Model-based bioequivalence analysis of pharmacokinetic crossover trials compared to standard non-compartmental analysis
A. Dubois (1), S. Gsteiger (2), E. Pigeolet (2) and F. Mentré (1)
(1) INSERM, U738, Paris, France; University Paris Diderot, Paris, France, (2) Novartis Pharma AG, Basel, Switzerland.
Objectives: To assess pharmacokinetic (PK) bioequivalence in crossover trials, tests are usually performed on the area under the curve (AUC) and the maximal concentration (Cmax) computed by a non-compartmental approach (NCA) as recommended by the guidelines [1,2]. Recently, bioequivalence tests based on nonlinear mixed effects models (NLMEM) have been developed [3,4,5]. Our objective is to mimic the standard bioequivalence analysis on AUC and Cmax using NLMEM and Wald test.
Methods: In NLMEM, to perform the bioequivalence Wald test, the treatment effect of the concerned parameter and the corresponding standard error (SE) are used. Unfortunately, the PK model cannot be usually parametrized using Cmax which is a secondary parameter of the model. Therefore, SE must be approximated and we propose to use the delta method [6] or simulations from the fixed effect estimates and their Fisher information matrix. We evaluate the bioequivalence Wald test performed on the treatment effect of AUC and Cmax by simulation using 1000 replicates. Crossover trials are simulated under the null hypothesis using different numbers of subjects (N) and of samples (n), with treatment effect on clearance and volume of distribution. We estimate the NLMEM parameters by the SAEM algorithm implemented in MONOLIX 2.4 [7,8]. Treatment effect of AUC and its SE are directly derived from clearance ones. Delta method and simulations are used to estimate the SE of the treatment effect on Cmax. Bioequivalence Wald tests are performed using the SE estimated by MONOLIX and the empirical SE computed as the standard deviation of 1000 replicates of the treatment effect estimate. The results of NCA and Wald tests are compared.
Results: Bioequivalence tests based on NCA show satisfactory properties, except when n is small or the residual error is high. For NLMEM using estimated SE, there is an inflation of the type I error for bioequivalence Wald test when N or n are small. This inflation is corrected by the used of empirical SE. The results for Cmax are satisfactory and similar for delta method and simulations.
Conclusions: We show that the standard bioequivalence analysis can be transposed to NLMEM context, allowing sparser sampling design than NCA. However in NLMEM, asymptotic tests are used and correction for small sample size should be considered.
References:
[1] FDA. Guidance for industry - statistical approaches to establishing bioequivalence. Technical report, FDA 2001.
[2] EMEA. Note for guidance on the investigation of bioavailability and bioequivalence. Technical report, EMEA 2001
[3] Dubois A, Gsteiger S, Pigeolet E and Mentré F. Bioequivalence tests based on individual estimates using non compartmental of model-based analyses: evaluation of estimates of sample means and type I error for different designs. Pharmaceutical Research. 2010; 27:92-104
[4] Panhard X Taburet AM, Piketti C and Mentré F. Impact of modeling intra-subject variability on tests based on non-linear mixed-effects models in crossover pharmacokinetic trials with application to the interaction of tenofovir on atazanavir in HIV patients. Statistics in Medicine. 2007; 26:1268-1284.
[5] Dubois A, Lavielle M, Gsteiger S, Pigeolet E and Mentré F. Extension of the SAEM algorithm and evaluation of Wald and likelihood ratio tests for interaction or bioequivalence studies. 18th Meeting of Population Approach Group in Europe. 2009, St-Petersburg, Russia.
[6] Oehlert GW. A note on the delta method. The American Statistician. 1992; 46:27-29.
[7] Panhard X and Samson A. Extension of the SAEM algorithm for nonlinear mixed effects models with two levels of random effects. Biostatistics. 2009; 10:121-135.
[8] http://www.monolix.org/
