DEVELOPING
`
`SOLID ORAL
`
`DOSAGE FORMS:
`
`PHARMACEUTICAL
`
`THEORY AND
`
`PRACTICE
`
`Executive editors
`
`Yihong Qiu, Abbott Laboratories, IL, USA
`
`Yisheng Chen, Novast Laboratories, Nantong, China
`
`Geoff G. Z. Zhang, Abbott Laboratories, IL, USA
`
`Associate editors
`
`Lirong Liu, Pfizer Inc, N], USA
`
`William R. Porter, Abbott Laboratories, IL, USA
`
` AMSTERDAM 6 BOSTON 0 HEIDELBERG 0 LONDON 0 NEW YORK 0 OXFORD
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`
`
`CHAPTER
`
`15
`
`Bioavailability and Bioequivalence
`
`Hao Zhu, Honghui Zhou and Kathleen Seitz
`
`15.1 GENERAL BACKGROUND
`
`Substituting one oral dosage formulation for
`another has been a common practice for many years
`in the drug development industry, as well as in the
`clinic. During drug development, for example, indus-
`try scientists frequently evaluate different versions of
`investigational drug products or dosage formulations,
`and thereby often need to conduct bioequivalence
`studies. In turn, prescribing clinicians use the bio-
`availability and bioequivalence data provided on the
`product label to select an optimal treatment regimen
`for their patients. Consequently, the overall therapeu-
`tic success of any drug substitution in the clinic will
`ultimately depend on multiple factors. These factors
`include the pharmacokinetics of the comparator and
`reference drugs, as well as the appropriateness of the
`study design and statistical criteria that were used to
`initially demonstrate bioequivalence.
`Bioequivalence has evolved as a specific regulatory
`requirement over the last 40 years. In the early 19605,
`researchers noticed that the bioavailability of a thera-
`peutic drug product could vary depending on its oral
`dosage formulation.1 Almost 15 years later, in 1977,
`the US Food and Drug Administration (FDA) initially
`published their recommended procedures for spon-
`sors to use in studies of bioequivalence.1 Since then,
`the FDA has continued to refine and revise its guid-
`ance on bioequivalence, other international regula-
`tory agencies have published their own guidelines,
`and pharmaceutical
`industry professionals world-
`wide have contributed their statistical expertise and
`
`scientific opinions. Nevertheless, several major con-
`troversies have yet to be resolved. Issues pertaining to
`the selection of the most appropriate statistical criteria
`to use to sufficiently demonstrate bioequivalence are
`still frequently debated. Other topics of discussion
`include a determination of exactly when (or under
`what specific circumstances) should formal tests of
`bioequivalence be required from a regulatory stand-
`point, and for which type or class of drug.
`Under the Food, Drug and Cosmetic (FD&C) Act of
`1938 and the 1962 Kefauver—Harris Amendment, spon-
`sors were required to provide safety and efficacy data
`to support all claims for the active ingredients in a
`new drug product before it could be approved for sale.
`Scientific standards later set by the FDA, however,
`have since allowed sponsors to lawfully make appro-
`priate drug substitutions without necessarily having
`to conduct additional
`time-consuming, and expen-
`sive, clinical safety and efficacy studies. That is, in the
`absence of additional clinical studies (and under spe-
`cific circumstances), an appropriate set of biopharma-
`ceutical, pharmacokinetic, and statistical evaluations
`may now be used to establish that a test drug formu-
`lation is bioequivalent (and thereby therapeutically
`interchangeable) with a reference drug formulation.
`The information included in this chapter will pro—
`vide the reader with an overview of the clinical, phar-
`macokinetic, and statistical
`issues associated with
`
`bioavailability and bioequivalence studies of oral
`dosage formulations. The current international regu-
`latory perspectives will also be presented, along with
`a detailed comparison of the various criteria presently
`
`Dwelnpmg Solid Oral Dosage Forms Pharmaceutical Theory and Practice
`lSBN: 978»0—444—53242.8
`
`341
`
`Copyright © 200‘). Elscvwr Inc.
