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

Xavière Panhard, France Mentré

INSERM E0357, Department of Epidemiology, Biostatistics and Clinical Research,
University Hospital Bichat – Claude Bernard, Paris, France.

Objectives : Evaluation of tests based on non linear mixed- effects models (NLMEM) in pharmacokinetic interaction and bioequivalence cross- over trials comparing a test and a reference treatment (or formulation). Comparison to standard tests recommended by FDA [1] and EMEA [2,3], based on non compartimental (NC) AUC.

Methods : We proposed 4 tests based on NLMEM for AUC comparisons in interaction cross-over trials: a likelihood-ratio test (LRT), a Wald test and two tests, parametric and non parametric, comparing the individual Empirical Bayes (EB) estimates. These tests were adapted to the case of equivalence, except the LRT which does not have any simple extension. For both interaction and equivalence studies, we evaluate by simulation the type I error a (5000 simulated studies) and the power (1000 simulated studies for each alternative hypothesis) of these tests. Data for a usual PK model were simulated using Splus software and analysed with its function nlme [4]. As the estimation of a is expected to be different from its nominal value, we use a correction of the significance threshold for the evaluation of the power of interaction tests. That correction is not performed on bioequivalence tests, for which the null hypothesis is composite. Different configurations of the number of subjects N (12, 24 and 40 ) and of the number of samples per subjects n (3, 5 and 10) were studied.

Results : In the original configuration (N=12, n=10), the two global test (LRT and Wald) have a type I error a far superior to 5%, decreasing when N increases. When N is fixed, a increases with n. Power is satisfactory for both tests, after correction of the significance thresholds. Results of EB and NC tests are similar with satisfactory powers and a type I error rate close to 5%, except when n=3 for EB tests (that particular number of samples does not allow for the calculation of the NC AUC). Similar results were obtained for equivalence tests.

Conclusion : NLMEM can be useful for early phases cross- over studies. The evaluation by simulation of the properties of the tests is however necessary because of the inflation of the type I error. These methods were evaluated in the ANRS 110 trial, which studies the absence of PK interaction between nelfinavir, a protease inhibitor, and a cholesterol lowering drug.

References :
[1] FDA. Guidance for industry – population pharmacokinetic, 1999.
[2] EMEA. Note for guidance on the investigation of bioavaibility and bioequivalence, 2000.
[3] EMEA. Note for guidance on the investigation of drug interaction, 1998.
[4] Pinheiro JC and Bates DM. Mixed-effect models in S and Splus. Springer- Verlag, New York, 2000.

Reference: PAGE 12 (2003) Abstr 375 [www.page-meeting.org/?abstract=375]

Poster: poster