the estimation of within-subject variability.…”

“…In this simulation study, we use rather similar settings as those of the simulation studies performed by Panhard et al (14,25). However, we simulate two-period, two-sequence crossover pharmacokinetic trials, whereas they simulate twoperiod, one-sequence crossover trials.…”

“…These data are classical ones in population pharmacokinetics (17) and are used in previous simulation studies done by Panhard et al (14,25). The theophylline data include twelve subjects receiving a single oral dose of theophylline depending on their body weight (from 3 to 6 mg).…”

“…We simulate trials with four different designs, which are also used by Panhard et al (14,25). We simulate with the original design with N=12 subjects and n=10 samples per subject and per period, taken at the times of the initial study (0.25, 0.5, 1, 2, 3.5, 5, 7, 9, 12 and 24h after dosing).…”

Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models

“…These models can also lead to a better understanding of the biological system and help to interpret ambiguous results. However, the use of NLMEM is rather recent and still rare in early phases of drug development and/or to analyse crossover studies despite its several advantages .…”