Evaluation of model-integrated evidence approaches for pharmacokinetic bioequivalence studies using model averaging methods

Conventional approaches for establishing bioequivalence (BE) between test and reference formulations using non-compartmental analysis (NCA) may demonstrate low power in pharmacokinetic (PK) studies with sparse sampling. In this case, model-integrated evidence (MIE) approaches for BE assessment have been shown to increase power, but may suffer from selection bias problems if models are built on the same data used for BE assessment. This work presents model averaging methods for BE evaluation and compares the power and type I error of these methods to conventional BE approaches for simulated studies of oral and ophthalmic formulations. Two model averaging methods were examined: bootstrap model selection and weight-based model averaging with parameter uncertainty from three different sources, either from a sandwich covariance matrix, a bootstrap, or from sampling importance resampling (SIR). The proposed approaches increased power compared with conventional NCA-based BE approaches, especially for the ophthalmic formulation scenarios, and were simultaneously able to adequately control type I error. In the rich sampling scenario considered for oral formulation, the weight-based model averaging method with SIR uncertainty provided controlled type I error, that was closest to the target of 5%. In sparse-sampling designs, especially the single sample ophthalmic scenarios, the type I error was best controlled by the bootstrap model selection method.

Development and comparison of model-integrated evidence approaches for bioequivalence studies with pharmacokinetic end points

By applying nonlinear mixed-effect (NLME) models, model-integrated evidence (MIE) approaches are able to analyze bioequivalence (BE) data with pharmacokinetic end points that have sparse sampling, which is problematic for non-compartmental analysis (NCA). However, MIE approaches may suffer from inflation of type I error due to underestimation of parameter uncertainty and to the assumption of asymptotic normality. In this study, we developed a MIE BE analysis method that is based on a pre-defined model and consists of several steps including model fitting, uncertainty assessment, simulation, and BE determination. The presented MIE approach has several improvements compared with the previously reported model-integrated methods: (1) treatment, sequence, and period effects are only added to absorption parameters (such as relative bioavailability and rate of absorption) instead of all PK parameters; (2) a simulation step is performed to generate confidence intervals of the pharmacokinetic metrics for BE assessment; and (3) in an effort to maintain type I error, two more advanced parameter uncertainty evaluation approaches are explored, a nonparametric (case resampling) bootstrap, and sampling importance resampling (SIR). To evaluate the developed method and compare the uncertainty assessment methods, simulation experiments were performed for BE studies using a two-way crossover design with different amounts of information (sparse to rich designs) and levels of variability. Based on the simulation results, the method using SIR for parameter uncertainty quantification controls type I error at the nominal level of 0.05 (i.e., the significance level set for BE evaluation) even for studies with small sample size and/or sparse sampling. As expected, our MIE approach for BE assessment exhibited higher power than the NCA-based method, especially as the data becomes sparser and/or more variable.

Model-based bioequivalence approach for sparse pharmacokinetic bioequivalence studies: Model selection or model averaging?

Conventional pharmacokinetic (PK) bioequivalence (BE) studies aim to compare the rate and extent of drug absorption from a test (T) and reference (R) product using non-compartmental analysis (NCA) and the two one-sided test (TOST). Recently published regulatory guidance recommends alternative model-based (MB) approaches for BE assessment when NCA is challenging, as for long-acting injectables and products which require sparse PK sampling. However, our previous research on MB-TOST approaches showed that model misspecification can lead to inflated type I error. The objective of this research was to compare the performance of model selection (MS) on R product arm data and model averaging (MA) from a pool of candidate structural PK models in MBBE studies with sparse sampling. Our simulation study was inspired by a real case BE study using a two-way crossover design. PK data were simulated using three structural models under the null hypothesis and one model under the alternative hypothesis. MB-TOST was applied either using each of the five candidate models or following MS and MA with or without the simulated model in the pool. Assuming T and R have the same PK model, our simulation shows that following MS and MA, MB-TOST controls type I error rates at or below 0.05 and attains similar or even higher power than when using the simulated model. Thus, we propose to use MS prior to MB-TOST for BE studies with sparse PK sampling and to consider MA when candidate models have similar Akaike information criterion.

A Bayesian framework for virtual comparative trials and bioequivalence assessments

Introduction

In virtual bioequivalence (VBE) assessments, pharmacokinetic models informed with in vitro data and verified with small clinical trials' data are used to simulate otherwise unfeasibly large trials. Simulated VBE trials are assessed in a frequentist framework as if they were real despite the unlimited number of virtual subjects they can use. This may adequately control consumer risk but imposes unnecessary risks on producers. We propose a fully Bayesian model-integrated VBE assessment framework that circumvents these limitations.

