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

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.

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.

Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Evaluation of Truncated AUC as an Alternative Measure to Assess Pharmacokinetic Comparability in Bridging Biologic-Device Using Prefilled Syringes and Autoinjectors

Pharmacokinetic (PK) comparisons between therapeutic biologics have largely been based on the total area under the concentration-time curve (AUC) and the maximum concentration (Cmax ). For biologics with a long half-life, a PK comparability study may be long in duration and costly to conduct. The goal of this study was to evaluate whether a truncated AUC (tAUC) can be used to assess PK comparability when bridging prefilled syringe (PFS) and autoinjector (AI) treatment options for biologics with a long half-life. Fifteen biologics license applications (BLAs) were included to determine the concordance and geometric percent coefficient of variation (%CV) between tAUCs evaluated on days 7, 14, 21, and 28 and AUC evaluated to infinity (AUC0-inf ). Concordance is established if the tAUCs are comparable with AUC0-inf . Trial simulation was performed to examine the effect of the absorption rate constant (ka ) and sample size on the concordance of tAUCs. The tAUCs evaluated on day 14, 21, and 28 had 100% concordance with AUC0-inf for all 15 BLAs. The concordance of tAUC evaluated at day 7 was 87.5%. Based on the trial simulation, tAUC evaluated to day 28 post-dose can achieve high concordance (≥85%) for biologics exhibiting linear or nonlinear elimination with a ka of ≥0.1/day and with a sample size of 70 subjects per arm. tAUC appears to be a promising alternative PK measure, relative to AUC0-inf , for PK comparability assessments.

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.