Bioequivalence tests based on individual estimates using non-compartmental or model-based analyses: evaluation of estimates of sample means and type I error for different designs

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.

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.

Pharmacokinetics and Pharmacodynamics of Bimagrumab (BYM338)

BACKGROUND

Bimagrumab is a human monoclonal antibody binding to the activin type II receptor with therapeutic potential in conditions of muscle wasting and obesity. This phase I study evaluated the pharmacokinetics (PK), pharmacodynamics (PD), and safety of various dose regimens of bimagrumab and routes of administration in healthy older adults.

METHODS

This was a randomized, double-blind, placebo-controlled, parallel-arm, multiple-dose study in older adult men and women (aged ≥ 70 years, body mass index [BMI] 18-34 kg/m²) with stable health and diet. The study comprised seven treatment groups (Cohorts 1-7). Participants received bimagrumab or placebo treatment every 4 weeks for three doses (Cohorts 1 [700 mg] and 2 [210 mg] intravenous infusion; Cohorts 3 [1500 mg] and 4 [525 mg] subcutaneous infusion), or every week for 12 doses (Cohorts 5 [300 mg], 6 [150 mg], and 7 [52.5 mg] subcutaneous bolus injection) and were followed up until week 20. Blood samples were collected for bimagrumab PK analysis. PD were assessed by dual energy X-ray absorptiometry to quantify the change from baseline in lean body mass (LBM) and fat body mass (FBM) compared with placebo. Safety was assessed throughout the study.

RESULTS

Eighty-four of 91 (92.3%) randomized participants (mean age 74.5 years; BMI 28.0 kg/m²) completed the study. Demographic characteristics were generally balanced across the groups. A target-mediated drug disposition profile was observed following both intravenous and subcutaneous administration. The absolute subcutaneous bioavailability was estimated at approximately 40%. LBM increased by 4-6% (1.5-2 kg) from baseline throughout the treatment period for intravenous and subcutaneous regimens, except for the 52.5 mg subcutaneous dose, which did not differ from placebo. Concurrently, there was a decrease in FBM (approximately 2-3 kg) for all intravenous and subcutaneous regimens. Bimagrumab was generally safe and well tolerated; adverse events were mostly mild to moderate in severity.

CONCLUSIONS

Dose levels of bimagrumab administered weekly subcutaneously resulted in PK profiles and PD effects comparable with monthly intravenous dosing, which supports the feasibility of the subcutaneous route of administration for bimagrumab for future clinical development.

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.

Simulation Models for Prediction of Bioavailability of Medicinal Drugs-the Interface Between Experiment and Computation

The oral drug bioavailability (BA) problems have remained inevitable over the years, impairing drug efficacy and indirectly leading to eventual human morbidity and mortality. However, some conventional lab-based methods improve drug absorption leading to enhanced BA, and the recent experimental techniques are up-and-coming. Nevertheless, some have inherent drawbacks in improving the efficacy of poorly insoluble and low impermeable drugs. Drug BA and strategies to overcome these challenges were briefly highlighted. This review has significantly unravelled the different computational models for studying and predicting drug bioavailability. Several computational approaches provide mechanistic insights into the oral drug delivery system simulation of descriptors like solubility, permeability, transport protein-ligand interactions, and molecular structures. The in silico techniques have long been known still are just being applied to unravel drug bioavailability issues. Many publications have reported novel applications of the computational models towards achieving improved drug BA, including predicting gastrointestinal tract (GIT) drug absorption properties and passive intestinal membrane permeability, thus maximizing time and resources. Also, the classical molecular simulation models for free solvation energies of soluble-related processes such as solubilization, dissolutions, supersaturation, and precipitation have been used in virtual screening studies. A few of the tools are GastroPlus^TM that supports biowaiver for drugs, mainly BCS class III and predicts drug compounds' absorption and pharmacokinetic process; SimCyp® simulator for mechanistic modelling and simulation of drug formulation processes; pharmacodynamics analysis on non-linear mixed-effects modelling; and mathematical models, predicting absorption potential/maximum absorption dose. This review provides in silico-experiment annexation in the drug bioavailability enhancement, possible insights that lead to critical opinion on the applications and reliability of the various in silico models as a growing tool for drug development and discovery, thus accelerating drug development processes.

