Impact of truncated area under the curve on failed bioequivalence studies: a computer simulation analysis

The common measures used in a bioequivalence study are area under the curve (AUC) and the maximum plasma concentration. Estimation of AUC requires frequent blood samples. For long half-life drugs, sampling for long periods of time may become cumbersome. To resolve this issue some investigators have suggested the use of truncated AUC in bioequivalence studies for long half-life drugs. The suggested length of time for the truncated AUC is 72 hours. Many studies have been conducted to show that truncated AUC till 72 hours is a suitable approach. However, the suitability of truncated AUC for failed bioequivalence study has not been demonstrated. This report of simulated plasma concentration versus time data evaluates the suitability of truncated AUC for failed bioequivalence study of two hypothetical drugs. The results of the study indicate that the truncated approach for the estimation of the AUC for long half-life drugs in bioequivalence studies may be useful but it also increases the probability of accepting drugs as being bioequivalent when they are not.     

A limited sampling approach in bioequivalence studies: application to long half-life drugs and replicate design studies.

OBJECTIVES: The objectives of this study was to develop a limited sampling model (LSM) to predict the area under the curve (AUC) and the maximum plasma concentration (Cmax) for the assessment of bioequivalence studies. METHODS: Two drugs (A and B) were selected for this purpose. Drug A was chosen to test bioequivalence of two formulations with a long half-life (> 35 hours), whereas drug B was chosen to test the bioequivalence of two formulations (half-life = 12 hrs) with a replicate design study. The LSM for both drugs was developed using 5 blood samples each from 15 healthy subjects. The relationship between plasma concentration (independent variable) at selected time points with the AUC or Cmax (dependent variable) was evaluated by multiple linear regression analysis. The multiple linear regression which gave the best correlation coefficient (r) for 5 sampling time vs AUC or Cmax was chosen as the LSM. The predicted AUC and Cmax from the LSM were then used to assess bioequivalence of two different formulations of each drug following a single oral dose. RESULTS: The model provided good estimates of both AUC and Cmax for both drugs. The 90% confidence intervals on log-transformed observed and predicted AUC and Cmax were comparable for both drugs. CONCLUSIONS: The method described here may be used to estimate AUC and Cmax for bioequivalence studies for drugs with long half-lives or for highly variable drugs which may require replicate design studies without detailed blood sampling.     

Statistical aspects of bioequivalence testing between two medicinal products.

A generic drug product (test product) is bioequivalent to an innovator product (reference product) when their bioavailabilities in the same molar dose are similar. Bioavailability is expressed by pharmacokinetic parameters such as the area under plasma concentration-time curve (AUC), the maximum plasma concentration (Cmax) and the time of maximum plasma concentration (tmax). The assessment of bioequivalence is carried out by in vivo bioequivalence studies. This paper examines and appraises design issues for performing a bioequivalence study: the use of crossover, parallel, replicated, and add-on designs; and the determination of sample size. In addition, it presents the valid statistical approaches for proving bioequivalence: average bioequivalence on transformed and untransformed data; parametric and non-parametric analyses; moment based individual bioequivalence; direct curve comparison metrics.     

Assessing Bioequivalence Using Genomic Data

Abstract

For approval of a generic drug product, the assessment of bioequivalence in drug absorption is usually considered as a surrogate for evaluation of drug efficacy and safety in clinical studies. For some drug products, the United States Food and Drug Administration indicates that the assessment of similarity between dissolution profiles may be used as a surrogate for assessment of bioequivalence. Along this line, we propose assessing bioequivalence using genomic data collected from the same individuals, assuming that there is an established relationship between pharmacokinetic and genomic data. Because there may be a bias in the prediction of pharmacokinetic data using genomic data and the variations in these two types of data are different, we propose to assess bioequivalence based on sensitivity analysis of prediction bias and variation difference within some predetermined limits. Our methods are derived for average, population, and individual bioequivalence.     