`All rights reserved
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`342
`
`15, BIOAVAILABILITY AND BIOEQUIVALENCE
`
`being used in the pharmaceutical industry to demon-
`strate bioequivalence.
`
`15.2 DEFINITIONS AND KEY CONCEPTS
`
`Bioavailability essentially describes the overall rate
`and extent of drug absorption. Data from bioavail-
`ability studies are routinely used to identify a drug
`product’s pharmacokinetics, optimize a therapeutic
`dose regimen, and support product labeling require-
`ments. Bioequivalence, on the other hand, gener—
`ally describes the extent to which the bioavailability
`of one particular drug product (i.e., the test product)
`compares with that of another known drug product
`(i.e., the reference product). Data from bioequivalence
`studies are often used to establish a link between dif-
`
`ferent investigational drug formulations (e.g., an early
`phase 1 formulation versus a later phase 3 formula-
`tion). Bioequivalence studies may also be required
`during the post-approval period in certain situations,
`such as whenever a major change occurs in a manu-
`facturing method for an approved drug product.
`Bioequivalence studies are also generally required to
`compare generic versions of a drug product with the
`corresponding reference-listed drug.
`Regulatory requirements
`for bioavailability and
`bioequivalence data submitted with new drug applica-
`tions (NDAs) and supplemental applications are specifi-
`cally addressed in the US Code of Federal Regulations,2
`and a corresponding FDA guidance document has
`been published.3 The following sections will provide an
`overview of the key concepts, and general underlying
`principles, of bioavailability and bioequivalence.
`
`15 .2.1 Bioavailability
`
`When a drug is administered orally (or by any
`other extravascular route), a sufficient amount of the
`administered dose must be absorbed over a certain
`
`time period before the intended pharmacologic effect
`can manifest. Thus, the bioavailability of an orally
`administered drug clearly depends on a combination
`of factors,
`including the physiochemical character-
`istics of the drug formulation, and the physiological
`state of the gastrointestinal (GI) system.
`Bioavailability of an oral dosage form is defined3 as:
`
`"the rate and extent to which the active ingredient or
`active moiety is absorbed from a drug product and becomes
`available at the site of action"
`
`two specific
`From a pharmacokinetic perspective,
`types of bioavailability can be considered: absolute
`
`bioavailability, and relative bioavailability. Absolute
`bioavailability is a special case in which the systemic
`exposure of an extravascular dosage form is deter-
`mined relative to that of its intravenous (IV) dosage
`form. Relative bioavailability, in contrast, compares
`the rate and extent of absorption of one dosage for-
`mulation (e.g., oral solution) to another dosage formu-
`lation (e.g., oral capsule). Relative bioavailability can
`also sometimes compare the rate and extent of absorp-
`tion for one drug product with two different adminis-
`tration routes (e.g., intramuscular and subcutaneous).
`For the most part, absolute bioavailability is gen—
`erally determined by comparing the extent of drug
`absorption after an extravascular versus an intrave-
`nous (e.g.,
`infusion or bolus) administration. Thus,
`valid extravascular and IV data are both typically
`required for the calculation of absolute bioavailability.
`In operational terms, this means two series of phar-
`macokinetic samples must be collected—one extravas-
`cular series, and one IV series—using a suitable
`biological matrix (e.g., blood, plasma or serum), and
`appropriate sampling schedules. In addition, drug
`concentrations from each series must be analyzed
`using a validated drug assay.
`Measured concentration data from each series are
`
`then plotted, and the area under the drug concentration—
`time curves (AUC) estimated (e.g., by applying a
`numerical integration formula such as the trapezoidal
`rule). Assuming clearance remains constant AUC
`is directly proportional
`to the amount of drug
`absorbed. Thus absolute oral bioavailability (P) can be
`calculated:
`
`
`2 Div Aucpo
`DP,
`‘ ALICw
`
`where:
`
`Div and DPO are the intravenous and oral doses
`administered, respectively
`AUC,,, and AUC},0 are the AUC estimates for the
`intravenous and oral routes, respectively.