Methods

We illustrate our approach with a case study on a hypothetical paliperidone palmitate (PP) generic long-acting injectable suspension formulation using a validated population pharmacokinetic model published for the reference formulation. BE testing, study power, type I and type II error analyses or their Bayesian equivalents, and safe-space analyses are demonstrated.

Results

The fully Bayesian workflow is more precise than the frequentist workflow. Decisions about bioequivalence and safe space analyses in the two workflows can differ markedly because the Bayesian analyses are more accurate.

Discussion

A Bayesian framework can adequately control consumer risk and minimize producer risk . It rewards data gathering and model integration to make the best use of prior information. The frequentist approach is less precise but faster to compute, and it can still be used as a first step to narrow down the parameter space to explore in safe-space analyses.

Model-Based Bioequivalence Analysis to Assess and Predict the Relative Bioavailability of Valproic Acid Formulations

BACKGROUND AND OBJECTIVE

Model-based bioequivalence (MBBE) encompasses the use of nonlinear mixed effect models supporting the estimation of pharmacokinetic endpoints to assess the relative bioavailability between multi-source drug products. This application emerges as a valuable alternative to the standard non-compartmental analysis (NCA) in bioequivalence (BE) studies in which dense sampling is not possible. In this work, we aimed to assess the application of MBBE compared to traditional methods in evaluating the relative bioavailability of two formulations with different drug release properties. Additionally, we sought to predict the performance of a modified-release formulation in a multiple-dose scenario, leveraging data from a single-dose study.

METHODS

MBBE analysis was implemented to estimate the BE endpoints (90% CI for the Test/Reference geometric mean ratio, T/R GMR) in area under the concentration-time curve (AUC) and maximum concentration (Cmax) using data from a single-dose, 2-period, 2-sequence BE study performed in 14 healthy subjects between a locally developed valproic acid extended-release formulation (Test) and the brand-name delayed-release formulation (Reference).

RESULTS

Results were compared with the standard approach, revealing that MBBE analysis achieved higher discrimination between formulations for Cmax, addressing limitations of the experimental sampling design and highlighting an advantage for this model-based analysis even when rich data are available. Additionally, the bioequivalence outcome under the multiple-dose scenario was predicted through a simulation-based study for both total and unbound valproic acid concentrations, considering the impact of valproic acid saturable binding on BE conclusions.

CONCLUSIONS

The MBBE analysis was superior to the NCA approach in detecting product-related differences, overcoming limitations in the study experimental design. Predictions for the multiple-dose scenario preclude that the extended-release properties of the Test formulation would persist at steady state, resulting in lower peak-to-trough fluctuation and bioequivalent performance in terms of the extent of drug absorption. Overall, these results should discourage unnecessary experimentation in healthy subjects.

Evaluation of product bioequivalence when subject blood volume necessitates limited sampling strategies

In a traditional blood level bioequivalence (BE) study, every subject provides drug concentrations at each blood sampling time. However, this approach is not suitable for animals whose blood volume limits or prohibits multiple sample collections. In our previous research, we presented an approach that can be applied to studies using a destructive sampling design where each animal provides only 1 blood sample that is then incorporated into a composite profile. Another situation we sometimes face is that of when the animals can contribute more than one sample but are still limited in the number of blood draws (e.g., 3) such that a complete profile per animal is not feasible. Unlike the destructive sampling situation, we cannot combine all blood samples into a single "composite" profile and ignore the correlation of values obtained from the same subject. To avoid the complexities associated with needing to include a covariance component among experimental units into the statistical model, we propose an approach whereby study subjects are randomly assigned to housing unit (e.g., cage or pen) and then randomly assigned to a sampling schedule within each housing unit. In doing so, housing unit rather than the individual subject serves as the experimental unit. This article provides an assessment of this alternative approach to assess product BE when only a limited number of samples can be obtained per study subject.

Evaluation of model-based bioequivalence approach for single sample pharmacokinetic studies

In a traditional pharmacokinetic (PK) bioequivalence (BE) study, a two-way crossover study is conducted, PK parameters (namely the area under the time-concentration curve [AUC] and the maximal concentration [C max ]) are obtained by noncompartmental analysis (NCA), and the BE analysis is performed using the two one-sided test (TOST) method. For ophthalmic drugs, however, only one sample of aqueous humor, in one eye, per eye can be obtained in each patient, which precludes the traditional BE analysis. To circumvent this issue, the U.S. Food and Drug Administration (FDA) has proposed an approach coupling NCA with either parametric or nonparametric bootstrap (NCA bootstrap). The model-based TOST (MB-TOST) has previously been proposed and evaluated successfully for various settings of sparse PK BE studies. In this paper, we evaluate, via simulations, MB-TOST in the specific setting of single sample PK BE study and compare its performance to NCA bootstrap. We performed BE study simulations using a published PK model and parameter values and evaluated multiple scenarios, including study design (parallel or crossover), sampling times (5 or 10 spread across the dosing interval), and geometric mean ratio (of 0.8, 0.9, 1, and 1.25). Using the simulated structural PK model, MB-TOST performed similarly to NCA bootstrap for AUC. ForC max , the latter tended to be conservative and less powerful. Our research suggests that MB-TOST may be considered as an alternative BE approach for single sample PK studies, provided that the PK model is correctly specified and the test drug has the same structural model as the reference drug.

