Morgane Philipp (1), Adrien Tessier (2), Stella Grosser (4), Wanjie Sun (4), Guoying Sun (4), Kairui Feng (3), Liang Zhao (3), Lanyan Fang (3), Mark Donnelly (3), France Mentré (1), Julie Bertrand (1)
(1) University of Paris, INSERM, IAME, UMR 1137, 75006 Paris, France (2) Clinical Pharmacometrics, Quantitative Pharmacology, Servier, France (3) Division of Quantitative Methods and Modeling, Office of Research and Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring MD 20993, USA (4) Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring MD 20993, USA
Introduction: Pharmacokinetic (PK) bioequivalence (BE) studies compare a reference (R) to a test (T) treatment in terms of exposure, i.e., the area under the curve (AUC) and maximum plasma concentration (Cmax). Regulatory authorities recommend estimating AUC and Cmax using a non-compartmental analysis (NCA) and assessing BE using a two one-sided test (TOST) on the treatment effect (beta_T) [1, 2]. When PK variability is large, FDA recommends the reference-scaled average BE approach [1], but BE optimal test (BOT) may also serve as an alternative approach to TOST [3]. Due to challenges using NCA in PK studies with sparse samples, model-based (MB) approaches have been proposed for BE assessment [4]. However, model selection, prior to applying TOST (or BOT) methods, remains a challenge.
Objective: To evaluate the robustness of the MBBE approach to model misspecification and the impact of model selection (MS) and model averaging (MA) in PK BE studies with sparse samples.
Methods: A real case study was performed on data from a BE study using a single-dose, two-way crossover study design. MMBE was assessed using: i) MS on the R arm only, ii) MS on the R and T arms, and iii) MA on the R and T arms [5]. We considered a pool of 10 models varying the number of compartments for the distribution (1 or 2-COMPT) and the absorption type: transit compartments (TRANSIT), delayed (LAG), zero or first-order (0/1-order). The same PK model was assumed for the R and T arms.
Then, a simulation study was conducted based on the real case data. Two hundred data sets were simulated with 3 different PK models (TRANSIT_1-COMPT, TRANSIT_2-COMPT and LAG_0-ORDER_2-COMPT), i.e., 600 datasets in total, with 20 subjects per sequence and 6 sampling times per period, under the null hypothesis (H0: R and T are not BE) and 200 data sets were simulated using the TRANSIT_2-COMPT model under the alternative hypothesis (H1: R and T are BE). MBBE was assessed: i-v) using each of the 3 models mentioned above and two additional models (LAG_1-ORDER_2-COMPT and LAG_0-ORDER_1-COMPT), vi) MS on the R arm only, vii) MS on the R and T arms, and viii) MA on the R and T arms. MS and MA were utilized on a pool of models with and without the model used to simulate the data.
Results: In the real case study, BE was concluded following MS on the R arm only, MS on the R and T arms, and MA on the R and T arms. Both MS scenarios selected the TRANSIT_2-COMPT model and MA assigned a weight of 1 to this model and weights of 0 to the other models in the pool. The models with the closest AIC were TRANSIT_1-COMPT and LAG_0-ORDER_2-COMPT.
In the simulation study, performing MS on the R arm only or on the R and T arms led to the same distribution in terms of MS, whether the simulated model was included or excluded from the candidate pool.
In most cases during MA, one model was assigned a weight of 1 and thus MA was equivalent to MS, regardless of whether the simulated model was included in the candidate pool or not. When it was not, MA was performed using two models at most.
Under H0, model misspecification did not impact the type I error for AUC. MA could not be discriminated from MS based on the R arm only or the R and T arms, regardless of whether the simulated model was included or excluded from the selection pool. For Cmax, type I errors were either not significantly different from the nominal level of 5% or too conservative (i.e., significantly below 5%). When simulating TRANSIT_1-COMPT models, MS and MA were driven by the TRANSIT models and thus led to conservative type I errors. When simulating 2-COMPT models, MS and MA were driven by the simulated model or the closest absorption model and type I errors were close to or below 5% for TRANSIT and LAG_0-ORDER, respectively. Across the simulated models, MA led to more conservative type I errors and removing the simulated model from the pool of candidate models led to an observed increase for the latter.
Under H1, MS and MA, whether the simulated model was included or excluded from the candidate pool, showed powers greater than 50%, similar to the simulated model for AUC and better for Cmax.
Conclusions: The MBBE approach appears to be robust to model misspecification. MS and MA led to type I errors around or below 5% and ensured a reasonable power. No added value was observed with MA compared to MS. Further work is needed to assess the robustness when R and T have different PK models.
References:
[1] U.S. Food and Drug Administration (August 2021). Bioequivalence studies with pharmacokinetic endpoints for drugs submitted under an ANDA. https://www.fda.gov/media/87219/download
[2] D. J. Schuirmann (1987). “A comparison of the Two One-Sided Tests Procedure and the Power Approach for assessing the equivalence of average bioavailability”. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680.
[3] K. Möllenhoff, F. Loingeville, J. Bertrand, T. T. Nguyen, S. Sharan, Liang Zhao, L. Fang, G. Sun, S. Grosser, F. Mentré, H. Dette (2022). Efficient model-based bioequivalence testing. Biostatistics (Oxford, England), 23(1), 314–327.
[4] A. Dubois, M. Lavielle, S. Gsteiger, E. Pigeolet and F. Mentré (2011). Model-based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm. Statistics in Medicine, 30(21), 2582–2600.
[5] S. Buatois, S. Ueckert, N. Frey, S. Retout and F. Mentré (2018). Comparison of Model Averaging and Model Selection in Dose Finding Trials Analyzed by Nonlinear Mixed Effect Models. The AAPS Journal, 20(3), 56.
Reference: PAGE 30 (2022) Abstr 10074 [www.page-meeting.org/?abstract=10074]
Poster: Methodology - Model Evaluation