生物利用度和生物等效性分析软件简介

考虑生物利用度的影响因素,仿制药物（或制剂）与参比对象采用相同的等效剂量,应能达到生物等效。生物利用度一般用以下几个药代动力学参数衡量：曲线下面积（AUC）,峰浓度（Cmax）,达峰时间（tmax）。本论文以双交叉生物等效性试验为例,介绍自主开发的生物等效性分析软件BA＆BE,该软件使用便捷、界面友好,可用于临床药理和新药研发等相关领域。软件允许用户直接在网格界面进行数据录入,设置变量和参数。系统便可自行对原始数据进行方差分析（ANOVA）、生物利用度和生物等效性的计算并生成报表。该软件将有助于科研人员更迅速、准确地进行数据分析和提交结果。     

Evaluation of Bioequivalence of Highly Variable Drugs Using Clinical Trial Simulations. II: Comparison of Single and Multiple-Dose Trials Using AUC and Cmax

Purpose. Evaluating of the effects of high intrasubject variability in clearance (CL) and volume of distribution (V), on 90% confidence intervals (CIs) for AUC (Area Under the concentration Curve) in single and multiple-dose bioequivalence studies. The main methodology was Monte Carlo simulation, and we also used deterministic simulation, and examination of clinical trials. The results are compared with those previously observed for Cmax (maximum concentration.) Methods. The time course of drug concentration in plasma was simulated using a one-compartment model with log-normal statistical distributions of intersubject and intrasubject variabilities in the pharmacokinetic parameters. Both immediate-release and prolonged-release products were simulated using several levels of intrasubject variability in single-dose and multiple-dose studies. Simulations of 2000 clinical bioequivalence trials per condition (138 conditions) with 30 subjects in each crossover trial were carried out. Simulated data were compared with data from actual bioequivalence trials. Results. The current simulations for AUC show similar probabilities of failure for single-dose and multiple-dose bioequivalence studies, even with differences in the rate of absorption or fraction absorbed. AUC values from prolonged-release scenario studies are more sensitive to changes in the first order absorption rate constant ka, and to variability in CL and V than AUC from studies of immediate-release studies. Conclusions. We showed that multiple-dose designs for highly variable drugs do not always reduce intrasubject variability in either AUC or Cmax, although the behavior of AUC differs from Cmax. Single dose AUC to the last quantifiable concentration was more reliable than either single dose AUC extrapolated to infinity, or multiple dose AUC during a steady-state interval. Multiple-dose designs may not be the best solution for assessing bioequivalence of highly variable drugs.     

PARTIAL-AREA METHOD IN BIOEQUIVALENCE ASSESSMENT: NAPROXEN

Regulatory authorities require demonstration of bioequivalence through comparisons of different pharmacokinetic parameters, the area under the plasma concentration–time curve (AUC), the maximum plasma concentration (C_max), and the time to reach peak concentration (T_max). The applicability and validity of regulatory requirements have been widely criticized on statistical and clinical relevance grounds. For most noncomplicated absorption models, the AUC correlates well with the extent of absorption. However, in nonlinear models of absorption, in mechanisms involving recycling of drugs, and for drugs with long half-life, the use of total AUC (from zero to infinity) can give erroneous and clinically irrelevant results since the area is mostly determined by elimination phase or by recycling. The calculation of total AUC also involves prolonged sampling, adding to the cost and risks associated with bioequivalence studies. The use of C_max or T_max as a measure of rate of absorption, to correlate with clinical relevance, is widely criticized on logical, technical, and statistical grounds. For drugs used on a multiple-dose basis, C_max and T_max evaluations become redundant since the average plateau concentration is not affected by these parameters. To resolve the drawbacks in the traditional methodology of bioequivalence evaluation, the use of partial areas in lieu of total AUC, T_max, and C_max is suggested. This study investigates the logic and robustness of the partial-area method in establishing bioequivalence. We conclude that the 5 h AUC is a more relevant parameter to establish naproxen bioequivalence than AUC_inf. We recommend against using symmetrical confidence intervals and report excellent agreement among several methods of calculating confidence intervals, probability values, and nonparametric tests. We suggest that a single-point short-term AUC is a better indicator of the bioequivalence of generic products than the total AUC, C_max, and T_max as required currently by the regulatory authorities. © 1997 by John Wiley & Sons, Ltd.     

Bioequivalence studies: biometrical concepts of alternative designs and pooled analysis.