Characterizing Absorption Properties of Dispersible Pretomanid Tablets Using Population Pharmacokinetic Modelling

BACKGROUND AND INTRODUCTION

The dispersible tablet formulation (DTF) of pretomanid has been developed to facilitate future use in children. This work aimed to assess the pharmacokinetics (PK) and relative bioavailability of the DTF compared to the marketed formulation (MF) and the potential influence of dose.

METHODS

Pretomanid DTF was investigated in a single-dose, randomized, four-period, cross-over study, with 7 days of washout between doses. Forty-eight healthy volunteers were enrolled and randomized into one of two panels to receive doses either in the fasted state or after a high-fat meal. Each volunteer received doses of 10, 50, and 200 mg DTF, and 200 mg MF pretomanid. Blood samples for pharmacokinetic assessment were drawn following a rich schedule up to 96 h after each single dose. The study data from the panel receiving the high-fat meal were analyzed using a nonlinear mixed-effects modeling approach, and all data were characterized with noncompartmental methods.

RESULTS

A one-compartment model with first-order elimination and absorption through a transit compartment captured the mean and variability of the observed pretomanid concentrations with acceptable precision. No significant difference in bioavailability was found between formulations. The mean absorption time for the DTF was typically 137% (86-171%) of that for the MF. The bioavailability was found to be dose dependent with a small positive and larger negative correlation under fed and fasted conditions, respectively.

CONCLUSION

Using data from a relative bioavailability study in healthy adult volunteers, a mathematical model has been developed to inform dose selection for the investigation of pretomanid in children using the new dispersible tablet formulation. Under fed conditions and at the currently marketed adult dose of 200 mg, the formulation type was found to influence the absorption rate, but not the bioavailability. The bioavailability of the DTF was slightly positively correlated with doses when administered with food.

CLINICAL TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT04309656, first posted on 16 March 2020.

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.

Efficient model-based bioequivalence testing

The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard, the PK parameters area under the curve (AUC) and $C_{\max}$ are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency, the formulations are declared to be sufficiently similar if the $90\%$ confidence interval for these ratios falls between $0.8$ and $1.25 $. As NCA is not a reliable approach in case of sparse designs, a model-based alternative has already been proposed for the estimation of $\rm AUC$ and $C_{\max}$ using nonlinear mixed effects models. Here we propose another, more powerful test than the TOST and demonstrate its superiority through a simulation study both for NCA and model-based approaches. For products with high variability on PK parameters, this method appears to have closer type I errors to the conventionally accepted significance level of $0.05$, suggesting its potential use in situations where conventional bioequivalence analysis is not applicable.

Sensitivity of Pegfilgrastim Pharmacokinetic and Pharmacodynamic Parameters to Product Differences in Similarity Studies

In this work, a previously developed pegfilgrastim (PG) population pharmacokinetic-pharmacodynamic (PKPD) model was used to evaluate potential factors of importance in the assessment of PG PK and PD similarity. Absolute neutrophil count (ANC) was the modelled PD variable. A two-way cross-over study was simulated where a reference PG and a potentially biosimilar test product were administered to healthy volunteers. Differences in delivered dose amounts or potency between the products were simulated. A different baseline absolute neutrophil count (ANC) was also considered. Additionally, the power to conclude PK or PD similarity based on areas under the PG concentration-time curve (AUC) and ANC-time curve (AUEC) were calculated. Delivered dose differences between the products led to a greater than dose proportional differences in AUC but not in AUEC, respectively. A 10% dose difference from a 6 mg dose resulted in 51% and 7% differences in AUC and AUEC, respectively. These differences were more pronounced with low baseline ANC. Potency differences up to 50% were not associated with large differences in either AUCs or AUECs. The power to conclude PK similarity was affected by the simulated dose difference; with a 4% dose difference from 6 mg the power was approximately 29% with 250 subjects. The power to conclude PD similarity was high for all delivered dose differences and sample sizes.

