Introduction: Valproic acid (VPA) is a narrow therapeutic index drug widely prescribed for the treatment of epilepsy, psychiatric disorders, and migraine. First available as an enteric-coated immediate release formulation (IR), its fast absorption profile and short half-life motivated the development of extended-release formulations (ER) to reduce both daily administrations and pharmacokinetic peak-to-trough fluctuation (PTF). A local product (Test) was developed in collaboration between our group and a local laboratory to reduce PTF. It was primarily approved for marketing in Uruguay after showing ER properties in a relative bioavailability study versus Depakote® IR (Abbot, Reference) under single dose fasting conditions. The regulatory authority has required to further evaluate the Test product in a multiple-dose scenario with healthy subjects, a study that did not receive the authorization of the Ethics Committee on Human Experimentation due to safety concerns. The aim of this work was to: (I) evaluate methods for model-based bioequivalence (BE) assessment using a non-linear mixed effects (NLME) model developed with single dose data. (II) predict the Test performance in the multiple-dose scenario relative to the IR formulation.
Methods: VPA plasma concentrations obtained in a 2 treatment, 2-period, 2 sequence, crossover study conducted with 14 healthy subjects to assess the relative bioavailability of the Test product versus Depakote® IR after a single dose of 500 mg given in fasting conditions were used to develop a population pharmacokinetic model in NONMEM 7.4. Model selection was based on Akaike Information Criteria (AIC), parameter uncertainty and goodness of fit plots including estimation-based and simulation-based diagnostics. Model development was managed within the PsN-Pirana-Xpose platform. The distribution of secondary pharmacokinetic metrics (AUC0-T, Cmax, Tmax, PTF) was computed using the R-package ncappc  after simulating 1000 clinical trials using the developed model with uncertainty in parameters. Results obtained with the original sampling and with an alternative extensive sampling design were compared. Two methods were evaluated for estimation of BE metrics: A) a 90% nonparametric confidence interval for the T/R ratio was computed taking the 5th and the 95th percentiles from the distribution of medians computed in each simulated study from the individual T/R ratios; B) a 90% parametric CI for the T/R ratio was obtained from the T/R geometric means and the residual variances obtained in each simulated study through standard average bioequivalence analysis. The results obtained with these methods were compared with the result observed in the single-dose study after traditional non-compartmental average BE analysis. Predictive performance of the NLME model for VPA pharmacokinetics in the multiple-dose scenario was assessed using reported data for Depakote® in healthy subjects , computing the predictive errors (100*Pred/Obs) for the mean and the inter-individual standard deviation of AUC and Cmax. Finally, the BE outcome of a simulated multiple-dose study after fasting administration of 500 mg q12 for 5 days was assessed with methods A and B.
Results: A 2-compartment pharmacokinetic NLME model with first-order lagged absorption and linear elimination was developed from the single dose bioequivalence data. Confidence intervals obtained for the T/R AUC and Cmax ratios with simulation-based methods under extensive sampling were: [0.84-0.97] and [0.61-0.78] respectively for method A; [0.84-0.96] and [0.61-0.78] respectively for method B. Predictive errors for the model steady-state predictions of AUC and Cmax were below 15% for 500 mg q12. The 90%CI predicted for the T/R AUC and PTF ratios in a multiple-dose BE study were: [0.85-0.97] and [0.64-0.92] respectively for method A; [0.85-0.96] and [0.62-0.94] respectively for method B. The extensive sampling time scheme showed a better characterization of the relative VPA exposure after the administration of the different formulations.
Conclusions: We present two alternative ways of assessing bioequivalence from a model-based approach. Results of both methods indicate that BE conclusions obtained in the single-dose in vivo study would hold under multiple-dose administration of 500 mg twice daily. Model-based approach with an extensive sample time scheme allows to appreciate bigger differences in VPA exposure between reference and test formulations, due to the better estimation for Cmax.
References:  Acharya C et al. 2016. A diagnostic tool for population models using non-compartmental analysis: the ncappc package for R. Comput. Methods Programs. Biomed. 127: 83-93.  Dutta S, Zhang Y. 2004. Bioavailability of divalproex extended-release formulation relative to the divalproex delayed-release formulation. Biopharm. Drug. Dispos. 25:345-352.