Full text of DOI:10.1177/00912700022009558

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DRUG DEVELOPMENT
Who Needs Individual Bioequivalence
Studies for Narrow Therapeutic Index Drugs?
A Case for Warfarin
Avraham Yacobi, PhD, Eric Masson, PharmD, Daniel Moros, MD, Derek Ganes, PhD,
Claude Lapointe MSc, Zohreh Abolfathi, PhD, Marc LeBel, PharmD, Yechiel Golander, PhD,
Darlene Doepner, BA, Tamar Blumberg, BSc, Yoram Cohen, PhD, and Barrie Levitt, MD
Warfarin is, among drugs, considered to have a narrow thera-
peutic index for which individual bioequivalence has been
suggested. To establish the propriety of “switching,” an indi-
vidual bioequivalence study involving a replicate-design
study and three “switchings” in healthy subjects was under-
taken using the U.S.-brand warfarin sodium tablet and a
generic product. A randomized, single-center, open-label, single-
dose, four-way crossover replicate bioequivalence study was
performed in 24 healthy male volunteers in which each sub-
ject received the same 5 mg warfarin test and reference tablets
twice on different occasions under fasting conditions. Con-
centrations of warfarin in plasma were measured by a vali-
dated specific HPLC method. The individual pharma-
cokinetic parameters obtained with test and reference prod-
ucts were compared using pooled data and Liu’s method.
Bioequivalence was shown with both average and individual
bioequivalence methods. The individual bioequivalence as-
sessment did not show a subject-by-formulation interaction,
nor did it add value to the bioequivalence assessment of
warfarin.
Journal of Clinical Pharmacology, 2000;40:1-10
©2000 the American College of Clinical Pharmacology
he confidence of physicians, pharmacists, and
does not detect a possible subject-by-formulation (S•F)
interaction, which may be different for different prod-
ucts. Therefore, as part of an effort to ensure approval
of high-quality drug products, the Food and Drug
Administration (FDA) has considered the use of an in-
dividual bioequivalence approach through replicate-
administration design studies in which both the brand
and generic products are given twice on different occa-
sions in a four-way crossover design. It is suggested that
the use of individual bioequivalence method provides
more data and more assurance that brand and generic
products (reference and test products, respectively)
will be interchangeable (i.e., the generic product would
be both prescribable and switchable with the brand).
Many have argued that these additional data are unnec-
essary and that the use of this more complex design is
not required to prove bioequivalence.
T
patients in the safety and efficacy of interchange-
ability between an innovator drug and a generic equiv-
alent is central to the use of generic drugs in clinical
medicine. A standard two-way crossover, single-dose
study design is routinely employed to establish
interchangeability between brand and generic prod-
ucts as well as the bioequivalence of different formula-
tions of the brand. However, the variability of drug
pharmacokinetics among individual patients has led to
questions about this design for bioequivalence studies.
The standard two-way crossover, single-dose design
From Taro Research Institute, Ltd., Israel; Taro Pharmaceuticals USA, Inc.,
Hawthorne, New York; the Department of Neurology, Mount Sinai, School
of Medicine, New York; the Department of Medicine, Albert Einstein Col-
lege of Medicine, Bronx, New York; and Anapharm, Inc., Sainte-Foy and
Faculté de Pharmacie, Université Laval, Sainte-Foy, Q uébec, Canada. Eric
Masson, Marc LeBel, and Barrie Levitt are members of the American Col-
lege of Clinical Pharmacology. Supported by Taro Research Institute, Taro
Pharmaceutical USA, Inc., Hawthorne, New York. Submitted for publica-
tion December 14, 1999; revised version accepted April 17, 2000. Ad-
dress for reprints: Avraham Yacobi, PhD, Taro Research Institute, Taro
Pharmaceutical USA, Inc., 5 Skyline Drive, Hawthorne, NY 10532.
Warfarin is given as the amorphous sodium salt or as
a crystalline sodium clathrate salt; either one meets the
requirements of the USP for warfarin sodium. It readily
dissolves in water. The tablet disintegrates rapidly and
dissolves in aqueous media, including the gastrointes-
tinal fluids, and warfarin is absorbed rapidly and al-
J Clin Pharmacol 2000;40: 826-835
826

YACOBI ET AL
most completely. To test DuPont’s claima for the need
tured: 03-97) in each treatment period identified as T1
and T2.
for an individual bioequivalence test to prove bio-
equivalence, prescribability, and switchability or
interchangeability of a generic warfarin product, a
replicate-design study in normal subjects was con-
ducted, and the results are presented in this paper.
