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

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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.

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