`
`In contrast to absolute bioavailability, relative bio-
`availability essentially compares the rate and extent of
`absorption of one dosage formulation (e.g., oral solu-
`tion) to that of another (e.g., oral capsule). Over the
`course of a typical drug development cycle, several
`relative bioavailability studies could potentially be
`required (e.g., to compare the in viva performance of an
`earlier stage formulation versus the later stage formu-
`lation). Depending on the overall pace of drug devel-
`opment, new dosage formulations are often still being
`prepared while a new molecular entity progresses
`from the nonclinical stage into the early clinical stage.
`In cases where the final product is intended as a solid
`
`I], BIOPHARMACEUTICAL AND PHARMACOKINETIC EVALUATIONS OF DRUGS MOLECULES AND DOSAGE FORMS
`
`InnoPharma Exhibit 1023.0004
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`

`

`
`
`15.2 DEFINITIONS AND KEY CONCEPTS
`
`343
`
`early drug exposure. Cmax is used to describe peak
`exposure. For a single dose study, both AUC0_T and
`AUCL-Hc are used to measure the total exposure. If a
`multiple dose study is appropriate, the AUCO,T at
`steady state (where T is the dosing interval) is used to
`describe total exposure.
`Pharmacodynamic assessments may also some-
`times be performed. For instance, if the systemic expo-
`sure of the drug is too low to be reliably detected or if
`an appropriate bioanalytical methodology cannot be
`developed to support a pharmacokinetic assessment,
`an appropriate pharmacodynamic assessment (i.e., a
`reliable and predictable surrogate marker) may suf-
`fice. Pharmacodynamic measurements are usually not
`recommended if pharmacokinetic measurements are
`available.
`
`Pharmacokinetic bioequivalence methods can be
`quite challenging for drugs with minimal systemic bio-
`availability. Drug classes that typically show minimal
`systemic bioavailability are ophthalmic, dermal, intra—
`nasal, and inhalation drugs. Nevertheless, pharmaco-
`dynamic assessments are not routinely used to show
`bioequivalence, for several reasons. First, very few val-
`idated, predictable surrogate biomarkers are available
`that are also considered acceptable surrogates by the
`regulatory authorities. Secondly, pharmacodynamic
`studies generally require prohibitively large sample
`sizes since intra- and inter-subject variability levels
`tend to be relatively high. Some examples of biological
`markers that have been successfully used for bioequiv-
`alence testing are skin blanching4 with corticosteroids,
`and stomach acid neutralization with antacids.5
`
`15.2.3 Pharmaceutical Equivalence and
`Therapeutic Equivalence
`
`Drug products are considered to be pharmaceuti-
`cal equivalents if they contain the same active ingredi-
`ent, in the same amount, with identical dosage forms,
`and identical routes of administration. Furthermore,
`
`drug products are considered to be therapeutically
`equivalent only if they are pharmaceutical equivalents
`(as described above) that are expected to produce the
`same clinical effects, and have similar safety profiles
`when they are administered to patients under the
`same conditions as specified in the product labeling
`information.
`
`Therapeutic equivalence is thus an ultimate meas-
`ure of the interchangeability of two distinct drug
`products or formulations. Therapeutic equivalence
`may be reasonably inferred from results of appropri-
`ately designed in viva pharmacokinetic bioequivalence
`studies.
`
`oral dosage form, for example, oral solutions or sus-
`pensions might be the only formulations ready for
`use. Solid prototype formulations, such as capsules,
`might also be ready for use in early phase 1; however
`these prototypes are often far from the final market-
`able form. Under these types of circumstances, there-
`fore, an estimate of the drug’s relative bioavailability
`is needed.
`
`Relative bioavailability (PM) can be calculated:
`
`A
`
`~ DA AUCB
`PM _ “[7 MC
`B
`
`where:
`
`DA and DB are the doses administered for drug for-
`mulation A and B, respectively
`AUCA and AUCB are the AUC estimates for the A
`and B formulations, respectively.
`
`15.2.2 Bioequivalence
`
`Bioequivalence is defined3 as:
`
`“the absence of a significant difference in the rate and
`extent
`to which the active ingredient or active moiety in
`pharmaceutical equivalents or pharmaceutical alternatives
`becomes available at the site of drug action when adminis—
`tered at the same molar dose under similar conditions in an
`
`appropriately designed study.”
