Evaluation by simulation of tests based on non‐linear mixed‐effects models in pharmacokinetic interaction and bioequivalence cross‐over trials

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Abstract
We propose tests based on non‐linear mixed effects models (NLMEM) in pharmacokinetic interaction and bioequivalence cross‐over trials comparing two treatments or two formulations. To compare the logarithm of the area under the curve (AUC) using these models, two approaches are studied: in the first one, concentration data are analysed globally, with and without the estimation of a treatment effect; and in the second one, they are analysed separately in each treatment group with the estimation of the individual parameters. Four tests for comparison of the logarithm AUC between two treatment arms are studied: a likelihood‐ratio test (LRT), a Wald test and two tests, parametric and non‐parametric, comparing the individual Empirical Bayes (EB) estimates. These tests are adapted to the case of equivalence, except the LRT which does not have any simple extension. We evaluate by simulation of the type I error and the power for both comparison and equivalence tests. They are compared to the standard tests recommended by the FDA and the EMEA, based on non‐compartmental (NC) AUC. Trials for a usual PK model are simulated under H0 and several H1 using S‐plus software and analysed with the nlme function. Different configurations of the number of subjects (n=12, 24 and 40) and of the number of samples per subject (J=10, 5 and 3) are studied. The type I error α of LRT and Wald comparison test in the 5000 replications of interaction cross‐over trials is found to be 20.9 per cent and 21.7 per cent, respectively, in the original design (n=12, J=10), which is far superior to 5 per cent, and decreases when n increases. When n is fixed, α is found to increase with J. Power is satisfactory for both tests, after correction of the significance threshold. Results of EB and NC tests are similar with satisfactory powers and a type I error close to 5 per cent, except when J=3 for EB tests. Similar results are obtained for equivalence tests, except for EB and NC Student tests, which are not of a great interest. NC tests keep their place when the number of samples per subject J is large, but NLMEM seem useful for cross‐over studies performed in special populations where J limited; the evaluation by Monte‐Carlo simulations of empirical threshold seems however necessary because of the inflation of the type I error. Copyright © 2005 John Wiley Sons, Ltd.