Design and inference for 3-stage bioequivalence testing with serial sampling data

A bioequivalence test is to compare bioavailability parameters, such as the maximum observed concentration (Cmax ) or the area under the concentration-time curve, for a test drug and a reference drug. During the planning of a bioequivalence test, it requires an assumption about the variance of Cmax or area under the concentration-time curve for the estimation of sample size. Since the variance is unknown, current 2-stage designs use variance estimated from stage 1 data to determine the sample size for stage 2. However, the estimation of variance with the stage 1 data is unstable and may result in too large or too small sample size for stage 2. This problem is magnified in bioequivalence tests with a serial sampling schedule, by which only one sample is collected from each individual and thus the correct assumption of variance becomes even more difficult. To solve this problem, we propose 3-stage designs. Our designs increase sample sizes over stages gradually, so that extremely large sample sizes will not happen. With one more stage of data, the power is increased. Moreover, the variance estimated using data from both stages 1 and 2 is more stable than that using data from stage 1 only in a 2-stage design. These features of the proposed designs are demonstrated by simulations. Testing significance levels are adjusted to control the overall type I errors at the same level for all the multistage designs.

Flexible multivariate nonlinear models for bioequivalence problems

Modelling the concentration of a drug in the bloodstream over time is usually done using compartment models. In pharmacokinetic data, they turn into highly nonlinear mixed-effects models (NLMEMs) when we take the heterogeneity between subjects into account. Fitting of NLMEMs can be difficult and may involve complex algorithms, with convergence critically depending on the initial values and maybe requiring data transformations. In this article, we propose a flexible alternative to the usual parametric compartment models, inspired by the Multivariate SuperImposition by Translation and Rotation (MSITAR) model but adapted to be applicable in this new field. A fully parametric one-compartment NLMEM is considered for comparison. We make use of a Bayesian approach and illustrate the method on a real dataset where the interest lies in contrasting the average and individual bioequivalence of a test and reference formulation of an anti-hypertensive drug.

Use of population approach non-linear mixed effects models in the evaluation of biosimilarity of monoclonal antibodies

PURPOSE

Population pharmacokinetic analyses (PPK) have been used to establish bioequivalence for small molecules and some biologicals. We investigated whether PPK could also be useful in biosimilarity testing for monoclonal antibodies (MAbs).

METHODS

Data from a biosimilarity trial with two trastuzumab products were used to build population pharmacokinetic models. First, a combined model was developed and similarity between test and reference product was evaluated by performing a covariate analysis with trastuzumab drug product (test or reference) on all model parameters. Next, two separate models were developed, one for each drug product. The model structure and parameters were compared and evaluated for differences.

RESULTS

Drug product could not be identified as statistically significant covariate on any parameter in the combined model, and the addition of drug product as covariate did not improve the model fit. A similar structural model described both the test and reference data best. Only minor differences were found between the estimated parameters from these separate models.

CONCLUSIONS

PPK can also be used to support a biosimilarity claim for a MAb. However, in contrast to the standard non-compartmental analysis, there is less experience with a PPK approach. Here, we describe two methods of how PPK can be incorporated in biosimilarity testing for complex therapeutics.

Population Pharmacokinetic Analysis of the Oral Absorption Process and Explaining Intra-Subject Variability in Plasma Exposures of Imatinib in Healthy Volunteers

BACKGROUND AND OBJECTIVE

Imatinib mesylate is presently the first-line treatment for chronic myeloid leukemia (CML). The aim of this study was to investigate the absorption and distribution kinetics of imatinib in healthy Iranian volunteers using nonlinear mixed effects modeling (NLMEM) to assess the overall, intra- and inter-subject variabilities in pharmacokinetic parameters after oral administration.

METHODS

This analysis was based on data from 24 healthy subjects who participated in a bioequivalence study after administering a single dose of 200 mg of each formulation. Imatinib concentrations were quantified using a validated liquid chromatography method. To simultaneously describe the imatinib pharmacokinetic profiles obtained with both formulations, a population pharmacokinetic model was applied to data using SAEM algorithm implemented in MONOLIX, whilst simulations were used by numerical solving of ordinary differential equations to calculate secondary parameters in individuals for bioequivalence studies.