`
`From a regulatory perspective, and for various stra-
`tegic reasons, bioequivalence studies may need to be
`conducted before a product is approved for use in the
`clinic or during the post—approval period. Depending
`on the particular research objective, for example, a
`pre-approval bioequivalence study might be required
`in an NDA submission to demonstrate the therapeutic
`link between the early phase dosage formulation and
`the to-be-marketed formulation. Bioequivalence stud-
`ies are also typically required in abbreviated NDAs
`for generic versions of brand name drugs.
`Two oral drug products can generally be considered
`to be bioequivalent if their respective concentration—
`time profiles are so similar that it would be unlikely
`that
`they would produce clinically significant dif-
`ferences in the pharmacological response. In other
`words, bioequivalent drug products with essentially
`the same systemic bioavailability should thus be
`able to produce similar, and predictable, therapeutic
`effects. Pharmacokinetic assessments in bioequiva-
`lence studies of solid oral drug products, therefore,
`typically include statistical comparisons of AUC and
`maximum concentration (Cmax). Different measures
`are sometimes needed to describe drug exposure.
`For example, partial AUC truncated to the median
`Tmax of the reference product can be used to describe
`
`11 BIOPHARMACEUTICAL AND PHARMACOKINETIC EVALUATIONS OF DRUGS MOLECULES AND DOSAGE FORMS
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`344
`
`15, BIOAVAILABILITY AND BIOEQUIVALENCE
`
`15.3 STATISTICAL CONCEPTS IN
`
`BIOEQU IVALENCE STUDIES
`
`A test (T) drug product and a reference (R) drug
`product can only be considered bioequivalent
`if
`equivalence of the rate and extent of drug absorption
`are demonstrated. This leads to three key questions:
`
`1. What are the pharmacokinetic measures that can
`be used to best characterize the rate and extent of
`
`drug absorption?
`2. What are the most appropriate statistical criteria to
`use to adequately demonstrate bioequivalence?
`3. How should a study be designed to sufficiently,
`and appropriately, capture the information
`necessary to show bioequivalence?
`
`Each of these major topics will be thoroughly dis-
`cussed in the next several sections.
`
`15.3.1 Selection and Transformation of
`
`Pharmacokinetic Measures
`
`In general, the pharmacokinetic measures that are
`typically used to describe the rate and extent of drug
`absorption include Cmax, time to reach Cmax (Tmax),
`and AUC. Whether this particular set of measures
`best reflects the actual rate and extent of drug absorp-
`tion, however, continues to be debated and discussed
`
`among many members of the industry and the regula-
`tory agencies.”
`The two most commonly used pharmacokinetic
`variables in bioequivalence studies are AUC, and
`Cmax. While Cmax, and Tmax, are both commonly used
`in standard in viva pharmacokinetic studies to reflect
`absorption rate, Cmax is specifically used in bioequiv-
`alence studies, whereas Tmax is not used as often
`because of the high interindividual variability typi-
`cally seen with this parameter. In addition to Cmax,
`AUC is also routinely used in bioequivalence studies.
`Assuming the in vivo clearance of a drug is constant
`for a given individual, AUC is directly proportional to
`the amount of drug being absorbed, and thus ideally
`describes the extent of drug absorption.
`To demonstrate equivalence,
`the mean AUC (or
`Cmax) values for two different products are directly
`compared. Mathematically, the easiest way is to do
`this is to calculate the difference between the two
`mean values. As an extension, the difference between
`
`the two log-transformed means can likewise be calcu-
`lated. Logarithmic transformation of AUC (or Cmax)
`provides several important advantages. A ratio com-
`paring log-transformed means can easily be converted
`
`back to a ratio of means in the normal scale, which can
`then be readily communicated to regulatory reviewers
`and prescribing clinicians. From a general clinical per-
`spective the ratio of the mean AUC (or Cmax), for the
`test versus the reference drugs, provides the most clin-
`ically relevant information. This is generally accepted
`in the industry, and has been recommended by the
`FDA Generic Drug Advisory Committee in 1991 .8'9’10
`From a pharmacokinetic perspective, pharma-
`cokinetic measures in bioequivalence studies can be
`expressed in a multiplicative fashion. AUC, for exam-
`ple, can be expressed as:
`
`F'D
`
`AUC0_OO :
`
`where:
`
`D is the dose given to a subject
`CL represents the clearance
`F is the bioavailability which is the fraction of the
`dose being absorbed (O S F S 1).
