Model-based bioequivalence analysis of recombinant human growth hormone using the SAEM algorithm: liquid or lyophilized formulations of Omnitrope® versus original lyophilized Genotropin®
Anne Dubois (1), Sigrid Balser (2), Sandro Gsteiger (3), Etienne Pigeolet (3) and France Mentré (1)
(1) INSERM UMR 738, University Paris Diderot, Paris France; (2) Hexal AG, Sandoz Biopharmaceutical Development, Holzkirchen, Germany; (3) Novartis Pharma AG, Basel, Switzerland
Objectives: To assess pharmacokinetic (PK) bioequivalence, 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 illustrate model-based bioequivalence tests on a crossover trial studying three formulations of recombinant human growth hormone.
Methods: To transpose the standard bioequivalence analysis to NLMEM, we use a statistical model taking into account treatment, period and sequence effects on all PK parameters. We also include between-subject and within-subject variability on all PK parameters. We estimate the NLMEM parameters by the SAEM algorithm implemented in MONOLIX 2.4 [6,7]. Bioequivalence Wald tests are then performed on the treatment effect of AUC and Cmax. Due to the exponential covariate model, for linear PK, tests on AUC are equivalent to tests on clearance. Since Cmax is a secondary parameter of the model, its treatment effect and the corresponding standard error are computed by the delta method [8] or simulations. To illustrate model-based bioequivalence tests on sparse data, we sparsify the given dataset. To optimize the sparse design, we use an approach based on the population Fisher information matrix implemented in the R package PFIM 3.2 [9].
We apply this methodology to a randomized, double-blind, 3-way crossover trial. This study was conduced to compare the PK parameters of Omnitrope® powder, Omnitrope® solution and Genotropin® powder after a single subcutaneous dose of 5 mg. Thirty-six healthy volunteers were recruited.
Results: A one compartment model with first order absorption with a lag time and first order elimination adequately describes the data. The statistical model includes 40 fixed effects and 10 variance parameters. Standard errors are judged satisfactory for all parameters. Bioequivalence criteria were met for AUC and Cmax and confirmed the results obtained by the NCA.
Conclusions: Contrary to NCA, the use of NLMEM allows the sparse sampling in bioequivalence assessments. This is an important improvement for studies in patients where rich sampling is difficult to implement. Models can also lead to better understanding of the biological system than a fully empirical approach and therefore help to interpret ambiguous results.
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] 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.
[7] http://www.monolix.org/
[8] Oehlert GW. A note on the delta method. The American Statistician. 1992; 46:27-29.
[9] http://www.pfim.biostat.fr/
