ON STATISTICAL POWER FOR AVERAGE BIOEQUIVALENCE TESTING UNDER REPLICATED CROSSOVER DESIGNS

In its recent guidance on bioequivalence, the U.S. Food and Drug Administration (FDA) recommends a two-sequence, four-period (2×4)replicated crossover design be used for assessment of population and individual bioequivalence [FDA. Guidance for Industry on Statistical Approaches to Establishing Bioequivalence; Center for Drug Evaluation and Research, Food and Drug Administration: Rockville, MD, 2001]. The recommended replicated crossover design not only allows estimates of both the inter-subject and the intra-subject variabilities and the variability due to subject-by-formulation interaction, but also provides an assessment of average bioequivalence (ABE). In this article, power function for assessment of ABE under a general replicated crossover design (i.e., a 2×2mreplicated crossover design) based on the traditional analysis of variance model and the mixed effects model as suggested by the FDA are studied. It is found that the power of a 2×2mreplicated crossover design depends upon the variability due to subject-by-formulation interaction and the number of replicates. Based on the derived power function, formula for sample size calculation for assessment of ABE under a 2×2mreplicated crossover design is also provided.     

Individual bioequivalence revisited.

For decades, the establishment of bioequivalence has generally relied on the comparison of population averages between the test and reference formulations. In the early 1990s, individual bioequivalence was proposed to ensure that an individual could be switched from the reference product to the test product with unchanged efficacy and safety. Since 1997, the US Food and Drug Administration (FDA) has published three guidance documents on the proposed criterion and statistical methodology for the individual bioequivalence approach. From a scientific stand-point, the individual bioequivalence criterion appears to offer several advantages for some drug products compared with the average criterion. It allows comparison of intraindividual variances, scaling the bioequivalence criterion to the reference variability and detection of an important subject-by-formulation interaction if it exists. Based on these considerations, the FDA has recently recommended replicate study designs for modified release dosage forms and highly variable drug products. The new criterion also promotes inclusion of a heterogeneous population of volunteers in bioequivalence studies. Despite all the advantages of the individual bioequivalence approach, questions remain on the optimal use of replicate study designs and the proposed criterion for evaluation of bioequivalence between formulations. In the finalised guidance documents, therefore, the FDA maintains the average bioequivalence criterion while allowing other criteria under certain circumstances. Collection and analysis of bioequivalence data from replicate study designs may permit further assessment and resolution of these questions.     

Population and individual bioequivalence: lessons from real data and simulation studies

The Food and Drug Administration (FDA) has proposed replacing the 1992 average bioequivalence (ABE) with population and individual bioequivalence (PBE & IBE), as outlined in the preliminary draft guidance of December 1997, which was subsequently replaced by the draft guidances of August 1999 and resolved in the final guidance of October 2000. This has led to considerable public debate among regulatory, academic, and industry experts at numerous conferences (e.g., FDA/AAPS March 1998, FDA/AAPS August-September 1999, FDA Pharmaceutical Sciences Advisory Committee September 1999) and in the literature. The final guidance calls for ABE to remain as the primary criterion by which new formulations may be judged ready for access to the marketplace. In addition, the FDA recommends the use of replicate study designs for the specific drug classes of controlled-release formulations and highly variable drugs. The final guidance also alludes to the possibility of a sponsor requesting alternative criteria such as PBE and IBE following consultation with the FDA. This procedure amounts to a data collection period during which data suitable to evaluate the operating characteristics of PBE and IBE would be generated, analyzed, and discussed among interested parties. A comprehensive review of currently available databases is useful in determining the ultimate value of this data collection period. This report provides an update to the previous publication by the authors. In all, 28 data sets from 20 replicate cross-over bioequivalence studies have been analyzed (n = 12-96) using the statistical methodology in the most recent FDA draft guidance. The results are presented below. ABE Pass: ABE Fail: Total: AUC/Cmax AUC/Cmax AUC/Cmax AUC/Cmax Pass PBE & IBE 20/14 1/3 21/17 Pass IBE only 1/0 0/0 1/0 Fail PBE and IBE 0/2 0/1 0/3 Fail IBE only 2/3 4/5 6/8 Total 23/19 5/9 28/28 Review of the database reveals many interesting features, most notably the lack of consistent results within a given data set across all three criteria. The sensitivity of subject-by-formulation interaction to sample size and inherent variability of the compounds is further explored through simulation studies. It is concluded that additional simulation assessments must be considered when evaluating the value of a data collection period for PBE and IBE assessment. It will be shown that definitive conclusions regarding some of the operating characteristics of PBE and IBE can be achieved through a combination of data-driven hypotheses followed by simulation studies to further evaluate the hypotheses. Some recommendations for further data collection will be made.     