`
`This equation clearly shows that each subject’s AUC
`value is inversely proportional to a specific CL value.
`This multiplicative term (CL) can thus be regarded as a
`function of subject. However, in the statistical analysis of
`bioequivalence, all factors (e.g., treatment, subjects, and
`sequence) that contribute to the variation in pharmacoki-
`netic measurements are considered to be additive effects.
`
`Westlake11 contends that the subject effect is not additive,
`if data are analyzed on the original scale. Logarithmic
`transformation of AUC yields an additive equation:
`
`log AUCO,GO = log D + log P — log CL
`
`which is therefore preferable in bioequivalence analy-
`ses. Similar arguments can also be applied to Cmax.
`Finally, from a statistical perspective, AUC (or Cmax)
`values in bioequivalence studies are often positively
`skewed, and the variances between the test and refer-
`
`ence groups may differ. This generates an inconsist-
`ency in the two major assumptions (i.e., normality,
`and homoscedasticity of the variance) of the statisti-
`cal analysis of bioequivalence. Log-transformation
`of AUC (or Cmax) values, however, makes the distri-
`bution appear more symmetric, closer to the normal
`distribution, and achieves a relatively homogeneous
`variance. Thus, major international regulatory agen-
`cies generally recommend using log-transformations
`of pharmacokinetic measurements like AUC or Cmax in
`bioequivalence analyses. However, one main drawback
`to using log-transformation is that, although the mean
`log AUC (or log Cmax) values are compared between
`the test and reference groups,
`log-transformation
`essentially compares the median AUC (or Cmax) values
`instead of the means from each group.12
`
`II. BIOPHARMACEUTICAL AND PHARMACOKINETIC EVALUATIONS OF DRUGS MOLECULES AND DOSAGE FORMS
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`InnoPharma Exhibit 1023.0006
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`
`
`15.3 STATISTICAL CONCEPTS IN BIOEQUIVALENCE STUDIES
`
`15.3.2 Variability in Pharmacokinetic
`Measures of Bioavailability
`
`15.3.3 Statistical Criteria for Evaluating
`Bioequivalence
`
`The variability in pharmacokinetic measurements
`(e.g., log AUC or log Cmax values) of bioavailability
`can be represented in two hierarchical layers.13'14 That
`is, bioavailability measurements can vary at the indi-
`vidual subject level, and at overall population level.
`Whenever oral bioavailability measurements
`are
`repeated over time, for example, an individual sub-
`ject’s values may vary from time to time, even if the
`same drug product is administered each time. This
`series of measures can then collectively form a distri—
`bution where the mean value represents the inherent
`bioavailability, and the variance reflects the within—
`subject variability. Of note, in addition to the changes
`in subject-level information over time, any intra— or
`inter-lot variability arising from the manufacture of
`the drug product over time will also be reflected in
`the within—subject variability.
`The second hierarchical layer of variability rep-
`resents the overall population level variance. In the
`overall study population,
`individual subjects may
`have variations in their own inherent bioavailability.
`In all, these variations collectively form a distribu-
`tion where the mean represents the population aver-
`age of the bioavailability, and the variance reflects the
`between-subject variability. For example, in a non-
`replicated parallel bioequivalence study, patients are
`divided into two groups and given either a test (T) or
`reference I product. The jth subject in the trial would
`have a bioavailability measurement (e.g., log AUC or
`log Cmax) of Yij, where i represents the product being
`given (1' = T or R). Then Yq- follows a distribution with
`mean pi], and variance 0,2“ representing the within-
`subject variability for a given product. The individ-
`ual means m]- (j = T or R) are jointly distributed with
`mean M}, and variance of”
`(where 0%,
`is the between
`subject variability).
`The total variance for each formulation is then
`
`derived as the sum of the Within- and between-subject
`variability 0Tj = 0%}. + 0%,]:
`.
`This model allows the correlation (p), between MT
`and MB. Then the subject-by-formulation interaction
`variance component is defined as:
`
`e=meW—W)
`: (GET _ 03102 + 2'(1_ :0)'03T ‘OBR
`
`In general, a linear mixed-effect model is used to
`evaluate bioequivalence. For crossover designs or
`repeated measurements, the means are given additional
`structure by including period and sequence effects.
`
`The statistical tools (i.e., criteria) available for use
`in bioequivalence analyses have evolved remarkably
`over the past few decades. This has mostly occurred
`through a joint effort by interested stakeholders (i.e.,
`professionals
`in academia,
`industry, and regula-
`tory agencies) to select the most appropriate tools
`to address research questions related specifically to
`bioequivalence.
`In the early 19705, bioequivalence
`was evaluated with a basic comparison of the mean
`AUC and Cmax values for the test versus reference
`drug products. That is, if the mean AUC and Cmax val-
`ues for the test product were within 20% of the mean
`values from the reference product, bioequivalence
`was concluded. Other relatively basic criteria (e.g.,
`the 75/75 or 75 / 75—125 rules) have also been used to
`demonstrate bioequivalence. According to these crite-
`ria, if the ratio of the AUC and Cmax of the test product
`versus those of the reference product was within 75%
`to 125% for at least 75% of the subjects, bioequivalence
`could be claimeddalfifl
`In accordance with the conclusions from a 1986
`
`the FDA began to
`FDA Bioequivalence Task Force,
`recommend a more standard approach for in viva
`bioequivalence studies in the early 19905.18 This
`approach is known as average bioequivalence,
`in
`which the statistical analysis of pharmacokinetic
`measurements (e.g., AUC and Cmax) is based on the
`two one-sided test (TOST) procedures to determine if
`the average values from the test product are compara-
`ble to those of the reference product. Using this pro-
`cedure, a 90% confidence interval for the difference of
`
`the pharmacokinetic measurements is calculated on a
`log scale. Bioequivalence is demonstrated if this calcu-
`lated confidence interval falls within the predefined
`bioequivalence limits (i.e., :022 with a log scale or
`0.8 to 1.25 with a regular scale).
`In the late 19905,
`the FDA subsequently recom-
`mended two different approaches.19 These new
`approaches are known as population bioequiva-
`lence, and individual bioequivalence, and each can be
`compared and contrasted to the standard approach
`(i.e., average bioequivalence). From a statistical point
`of view, for example, average bioequivalence focuses
`on comparing the population average values of the
`pharmacokinetic measurements from two product
`groups. By contrast, population bioequivalence and
`individual bioequivalence focus on comparing the
`average values, and their variances as well. These
`variance terms are included in the population and
`individual bioequivalence approaches to reflect the
`possibility that the test and reference drug products
`
`ll. BIOPHARMACEUTICAL AND PHARMACOKINETIC EVALUATIONS OF DRUGS MOLECULES AND DOSAGE FORMS
`
`InnoPharma Exhibit 1023.0007
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`

`
`
`15. BIOAVAILABILITY AND BIOEQUIVALENCE
`
`could differ in some ways other than in their average
`bioavailabilities.
`
`Population bioequivalence assumes an equal distri-
`bution of the test and reference formulation bioavail-
`
`abilities across all subjects in the population, and is
`intended to address the issue of drug prescribability.
`Drug prescribability refers to the clinician’s choice for
`prescribing a particular drug product versus another
`product to a new patient. For example, a clinician can
`choose to prescribe either the brand name drug or any
`number of generic versions that have been shown to
`be bioequivalent. The underlying assumption of drug
`prescribability is that the brand name drug product
`and its generic versions may be used interchangeably
`in terms of general efficacy and safety.