RESULTS

According to goodness-of-fit criteria, a two-compartment open model with sequential zero- then first-order absorption and first-order elimination was used as the structural pharmacokinetic model. Inter-individual variability (IIV) was considered for all parameters. Typical population estimates (% IIV) were fraction of the drug absorbed with a zero-order kinetic (Fr) of 0.153 (47.9 %) in period (Tk0) of 0.714 h (47.4 %), first-order absorption rate constant (k a) of 0.94 h(-1)(31.2 %), oral clearance of 19 L/h (27.9 %), central volume of distribution (V c/F) of 139 L (21.5 %), apparent peripheral volume of distribution (V p/F) of 130 L (29.7 %) and the apparent inter-compartment clearance (Q/F) of 29.6 L/h (41.8 %). Body mass index (BMI) was the only covariate found to significantly affect V p /F. The coefficient of variation for intra-individual plasma exposure (AUC0-∞) was 27.8 %.

CONCLUSIONS

Analyses using NLMEM for imatinib exhibited absorption complexities such as two input rates and medium to high intra-individual variability in drug exposure.

Comparison of Nonlinear Mixed Effects Models and Noncompartmental Approaches in Detecting Pharmacogenetic Covariates

Genetic data is now collected in many clinical trials, especially in population pharmacokinetic studies. There is no consensus on methods to test the association between pharmacokinetics and genetic covariates. We performed a simulation study inspired by real clinical trials, using the pharmacokinetics (PK) of a compound under development having a nonlinear bioavailability along with genotypes for 176 single nucleotide polymorphisms (SNPs). Scenarios included 78 subjects extensively sampled (16 observations per subject) to simulate a phase I study, or 384 subjects with the same rich design. Under the alternative hypothesis (H1), six SNPs were drawn randomly to affect the log-clearance under an additive linear model. For each scenario, 200 PK data sets were simulated under the null hypothesis (no gene effect) and H1. We compared 16 combinations of four association tests, a stepwise procedure and three penalised regressions (ridge regression, Lasso, HyperLasso), applied to four pharmacokinetic phenotypes, two observed concentrations, area under the curve estimated by noncompartmental analysis and model-based clearance. The different combinations were compared in terms of true and false positives and probability to detect the genetic effects. In presence of nonlinearity and/or variability in bioavailability, model-based phenotype allowed a higher probability to detect the SNPs than other phenotypes. In a realistic setting with a limited number of subjects, all methods showed a low ability to detect genetic effects. Ridge regression had the best probability to detect SNPs, but also a higher number of false positives. No association test showed a much higher power than the others.

How to combine non-compartmental analysis with the population pharmacokinetics? A study of tobacco smoke's influence on the bioavailability of racemic citalopram in rats

BACKGROUND

Citalopram (CIT) is an antidepressant drug from the group of selective serotonin reuptake inhibitors in which it is the most potent selective inhibitor of serotonin uptake currently available. Patients treated with CIT are often heavy cigarette smokers. Individual pharmacokinetic parameters cannot be directly estimated if full pharmacokinetic profiles are not available for each subject. Sparse sampling is common to experiments using small animals, such as the case that our study is concerned with.

METHODS

The aim of the study was to demonstrate how the two (non-compartmental analysis (NCA) and nonlinear mixed-effect (NLME)) approaches, used simultaneously, can help overcome specific limitations of these separate methods whilst at the same time preserve their respective benefits.

RESULTS

Despite the ultra-sparse design, the NLME approach enabled us to develop a pharmacostatistic model with the required covariate--exposition to the tobacco smoke.

CONCLUSIONS

A tobacco smoke slows down the absorption of the CIT and at the same time makes it more effective. The consistency of results obtained both with NCA and NLME decreased the risk of model misspecification and increased confidence in the final conclusions. Combining NLME with NCA may therefore be recommended for investigating pharmacokinetic properties of the drug in the sparse designs.