A bioequivalence study compares the bioavailability between a test and a reference drug product in terms of the rate and extent of drug absorption. Area under the plasma concentration-time curve (AUC) and maximum plasma concentration (Cmax) are the pharmacokinetic parameters that serve as characteristics for the assessment of the extent and rate of absorption, respectively. The experimental design of a bioequivalence study is usually a crossover and rarely a parallel or a paired comparative. The statistical assessment of bioequivalence is based on the 90% confidence interval for the ratio of the test mean to the reference mean for AUC and Cmax The aims of this paper are to: (i) investigate alternative designs to a crossover design for conducting bioequivalence studies; (ii) propose the statistical analysis of different designs for bioequivalence studies on the same products; and (iii) discuss their usefulness for the approval of new generic drug products. For this purpose, three case studies are illustrated and analysed. The first case study concerns the investigation of the merits of a crossover design relative to a parallel group design for highly variable drugs using as an example a bioequivalence study of tamoxifen products. The second case study concerns the pooled statistical analysis of two bioequivalent studies of the same levodopa products. The analyses of the individual studies failed to meet the regulatory criteria for bioequivalence. The one study design was a paired comparative and the other one a crossover. Under some assumptions the crossover design may be considered as a paired comparative and the data from the two studies may be analysed together as a paired comparative design. The third case study concerns the statistical pooled analysis of two bioequivalent studies of the same clodronate products. The one study was a three-period crossover pilot study and it was used to identify the variability of the active substance. Then, this variability was used to determine the number of subjects for the main pivotal study which was a two-period crossover. The pilot study design was converted into a two-period crossover design and the data from the two studies were analysed together as a two-period crossover design. The original data of the studies were modified accordingly.     

Bioequivalence testing by statistical shape analysis

Bioequivalence testing has been traditionally centered in summary variables such as AUC, C _max and t _max which filter out the intrinsic information conveyed by discrete sequential concentration–time observations. Comparing entire concentration–time profiles between test and reference formulations for bioequivalence purposes provides stronger evidence about either their similarity or their discrepancy. The Kullback–Leibler information criterion (KLIC) may be computed for each concentration–time across all subjects between formulations of the same drug, with a standard crossover study design. It has been shown that if properly scaled it follow a chi-squared distribution and dependent p-values may be computed in order to construct a bioequivalence criterion. Extensive simulations and real data were used to compare it with the current standard procedures. This statistical shape analysis method may provide important clinical and regulatory advantages.     

Determination of in Vivo Bioequivalence

The May and June 2001 issues of Pharmaceutical Research contained three articles related to the determination of in vivo Bioequivalence (1-3). The articles discussed: (a) the bioequivalence of highly variable drugs, (b) novel metrics for direct comparison of bioequivalence study plasma curves, and (c) the role of a microemulsion vehicle on cutaneous bioequivalence.An analysis of the relationship and potential impact of these articles on their respective areas of bioequivalence will be addressed in this commentory.     

Establishing bioequivalence for inhaled drugs; weighing the evidence

Introduction: During drug development and product life-cycle management, it may be necessary to establish bioequivalence between two pharmaceutical products. Methodologies to determine bioequivalence are well established for oral, systemically acting formulations. However, for inhaled drugs, there is currently no universally adopted methodology, and regulatory guidance in this area has been subject to debate.

Areas covered: This paper covers the current status of regulatory guidance on establishing the bioequivalence of topically acting, orally inhaled drugs, the value and limitations of in vitro and in vivo bioequivalence testing, and the practical issues associated with various approaches. The reader will gain an understanding of the issues pertaining to bioequivalence testing of orally inhaled drugs, and the current status of regulatory approaches to establishing bioequivalence in different regions.

Expert opinion: Establishing bioequivalence of inhaled drug products involves a multistep process; however, methodologies for each step have yet to be fully validated. Our lack of understanding about the relationship between in vitro, in vivo and clinical data suggests that in most cases, unless there is a high degree of pharmaceutical equivalence between the test and reference products, consideration of a combination of preclinical and clinical data may be preferable to abridged approaches relying on in vitro data alone.     

Assessing bioequivalence using genomic data

For approval of a generic drug product, the assessment of bioequivalence in drug absorption is usually considered as a surrogate for evaluation of drug efficacy and safety in clinical studies. For some drug products, the United States Food and Drug Administration indicates that the assessment of similarity between dissolution profiles may be used as a surrogate for assessment of bioequivalence. Along this line, we propose assessing bioequivalence using genomic data collected from the same individuals, assuming that there is an established relationship between pharmacokinetic and genomic data. Because there may be a bias in the prediction of pharmacokinetic data using genomic data and the variations in these two types of data are different, we propose to assess bioequivalence based on sensitivity analysis of prediction bias and variation difference within some predetermined limits. Our methods are derived for average, population, and individual bioequivalence.     

Tmax: An Unconfounded Metric for Rate of Absorption in Single Dose Bioequivalence Studies

Purpose. While peak drug concentration (Cmax) is recognized to be contaminated by the extent of absorption, it has long served as the indicator of change in absorption rate in bioequivalence studies. This concentration measure per se is a measure of extreme drug exposure, not absorption rate. This paper redirects attention to Tmax as the absorption rate variable. Methods. We show that the time to peak measure (Tmax), if obtained from equally spaced sampling times during the suspected absorption phase, defines a count process which encapsulates the rate of absorption. Furthermore such count data appear to follow the single parameter Poisson distribution which characterizes the rate of many a discrete process, and which therefore supplies the proper theoretical basis to compare two or more formulations for differences in the rate of absorption. This paper urges limiting the use of peak height measures based on Cmax to evaluate only for dose-dumping, a legitimate safety concern with, any formulation. These principles and techniques are illustrated by a bioequivalence study in which two test suspensions are compared to a reference formulation. Results. Appropriate statistical evaluation of absorption rate via Tmax supports bioequivalence, whereas the customary analysis with Cmax leads to rejection of bioequivalence. This suggests that the inappropriate use of Cmax as a surrogate metric for absorption rate contributes to the unpredictable and uncertain outcome in bioequivalence evaluation today.     

Bioequivalence of piracetam following acute administration of an oral solution or two tablet formulations in volunteers

In an open, non-randomized 3-way cross-over study, the bioavailability of 2-oxo-pyrrolidine-1-acetamide (piracetam, Encetrop) from two solid oral formulations and one liquid formulation was tested in 8 healthy male volunteers. The area under the concentration time curve, which is defined to be a measurement for bioequivalence among the three tested galenic formulations correlated very well with the area under the effect intensity-time curve, which was estimated in the same volunteers using electro-physiological methods. The different methods of estimation of bioequivalence show similarity between both solid galenic formulations, while the liquid form exhibits superiority in respect to the oral solid formulations.     

Power of the two one-sided tests procedure in bioequivalence

The power of the two one-sided tests procedure for testing bioequivalence is derived from the bivariate noncentral tdistribution. Power curves are shown and their use in planning bioequivalence experiments discussed. Sample sizes computed in the usual manner from an analysis of variance are shown to be too small to assure a declaration of bioequivalence except under favorable conditions.     

Experimental, extrapolated and truncated areas under the concentration–time curve in bioequivalence trials

Objective: The extrapolated area under the concentration–time curve (AUC_0–∞) for any drug is considered by operating guidelines as the primary parameter related to the extent of absorption in single-dose bioavailability and bioequivalence trials. Not more than 20% should be added to the experimental AUC (AUC_0–t) in the extrapolating procedure. However, in certain specific cases, it is problematic and, in other cases, impossible to respect the above requirement. It was intended to demonstrate that truncated AUC or AUC_0–t would be used in bioequivalence trials when the AUC cannot be extrapolated. Methods: AUC_0–t and truncated AUC were compared at various time intervals with AUC_0–∞ in a series of 19 single-dose bioequivalence trials covering 15 different drugs, each carried out on 12–24 healthy volunteers. Point estimators and 90% confidence intervals in the 0.80–1.25 and 0.70–1.43 ranges were statistically processed using log-transformed parameters. Results: In all the trials considered, overlapping point estimators and 90% confidence intervals were invariably obtained, regardless of the AUC used. Conclusion: The use of AUC_0–t or truncated AUC may be considered an ancillary procedure in bioequivalence trials when AUC cannot be extrapolated. This occurs with most extended-release formulations, endogenous substances, and poorly absorbed drugs. It also occurs in trials with one or more poor metabolisers, with drugs possessing very long elimination half-lives, and with bioassays having problems of sensitivity that preclude sufficiently precise plasma concentration measurement over the required sampling period. Received: 16 June 1999 / Accepted in revised form: 3 August 1999     