`focuses on
`Individual bioequivalence, however,
`drug switchability, and the assumption of equivari—
`ance of the distributions of the test and reference prod-
`uct bioavailabilities for each individual subject. Drug
`switchability describes the situation when a clinician
`prescribes an alternative drug product (e.g., a generic
`company’s version) to a patient who has already been
`titrated to a steady, therapeutic level of a previously-
`prescribed drug product (e.g., an innovator compa-
`ny’s drug product). Drug switchability is considered
`more critical, and also more clinically relevant, than
`drug prescribability, particularly for patients with
`chronic diseases requiring long-term drug therapy.
`Drug prescribability and drug switchability can be
`assessed by population bioequivalence and individual
`bioequivalence tests, respectively.”21 The population
`bioequivalence approach is not applicable to evalua-
`tions of drug switchability, however, because of a pos-
`sible subject-by-formulation interaction.22
`
`Average Bioequivalence
`
`Average bioequivalence indicates that two products
`may be considered equivalent if the difference in their
`population average value is relatively small, and con-
`tained within a predefined acceptable range. Under
`current regulatory guidance, the lower and upper lim-
`its (6L and 6U, respectively) of an acceptable range are
`defined as :0.22 in the log scale or from 0.8 to 1.25
`in the original scale. The selection of the lower and
`upper limits for equivalence is somewhat arbitrary,
`and is usually attributed to the general clinical obser-
`vation that for most drugs, a 20% change in dose does
`not significantly change the clinical outcome.
`In average bioequivalence,
`the hypotheses to be
`tested include:
`
`Ho:/1,T — HR 3 6L or #7 —;1.R 2 61
`
`HazéL <(/1.T — MR) < (5U
`
`where M and MR are the population averages of the
`pharmacokinetic measurement (e.g., log AUC or log
`Cmax) for the test and reference products, respectively,
`and 6L and 6H are the prespecified lower and upper
`limits, respectively.
`Average bioequivalence is systematically evalu—
`ated through the following set of procedures. First, a
`non-replicated or replicated bioequivalence study is
`conducted, and intensive blood samples are obtained
`from subjects who received either the test or reference
`product. Next, a non-compartmental analysis is per-
`formed to obtain the pharmacokinetic measurements
`(e.g., AUC or Cmax) and these results are log-trans—
`formed. A linear mixed-effect model is then fitted to the
`
`log AUC (or log Cmax), in which subject and period
`effects are eliminated so that the product (or formu-
`lation) effect, pT — MR, can —be estimated. The stand-
`ard error of the estimated product (or formulation)
`effect is estimated. The 90% confidence interval is
`
`then set by applying the standard error, and compar-
`ing it with the predetermined limits. If the 90% con-
`fidence interval falls within the predetermined upper
`and lower limits (i.e., 6L and (SH) bioequivalence can be
`concluded.
`
`For bioequivalence analyses, the confidence inter-
`val approach is considered more plausible than the
`conventional hypothesis test approach. Conventional
`hypothesis tests (e.g., t test or F test), generally test
`the null hypothesis that M — [LR = 0. Once the null
`hypothesis is rejected under a certain preset alpha
`level (e.g., a = 0.05), the type I error is under con-
`trol, and the probability of falsely declaring ineq-
`uivalence
`is
`also thereby controlled. However,
`controlling instead for the error of falsely declaring
`equivalence would actually be more meaningful in
`tests of bioequivalence. This relates to the power func-
`tion in a conventional hypothesis test. Power functions
`cannot be directly tested. However, a confidence inter-
`val can be linked to the power function that is defined
`as the probability that the confidence interval would
`not include an alternative value. Bioequivalence can
`then be concluded at a risk no greater than 10%, once
`the 90% confidence interval has no common points
`with the equivalence limits or the 90% confidence
`interval falls within the equivalence limits.
`Westlake23 initially suggested that a confidence
`interval approach could be applied in bioequivalence
`studies and, when it was first introduced, he proposed
`using a confidence interval centered on the point of
`exact equivalence (i.e., HT —;1,R = 0). Kirkwood,24 on
`the other hand, suggested using a conventional confi-
`dence interval, which is instead centered on the point
`estimate (0T — [1.12). Thus, with Westlake’s approach,
`equivalence is accepted if the probability of equivalence
`
`ll. BIOI‘H