A MODIFIED LARGE SAMPLE APPROACH IN THE ASSESSMENT OF POPULATION BIOEQUIVALENCE

The U.S. Food and Drug Administration (FDA) requires pharmaceutical companies to show bioequivalence between different formulations or generic companies to show bioequivalence between generic drugs and brand drugs before a9680186roval. In a recent FDA guidance on bioequivalence, new criteria were proposed for assessment of population and individual bioequivalence. In this article, computer simulation is used to compare a modified large sample (MLS) upper bound for the population bioequivalence ratio with the bootstrap upper bound recommended by the FDA. The comparison criteria are the ability to maintain the stated confidence level and the estimated power of tests based on these bounds.     

A modified large sample approach in the assessment of population bioequivalence

The U.S. Food and Drug Administration (FDA) requires pharmaceutical companies to show bioequivalence between different formulations or generic companies to show bioequivalence between generic drugs and brand drugs before approval. In a recent FDA guidance on bioequivalence, new criteria were proposed for assessment of population and individual bioequivalence. In this article, computer simulation is used to compare a modified large sample (MLS) upper bound for the population bioequivalence ratio with the bootstrap upper bound recommended by the FDA. The comparison criteria are the ability to maintain the stated confidence level and the estimated power of tests based on these bounds.     

Assessing bioequivalence and drug interchangeability

ABSTRACT

As indicated by the US Food and Drug Administration (FDA), approved generic drug products can be used as substitutes for their respective innovative drug products. The FDA, however, does not indicate that two generic copies of the same innovative drug can be used interchangeably, even though they have been shown to be bioequivalent to the same innovative drug product. As more and more generic drug products become available in the market place, it is a concern whether these approved generic drug products have the same quality and safety/efficacy and hence can be used interchangeably. To address the issue of drug interchangeability, several criteria such as individual bioequivalence criterion, a criterion based on the variability due to subject-by-drug interaction, and a scaled criterion for drug interchangeability (SCDI) have been proposed in the literature. In this article, the performances of these criteria, including a newly proposed reversed average bioequivalence criterion, are studied under a 2x4 replicated crossover design in terms of the percentage of passing at the best and worst possible scenarios of similarity. The goal of this paper is to investigate the interchangeability in terms of switchability between a generic (test) drug product and an originator (reference) drug product.     

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.     

The subject-by-formulation interaction in multivariate bioequivalence

This paper addresses hypothesis testing problems concerning the subject-by-formulation interaction matrix for the assessment of multivariate bioequivalence. Two problems are addressed: (a) the problem of testing if the subject-by-formulation interaction matrix itself is zero, and (b) the problem of testing if suitable scalar valued functions of the subject-by-formulation interaction matrix is below a threshold. Approximate tests are developed in both cases and the accuracy of the approximation is numerically investigated. The results are illustrated with an example. Even though the literature on univariate bioequivalence testing addresses average bioequivalence, variance bioequivalence and subject-by-formulation interaction, the literature on multivariate bioequivalence deals only with the problem of average bioequivalence. This work appears to be the first attempt to address tests for the subject-by-formulation interaction matrix for testing multivariate bioequivalence.     

