Lisa Wellin 1, Happy Phanio Djokoto 1, Grace Shalom Govere 1,2, Hélène Haguet 1, Lisa Hanquet 1, Reagan Kilela Songela 3, Camille Massaux 1, Adrien Olama 1, Jean-Michel Dogné 1,2, Flora T.  Musuamba 1,2
1 Clinical Pharmacology and Toxicology Research Unit (URPC), Namur Research Institute for Life Sciences (NARILIS), University of Namur (Namur, Belgium), 2 Federal Agency for Medicines and Health Products (FAMHP) (Brussels, Belgium), 3 Faculty of Pharmaceutical Sciences, University of Lubumbashi (Lubumbashi, Democratic Republic of the Congo )
Objectives: Bioequivalence (BE) of generic drugs is traditionally assessed using non-compartmental analysis (NCA) of exposure metrics such as AUC and Cmax, with conclusions based on the two one-sided tests (TOST) procedure[1]. Although widely accepted, NCA strongly depends on sample size and sampling density, which may limit feasibility in resource-limited settings[2]. Population pharmacokinetic (PopPK) modelling offers an alternative that integrates all available concentration–time data within a nonlinear mixed-effects (NLME) framework[3]. This study aimed to compare NCA and PopPK performance in terms of power and Type I error. It also quantified the effect of reduced sample size and sampling density on BE performance and determined when PopPK offers a clear advantage over NCA.
Methods: A stochastic simulation–estimation (SSE) framework was implemented in NONMEM using a published NLME PopPK model for amodiaquine[4]. This model was reimplemented and verified to ensure consistency with the original publication prior to simulating balanced 2×2 crossover BE trials under three relative bioavailability scenarios defined by the fixed formulation effect parameter θF (0.80, 0.95, 1.25)[5]. The value θF=0.95 represented a BE scenario used to estimate statistical power, while θF=0.80 and 1.25 represented non-BE scenarios at the regulatory limits used to evaluate Type I error. The reference design included 32 subjects and 18 sampling points over 72 hours. Reduced designs were generated by decreasing the sample size (24, 18, 12 subjects) or sampling density (15, 12, 8 time points). For each scenario, 500 stochastic trial replications were simulated to ensure adequate precision of power and Type I error estimates given Monte Carlo uncertainty, while maintaining computational feasibility. Parameters were estimated using first-order conditional estimation with interaction (FOCEI) implemented in NONMEM[6,7]. Each simulated trial was analysed using : first a standard NCA with TOST applied to AUC and Cmax (global decision requiring all metrics between 80 and 125%), then a population-level PopPK approach based on the formulation effect parameter θF and its standard error derived from the covariance step, and finally an individual-level PopPK approach based on empirical Bayesian estimates (EBEs). Statistical performance was assessed in terms of power and type I error control.
Results: Under the reference model (32 subjects, 18 samples), global NCA power was 80.4% with a Type I error of 1.2%. The covariance-based PopPK approach increased power to 92.1%, but showed an increased Type I error, which reached 10.8% in the upper non-BE scenario (θF = 1.25). The EBE-based PopPK approach had the highest power (95.2%) with a more moderate Type I error (6.6-7.8%). Reducing sample size considerably impacted the performance of NCA: global power fell to 66.6% (24 subjects), then to 49.6% (18 subjects), and finally to 16.4% (12 subjects). In contrast, PopPK approaches maintained power close to 80% down to 18 subjects and stayed higher than NCA even with 12 subjects. Reducing sampling density had a more moderate effect than reducing sample size. While NCA power declined under sparse sampling, PopPK approaches preserved high power even in simplified designs. Type I error for NCA remained conservative (less than 5%), whereas covariance-based PopPK approach often exceeded the nominal level of 5%. The EBE-based approach provided better control, although slightly above the nominal level in some cases.
Conclusions: In limited study designs, PopPK-based BE assessment showed higher statistical power than NCA, especially when sample size was decreased. However, this gain in power was associated with Type I error inflation, highlighting that the observed performance is dependent on how uncertainty is quantified. In NLME models, the standard errors obtained from the covariance matrix rely on local asymptotic approximations that may underestimate uncertainty when information is limited, leading to narrow confidence intervals. The EBE-based approach showed a slight improvement in Type I error control, although its reliability is affected by shrinkage in more constrained designs. Therefore, even though NCA saw a significant decrease in performance as the design was reduced, the PopPK approach seems more robust, provided that the uncertainty is correctly characterized. Empirical methods such as nonparametric bootstrapping or Sampling Importance Resampling (SIR)[8,9] could improve this quantification, although their computational cost did not allow for their application here. This study is based on a single model and should be considered as an illustrative example, suggesting that modelling-based approaches are a promising avenue if uncertainty is adequately managed.
References:
[1] European Medicines Agency (EMA). Guideline on the investigation of bioequivalence. London: EMA; 2010.
[2] Gabrielsson J. Pharmacokinetic and pharmacodynamic data analysis: concepts and applications. 5th ed. Stockholm: Swedish Pharmaceutical Press; 2016.
[3] Mould DR, Upton RN. Basic concepts in population modelling, simulation, and model-based drug development. CPT Pharmacometrics Syst Pharmacol. 2012;1(9):e6.
[4] Ali AM, Penny MA, Smith TA, Workman L, Sasi P, Adjei GO, et al. Population pharmacokinetics of the antimalarial amodiaquine: a pooled analysis to optimize dosing strategies. Antimicrob Agents Chemother. 2018;62(10):e02193-17.
[5] Chen X, Nyberg HB, Donnelly M, Zhao L, Fang L, Karlsson MO, et al. Development and comparison of model-integrated evidence approaches for bioequivalence studies with pharmacokinetic end points. CPT Pharmacometrics Syst Pharmacol. 2024;13(10):1734-1747.
[6] Bauer RJ. NONMEM tutorial part I: description of commands and options, with simple examples of population analysis. CPT Pharmacometrics Syst Pharmacol. 2019;8(8):525-537.
[7] Bauer RJ. NONMEM tutorial part II: estimation methods and advanced examples. CPT Pharmacometrics Syst Pharmacol. 2019;8(8):538-556.
[8] Thai HT, Mentré F, Holford NH, Veyrat-Follet C, Comets E. Evaluation of bootstrap methods for estimating uncertainty of parameters in nonlinear mixed-effects models: a simulation study in population pharmacokinetics. J Pharmacokinet Pharmacodyn. 2014;41(1):15–33.
[9] Dosne AG, Bergstrand M, Harling K, Karlsson MO. Improving the estimation of parameter uncertainty distributions in nonlinear mixed effects models using sampling importance resampling. J Pharmacokinet Pharmacodyn. 2016;43(6):583–596.
Reference: PAGE 34 (2026) Abstr 12206 [www.page-meeting.org/?abstract=12206]
Poster: Methodology - Other topics