Impact of model misspecification on model-based tests in PK studies with parallel design: real case and simulation studies

This article evaluates the performance of pharmacokinetic (PK) equivalence testing between two formulations of a drug through the Two-One Sided Tests (TOST) by a model-based approach (MB-TOST), as an alternative to the classical non-compartmental approach (NCA-TOST), for a sparse design with a few time points per subject. We focused on the impact of model misspecification and the relevance of model selection for the reference data. We first analysed PK data from phase I studies of gantenerumab, a monoclonal antibody for the treatment of Alzheimer’s disease. Using the original rich sample data, we compared MB-TOST to NCA-TOST for validation. Then, the analysis was repeated on a sparse subset of the original data with MB-TOST. This analysis inspired a simulation study with rich and sparse designs. With rich designs, we compared NCA-TOST and MB-TOST in terms of type I error and study power. With both designs, we explored the impact of misspecifying the model on the performance of MB-TOST and adding a model selection step. Using the observed data, the results of both approaches were in general concordance. MB-TOST results were robust with sparse designs when the underlying PK structural model was correctly specified. Using the simulated data with a rich design, the type I error of NCA-TOST was close to the nominal level. When using the simulated model, the type I error of MB-TOST was controlled on rich and sparse designs, but using a misspecified model led to inflated type I errors. Adding a model selection step on the reference data reduced the inflation. MB-TOST appears as a robust alternative to NCA-TOST, provided that the PK model is correctly specified and the test drug has the same PK structural model as the reference drug.

Model-Based Equivalent Dose Optimization to Develop New Donepezil Patch Formulation

Donepezil patch was developed to replace the original oral formulation. To accurately describe the pharmacokinetics of donepezil and investigate compatible doses between two formulations, a population pharmacokinetic model for oral and transdermal patches was built based on a clinical study. Plasma donepezil levels were analyzed via liquid chromatography/tandem mass spectrometry. Non-compartmental analyses were performed to derive the initial parameters for compartmental analyses. Compartmental analysis (CA) was performed with NLME software NONMEM assisted by Perl-speaks-NONMEM, and R. Model evaluation was proceeded via visual predictive checks (VPC), goodness-of-fit (GOF) plotting, and bootstrap method. The bioequivalence test was based on a 2 × 2 crossover design, and parameters of AUC and C_max were considered. We found that a two-compartment model featuring two transit compartments accurately describes the pharmacokinetics of nine subjects administered in oral, as well as of the patch-dosed subjects. Through evaluation, the model was proven to be sufficiently accurate and suitable for further bioequivalence tests. Based on the bioequivalence test, 114 mg/101.3 cm²–146 mg/129.8 cm² of donepezil patch per week was equivalent to 10 mg PO donepezil per day. In conclusion, the pharmacokinetic model was successfully developed, and acceptable parameters were estimated. However, the size calculated by an equivalent dose of donepezil patch could be rather large. Further optimization in formulation needs to be performed to find appropriate usability in clinical situations.

New Model-Based Bioequivalence Statistical Approaches for Pharmacokinetic Studies with Sparse Sampling

In traditional pharmacokinetic (PK) bioequivalence analysis, two one-sided tests (TOST) are conducted on the area under the concentration-time curve and the maximal concentration derived using a non-compartmental approach. When rich sampling is unfeasible, a model-based (MB) approach, using nonlinear mixed effect models (NLMEM) is possible. However, MB-TOST using asymptotic standard errors (SE) presents increased type I error when asymptotic conditions do not hold. In this work, we propose three alternative calculations of the SE based on (i) an adaptation to NLMEM of the correction proposed by Gallant, (ii) the a posteriori distribution of the treatment coefficient using the Hamiltonian Monte Carlo algorithm, and (iii) parametric random effects and residual errors bootstrap. We evaluate these approaches by simulations, for two-arms parallel and two-period, two-sequence cross-over design with rich (n = 10) and sparse (n = 3) sampling under the null and the alternative hypotheses, with MB-TOST. All new approaches correct for the inflation of MB-TOST type I error in PK studies with sparse designs. The approach based on the a posteriori distribution appears to be the best compromise between controlled type I errors and computing times. MB-TOST using non-asymptotic SE controls type I error rate better than when using asymptotic SE estimates for bioequivalence on PK studies with sparse sampling.