Bioequivalence Approaches for Highly Variable Drugs and Drug Products

Over the past decade, concerns have been expressed increasingly regarding the difficulty for highly variable drugs and drug products (%CV greater than 30) to meet the standard bioequivalence (BE) criteria using a reasonable number of study subjects. The topic has been discussed on numerous occasions at national and international meetings. Despite the lack of a universally accepted solution for the issue, regulatory agencies generally agree that an adjustment of the traditional BE limits for these drugs or products may be warranted to alleviate the resource burden of studying relatively large numbers of subjects in bioequivalence trials. This report summarizes a careful examination of all the statistical methods available and extensive simulations for BE assessment of highly variable drugs/products. Herein, the authors present an approach of scaling an average BE criterion to the within-subject variability of the reference product in a crossover BE study, together with a point-estimate constraint imposed on the geometric mean ratio between the test and reference products. The use of a reference-scaling approach involves the determination of variability of the reference product, which requires replication of the reference treatment in each individual. A partial replicated-treatment design with this new data analysis methodology will thus provide a more efficient design for BE studies with highly variable drugs and drug products. The opinions expressed in this report by the authors do not necessarily reflect the views or policies of the Food and Drug Administration (FDA).     

生物等效性评价的统计分析方法

生物等效性试验用于评价试验药(T)与注册药物(R)的生物等效性，以确定其效应相当。目前生物等效性平均、群体、个体生物等效性三种。平均生物等效性只评价观察指标的平均水平，而不考虑个体间的变异；而群体生物等效性既考虑了平均水平，又考虑了个体间的变异；个体生物等效性除考虑平均水平和个体变异。还考虑个体与药物间的交互作用。本文介绍了评价三种生物等效性的统计学原理，准则，等效性界值的确定，以及应用中的注意事项。并以实例说明。     

A Modern View of Excipient Effects on Bioequivalence: Case Study of Sorbitol

Purpose To examine the effect of common excipients such as sugars (sorbitol versus sucrose) on bioequivalence between pharmaceutical formulations, using ranitidine and metoprolol as model drugs.Methods Two single-dose, replicated, crossover studies were first conducted in healthy volunteers (N = 20 each) to compare the effect of 5 Gm of sorbitol and sucrose on bioequivalence of 150 mg ranitidine or 50 mg metoprolol in aqueous solution, followed by a single-dose, nonreplicated, crossover study (N = 24) to determine the threshold of sorbitol effect on bioequivalence of 150 mg ranitidine in solution.Results Ranitidine Cmax and AUC(0–∞) were decreased by ∼50% and 45%, respectively, in the presence of sorbitol versus sucrose. Similarly, sorbitol reduced metoprolol Cmax by 23% but had no significant effect on AUC(0–∞). An appreciable subject-by-formulation interaction was found for ranitidine Cmax and AUC(0–∞), as well as metoprolol Cmax. Sorbitol decreased the systemic exposure of ranitidine in a dose-dependent manner and affected bioequivalence at a level of 1.25 Gm or greater.Conclusions As exemplified by sorbitol, some common excipients have unexpected effect on bioavailability/bioequivalence, depending on the pharmacokinetic characteristics of the drug, as well as the type and amount of the excipient present in the formulation. More research is warranted to examine other ‘common’ excipients that may have unintended influence on bioavailability/bioequivalence.The opinions expressed in this article are those of the authors and do not necessarily represent the views or policies of the Food and Drug Administration.     

Some thoughts on drug interchangeability

Abstract

Current regulation for generic approval is based on the assessment of average bioequivalence. As indicated by the United States Food and Drug Administration (FDA), an approved generic drug can be used as a substitute for the innovative drug. FDA does not indicate that two generic copies of the same innovative drug can be used interchangeably even though they are bioequivalent to the same brand-name drug. In practice, bioequivalence between generic copies of an innovative drug is not required. However, as more generic drug products become available, it is a concern whether the approved generic drug products have the same quality and therapeutic effect as the brand-name drug product and whether they can be used safely and interchangeably. In this article, several criteria including a newly proposed criterion for assessing drug interchangeability are studied. In addition, comments on possible study designs and power calculation for sample size under a specific design are also discussed.     

The Subject-by-Formulation Interaction in Multivariate Bioequivalence

This paper addresses hypothesis testing problems concerning the subject-by-formulation interaction matrix for the assessment of multivariate bioequivalence. Two problems are addressed: (a) the problem of testing if the subject-by-formulation interaction matrix itself is zero, and (b) the problem of testing if suitable scalar valued functions of the subject-by-formulation interaction matrix is below a threshold. Approximate tests are developed in both cases and the accuracy of the approximation is numerically investigated. The results are illustrated with an example. Even though the literature on univariate bioequivalence testing addresses average bioequivalence, variance bioequivalence and subject-by-formulation interaction, the literature on multivariate bioequivalence deals only with the problem of average bioequivalence. This work appears to be the first attempt to address tests for the subject-by-formulation interaction matrix for testing multivariate bioequivalence.     

Bayesian approach to average bioequivalence using Bayes' factor

In recent years, bioavailability studies for assessment of bioequivalence between two or more drug formulations have become very popular in drug development. However the current practice for the assessment of bioequivalence suffers from certain serious drawbacks. For example, sometimes these tests fail to control the consumer's risk. In this article a new methodology based on the application of Bayes' factor for solving the average bioequivalence problem is proposed. We compare our approach with the existing methods by using real data sets from the Food and Drug Administration (FDA). Results are further explored using simulation studies.     

Bioequivalence evaluation of two brands of amoxicillin/clavulanic acid 250/125 mg combination tablets in healthy human volunteers: use of replicate design approach

The purpose of this study was to apply a replicate design approach to a bioequivalence study of amoxicillin/clavulanic acid combination following a 250/125 mg oral dose to 23 subjects, and to compare the analysis of individual bioequivalence with average bioequivalence. This was conducted as a 2-treatment 2-sequence 4-period crossover study. Average bioequivalence was shown, while the results from the individual bioequivalence approach had no success in showing bioequivalence. In conclusion, the individual bioequivalence approach is a strong statistical tool to test for intra-subject variances and also subject-by-formulation interaction variance compared with the average bioequivalence approach.     

Evaluation of the Bioequivalence of Highly-Variable Drugs and Drug Products

Purpose. To establish procedures for the effective evaluation of bioequivalence (BE) for highly-variable drugs and drug products (HVD/P). Methods. 2- and 4-period crossover BE studies with 24 subjects were simulated which generally assumed within-subject coefficients of variation of 40%. The relationship between the fraction of studies in which BE was accepted (the statistical power) and the ratio of geometric means (GMR) of the two formulations was evaluated for various methods of analysis. These included, primarily, scaled average BE (ABE), the corresponding approach of expanding BE limits (BEL), and, for comparison, unscaled ABE and scaled individual BE (IBE). Results. Scaled ABE and expanding BEL showed very similar properties in both 2- and 4-period studies. They had steeper power curves than scaled IBE. Unscaled ABE had very low statistical power. The acceptance of BE by unscaled and scaled ABE and expanding BEL was almost independent of subject-by-formulation interaction and the ratio of within-subject variations of the two formulations. By contrast, the conclusions reached by scaled IBE were strongly affected by these parameters. Conclusions. Scaled ABE and expanding BEL evaluate BE effectively for HVD/P in both 2- and 4-period investigations. However, additional, useful information can be obtained from 4-period studies.     

PhRMA perspective on population and individual bioequivalence

The Food and Drug Administration (FDA) issued a second-draft guidance in August 1999 on the subject of in vivo bioequivalence, which is based on the concepts of individual and population bioequivalence (IBE and PBE, respectively). The intention of this guidance is to replace the 1992 guidance that requires that in vivo bioequivalence be demonstrated by average bioequivalence (ABE). Although the concepts of population and individual bioequivalence are intuitively reasonable, a detailed review of the literature has not uncovered clinical evidence to justify the additional burden to the innovator and generic companies as well as the consumer that the new guidelines would impose. The criteria for bioequivalence described in the draft guidance employ aggregate statistics that combine information about differences in bioavailability between formulation means and differences in bioavailability variation of formulations between and within subjects. The purely technical aspects of the statistical approach are reasonably sound. However, PhRMA believes that important operational issues remain that need to be resolved before any changes to current practice are implemented. PhRMA believes that the ideals of prescribability and switchability are intuitively reasonable, but it is uncertain of the extent to which the proposed guidance can achieve these goals. It is not clear whether the attainment of such goals is necessary in the evaluation of bioequivalence given the role this plays in drug development, and the lack of clinical evidence argues against a pressing need to change current practice. PhRMA is concerned that the trade-off offered by the aggregate criteria may ultimately represent more harm than good to the public interest. PhRMA recommends more rigorous evaluation of methods based on two-way crossover designs before moving to methods that require more complex designs. One such method is identified herein and contains procedures for estimating prescribability and switchability. The possibility of a phase-in or trial period to collect replicate crossover data to further evaluate IBE and PBE and possibly allow market access based on these criteria as they are being evaluated has been proposed. PhRMA believes this is unprecedented and will offer little additional information beyond that which can be obtained by simulation or has already been collected by the FDA. Simulation studies have the advantage of allowing evaluation of the sensitivity of various procedures to represent the data patterns as created within the simulation. Operating characteristics by which proposed criteria can be adequately judged have not yet been defined. The limitations of ABE for highly variable drugs and narrow therapeutic drugs are well appreciated and may be addressed by means other than a wholesale change in the current criteria.     

Statistical evaluation of the scaled criterion for drug interchangeability

ABSTRACT

As more and more generic drug products become available in the marketplace, it is a concern whether these generic drug products can be used interchangeably in terms of their quality, safety, and efficacy. The United States Food and Drug Administration (FDA) indicates that an approved generic drug product can serve as a substitute for the innovative drug product. The FDA, however, does not indicate that approved generic drug products can be used interchangeably even if they are bioequivalent to the same innovative drug product. In the past decade, several criteria for assessing interchangeability were proposed in regulatory guidances and/or literature. Chow, Xu, and Endrenyi proposed a scaled criterion for drug interchangeability (SCDI), which takes both intra-subject variability and subject-by-drug variability into consideration. In this paper, the performance of this criterion is statistically evaluated by deriving the upper confidence limit of the test statistic and extrapolating expression of the power to facilitate sample size calculation. The performance of SCDI is also compared with that of the criterion for assessment of individual bioequivalence (IBE) for addressing drug switchability recommended by the FDA, which also takes into account the subject-by-drug variability, under various parameter specifications.     

Individual bioequivalence-has its time come?

A forthcoming draft Guidance of the Food and Drug Administration is expected to replace the current framework for the assessment of bioequivalence, based on the comparison of average kinetic responses, with a very different approach, the evaluation of individual bioequivalence. It emphasizes the estimation of intraindividual variances of the contrasted drug products as well as of the subject-formulation interaction, and requires the conduct of 4- (or 3-) period crossover bioequivalence trials. In order to facilitate the discussion of the draft Guidance and of the new approach, the underlying rationale, principles and procedures are described. Following this, various open questions are raised. It is suggested that their resolution should be carefully and widely discussed, and that more research and experience is needed before the possible implementation of the new approach.     

鼻用喷雾剂/气雾剂生物等效性评价及其统计学应用考量

目的 系统阐述局部作用的鼻用喷雾剂和鼻用气雾剂生物等效性（bioequivalence,BE）评估背景,以及美国、欧盟和中国监管机构对该类复杂药械组合BE评估的基本要求。方法 详细解释美国食品药品监督管理局（Food and Drug Administration,FDA）采用的创新性证据加权理念,和该类制剂BE评估的统计学原理、方法和考量。通过FDA颁布的布地奈德吸入混悬液指导原则和丙酸氟替卡松鼻用喷雾剂指导原则草案中的计算方法,通过R语言编程计算双侧和单侧群体生物等效性（population bioequivalence,PBE）计算统计学参数,并提供计算程序的伪代码。介绍了欧盟和中国对于鼻用喷雾剂和鼻用气雾剂相关的指导原则和评审理念。结果与结论 局部作用的鼻用喷雾剂/鼻用气雾剂为近年来新药及仿制药开发的热点,本文为该类制剂的研发、质量控制以及仿制制剂BE评价提供有益的思路与参考。