The use of pharmacometrics to optimize biosimilar development

Pharmacometric approaches can assist in biosimilar development by leveraging quantitative knowledge of the originator product characteristics such as dose-exposure and exposure-response information to support a targeted approach to clinical studies. The degree to which these approaches can be applied relies on the level of information known about the originator and information that supports application of the originator model to the biosimilar. A model-based approach testing the hypothesis that the biosimilar PK and/or PK/PD profile is similar to the originator in the target patient population is aligned with the central comparability exercise required for the biosimilar approval. This Commentary details the key opportunities in study design and study analysis where pharmacometrics approaches can aid biosimilar development.

Pharmacokinetic similarity of biologics: analysis using nonlinear mixed-effects modeling

Our objective was to show, using two examples, that a pharmacokinetic (PK) similarity analysis can be performed using nonlinear mixed-effects models (NLMEM). We used two studies that compared different biosimilars: a three-way crossover trial with somatropin and a parallel-group trial with epoetin-α. For both data sets, the results of NLMEM-based analysis were compared with those of noncompartmental analysis (NCA). For the latter analysis, we performed an NLMEM-based equivalence Wald test on secondary parameters of the model: the area under the curve and the maximal concentration. Somatropin PK was described by a one-compartment model and epoetin-α PK by a two-compartment model with linear and Michaelis-Menten elimination. For both studies, similarity of PK was demonstrated by means of both NCA and NLMEM, and both methods led to similar results. Therefore, for establishing similarity, PK data can be analyzed by either of the methods. NCA is an easier approach because it does not require data modeling; however, NLMEM leads to a better understanding of the underlying biological system.

Population pharmacokinetic and pharmacodynamic model-based comparability assessment of a recombinant human Epoetin Alfa and the Biosimilar HX575

The aim of this study was to develop an integrated pharmacokinetic and pharmacodynamic (PK/PD) model and assess the comparability between epoetin alfa HEXAL/Binocrit (HX575) and a comparator epoetin alfa by a model-based approach. PK/PD data-including serum drug concentrations, reticulocyte counts, red blood cells, and hemoglobin levels-were obtained from 2 clinical studies. In sum, 149 healthy men received multiple intravenous or subcutaneous doses of HX575 (100 IU/kg) and the comparator 3 times a week for 4 weeks. A population model based on pharmacodynamics-mediated drug disposition and cell maturation processes was used to characterize the PK/PD data for the 2 drugs. Simulations showed that due to target amount changes, total clearance may increase up to 2.4-fold as compared with the baseline. Further simulations suggested that once-weekly and thrice-weekly subcutaneous dosing regimens would result in similar efficacy. The findings from the model-based analysis were consistent with previous results using the standard noncompartmental approach demonstrating PK/PD comparability between HX575 and comparator. However, due to complexity of the PK/PD model, control of random effects was not straightforward. Whereas population PK/PD model-based analyses are suited for studying complex biological systems, such models have their limitations (statistical), and their comparability results should be interpreted carefully.

Non-compartmental estimation of pharmacokinetic parameters for flexible sampling designs

Pharmacokinetic (PK) studies aim to understand the kinetics of absorption, distribution, metabolism and elimination of a drug. Typically, such studies involve measuring the concentration of the drug in the plasma or blood at several time points after drug administration. In studying the PK behaviour, either the non-compartmental approach or alternatively a modelling approach can be utilized. Traditionally, the non-compartmental approach makes minimal assumptions about the data-generating process but requires the data to be collected in a very structured way. Conversely, the modelling approach depends heavily on assumptions about the data-generating process but does not impose a specific data structure. In this paper, we will discuss non-compartmental methods for estimating the area under the concentration versus time curve and other common PK parameters that use minimal assumptions about the data structure making it applicable to a wide range of PK studies. We will evaluate the methods using simulation and give an illustrative example.

Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models

Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or changing between periods. We use the expected standard errors of treatment effect to compute the power for the Wald test of comparison or equivalence and the number of subjects needed for a given power. We perform various simulations mimicking crossover two-period trials to show the relevance of these developments. We then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3.2 of the r function PFIM.

Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses

Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic χ(2) distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications.