Pharmacokinetic bioequivalence analysis of biologics using nonlinear mixed effects modeling
Anne Dubois (1), Sandro Gsteiger (2), Sigrid Balser (3), Etienne Pigeolet (2), Jean-Louis Steimer (2), Goonaseelan Pillai (2) and France Mentré (1)
(1) INSERM UMR 738, University Paris Diderot, Paris France; (2) Novartis Pharma AG, Basel, Switzerland; (3) HEXAL AG, Sandoz Biopharmaceuticals, Holzkirchen, Germany.
Introduction: Among the required information to assess the similarity between different formulations of biologics, a pharmacokinetic (PK) bioequivalence study is usually performed as for chemical drugs [1,2]. Bioequivalence tests are performed on the area under the curve (AUC) and the maximal concentration (Cmax) computed by non-compartmental approach (NCA). However, this approach could be inappropriate in some cases such as sparse sampling designs or nonlinear PK which is often exhibited by biologics. Then, nonlinear mixed effects models (NLMEM) can be used to analyse such data [3,4]. In that context, our objective was to illustrate PK NLMEM-based bioequivalence analysis using two examples.
Methods: NCA-based tests and NLMEM-based bioequivalence Wald tests were performed on two PK datasets from studies comparing different biosimilars: a three-way crossover trial on somatropin  and a multiple dose parallel group trial on epoetin alpha . To perform NLMEM-based bioequivalence Wald test, a statistical model taking account of formulation, period and sequence effects on all PK parameters was used. Between and within subject variability were included for all PK parameters. NLMEM analyses were performed using MONOLIX 3.1R2 . For both examples, bioequivalence tests were performed on the formulation effect of AUC and Cmax. From the somatropin dataset, two sparse datasets were produced with twice less sampling times than the original: the optimised (OD) and empirical design (ED) datasets. For somatropin, we estimated the standard error (SE) of the formulation effect of Cmax by the delta method. Because of the nonlinear PK of epoetin alpha, its structural PK model is written with differential equations. So, the formulation effect of AUC and Cmax, and their SE were estimated through simulations of PK profiles using the fixed effect estimates and their Fisher information matrix. Furthermore, we estimated the formulation effect on the proportion of the dose nonlinearly eliminated (PDNE) in our NLMEM-based analysis.
Results: Somatropin PK was described by a one-compartment model with delayed first order absorption and first order elimination. For the complete and both sparse datasets, the bioequivalence criteria were met for AUC and Cmax using NLMEM and NCA. For NLMEM estimates, the geometric means of AUC and Cmax were similar for the three datasets. For NCA estimates, they were lower for OD dataset compared to complete and ED datasets. Epoetin alpha PK was described by a two-compartment model with linear and Michaelis-Menten elimination. The bioequivalence of AUC and Cmax was demonstrated using NCA and NLMEM. By NLMEM, the test/reference ratio of PDNE was estimated as 0.95 with a 90% CI of [0.72; 1.24].
Conclusion: NLMEM-based equivalence tests were performed on secondary parameters of the models. NLMEM and NCA results were similar thereby demonstrating that NLMEM can be used for equivalence testing.References:
 FDA. Guidance for industry - statistical approaches to establishing bioequivalence. Technical report, FDA 2001.
 EMEA. Guideline on the investigation of bioequivalence. Technical report, EMEA 2010
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