On tier method for assessment of individual bioequivalence

The bioavailability and bioequivalence between drug products has become an important subject in drug development. The average bioavailability of the test (T) and the reference (R) products is currently specified in the FDA guidelines to be used for assessing the bioequivalence of the drug products. However, it has been recognized that the safety for the substitution of a reference drug product with a test drug product in patients, whose concentration may have been titrated to a steady efficacious and safe level, could be a concern. Therefore, it is suggested that individual bioequivalence within each subject be assessed to assure the safety of the drug switchability. This paper examines the statistical properties of TIER procedure that Anderson and Hauck (1) proposed to assess individual bioequivalence. It is shown that Anderson and Hauck's procedure could be improved by imposing some distribution assumption such as lognormal distribution for assessment of individual bioequivalence. This paper also compares the relative performance of the individual bioequivalence based on TIER procedure and the average bioequivalence based on two one-sided tests procedure suggested by Schuirmann (2). The relationship between equivalence limits for the improved TIER procedure and average bioequivalence is also examined.     

盐酸利托君片在中国健康志愿者体内的生物等效性

目的:研究不同生产厂家生产的利托君片的生物等效性。方法:根据身高体重相近原则,18例健康女性受试者采用双周期两交叉给药方案,分别一次性口服2片(10 mg.片-1)试验盐酸利托君片或参比盐酸利托君片,用LC-MS/MS内标法测定健康受试者血浆中盐酸利托君浓度,采用DAS 2.0.1软件计算药动学参数,并进行2种制剂的生物等效性评价。结果:经药动学参数计算其参比药t1/2=(2.623±1.223)h,Cmax=(12.425±6.891)ng·mL-1,Tmax=(0.769±0.555)h,AUC0~t=(28.416±9.102)ng·h·mL-1,AUC0~∞=(33.199±12.338)ng·h·mL-1;试验制剂t1/2=(2.539±0.670)h,Cmax=(14.475±11.262)ng·mL-1,Tmax=(0.741±0.509)h,AUC0~t=(30.499±11.402)ng·h·mL-1、AUC0~∞=(34.258±12.094)ng·h·mL-1。试验制剂的相对生物利用度AUC0~t=(109.6±23.0)%,AUC0~∞=(108.0±26.2)%。结论:受试制剂与参比...     

Bioequivalence of inhaled formoterol fumarate assessed from pharmacodynamic, safety and urinary pharmacokinetic data

This paper deals with a crossover trial on healthy volunteers performed to obtain combined pharmacodynamic, safety and pharmacokinetic data in order to assess the bioequivalence of formoterol fumarate (CAS 43229-80-7) delivered by mono-dose dry powder inhalers, as test and reference. The trial was carried out on 24 Caucasian healthy male and female volunteers treated with 12 micrograms formoterol fumarate bihydrate capsules for inhalation route. Pharmacodynamics was evaluated through a challenge test with methacholine on the forced expiratory volume in 1 s (FEV1). Safety was achieved from glucose and potassium serum levels assayed on timed samples over a 12-h period cost-dosing and from blood pressure, heart rate and ECG recording. Pharmacokinetics was obtained from urinary excretion of formoterol, assessed by a highly sensitive analytical method (LC-MS-MS). Pharmacodynamic, safety and pharmacokinetic results evidenced the bioequivalence of the two formulations investigated. This investigation is an interesting approach how to assess bioequivalence when the classical approach based on the similarity of plasma concentrations can not be applied.     

The impact of outlying subjects on decising of bioequivalence

As a consequence of a hearing on bioequivalence conducted by the Food and Drug Administration in 1986, the identification and the treatment of a potential outlier in bioequivalence trials has become an important issue in the assessment of bioequivalence because the exclusion of a statistically identified outlier may lead to a totally different conclusion on bioequivalence. In this paper, we examine the impact of a statistically identified outlying subject on the decision of bioequivalence through a simulation study under the structure or a standard two-way crossover design based on interval hypotheses for bioequivalence. The Hotelling T ² test suggested by Liu and Weng (1) is used for detection of an outlying subject.