Warfarin is, among drugs, considered to have a
narrow therapeutic index for which individual bio-
equivalence has been suggested. To establish the pro-
priety of “switching,” an individual bioequivalence
study involving a replicate-design study and three
“switchings” in healthy subjects was undertaken using
the U.S.-brand warfarin sodium tablet and a generic
product.
Reference formulations (R1 and R2). Each subject re-
ceived one tablet of 5 mg Coumadin® tablet, USP
(DuPont Pharma, USA, Lot No. ELB048A, expiration
date 01-00) in each treatment period identified as R1
and R2.
The volunteers were kept in the clinical facilities
from the night before the dosing to 36 hours after dos-
ing in each period. The subjects returned to the clinic
for six additional blood draws at 48, 72, 96, 120, 144,
and 168 hours postdose. No other drugs, tobacco, or
alcohol were permitted throughout the study. Compli-
ancewasassessedthroughaquestionnaireateachvisit.
No water was permitted 2 hours before and after dos-
ing. The drug was administered with 240 mL water af-
ter an overnight fast of 10 hours. Four hours after dos-
ing, a standard lunch was served. Blood samples (1 × 7
mL) were collected in evacuated tubes that contained
ethylenediamine tetra-acetic before each dose (0 hours)
and at 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 6, 8, 12, 16, 24,
36, 48, 72, 96, 120, 144, and 168 hours after dosing. The
total volume of blood collected from each subject was
666 mL. The blood samples were kept on ice before be-
ing centrifuged and then stored at –80°C before analy-
sis. Of the 24 subjects initially enrolled, 23 completed
the study. One subject dropped out of the study after
the first period for personal reasons.
MATERIALS AND METHODS
A single-center, single-dose, replicate-design, random-
ized, open-label, fasting, four-way crossover bio- equiv-
alence study in healthy male volunteers was con-
ducted at Anapharm, Inc. (Sainte-Foy, Québec).
Protocol and informed consent both in French and
English were approved by an independent institu-
tional review board prior to starting the study.
Healthy, nonsmoking, Caucasian male subjects ages
18 to 45 years and within ± 15% of ideal body weight
were included in the study. Each subject had a com-
plete physical exam, including laboratory tests (bio-
chemistry, hematology, HIV, hepatitis B and C, urinaly-
sis), within 28 days prior to dosing. Possible subjects
were excluded if they had the following conditions:
clinically significant medical disorders or impair-
ments, surgery within 4 weeks prior to dosing, con-
sumption of drugs affecting warfarin pharmacokinetics
within 30 days or any other prescription drugs within
14 days, deficiency in protein C or S, and active
bleeding.
Bioanalytical. Concentrations of warfarin were de-
termined by a validated HPLC method with reversed-
phase Hypersil-C18 column (150 × 4.6 mm, i.d.,
Phenomenex Luna) and fluorescence detection. Sepa-
ration of warfarin was achieved with a mobile phase
consisting of methanol/acetonitrile/type 1 grade wa-
ter/triethylamine (63.5/1/35.1/0.4) at a flow rate of 0.9
mL/min. Plasma samples were spiked with an internal
standard, extracted with hexane/methylene chloride
(5/1), and injected into a liquid chromatograph
(Shimadzu system) equipped with a fluorescence de-
tector (excitation and emission wavelengths of 305 and
380 nm, respectively). The lower limit of quantitation
was 20 ng/mL. Calibration curve for warfarin ranged
from 20 to 1500 ng/mL, with a determination coeffi-
cient (r2) greater than 0.996. Quality control (QC) sam-
ples (low, mid, high range) were prepared and stored
with study samples at –80°C. Accuracy of QC stan-
dards ranged from 96.2% to 102.59%. Precision (CV%)
was 2.78% to 7.8%.
After obtaining their consent in writing, each subject
was randomized to one of the following two sequences
used in this four-way crossover study:
Sequence 1: T1, R1, T2, R2
Sequence 2: R1, T1, R2, T2
Test formulations (T1 and T2). Each subject received
one tablet of 5 mg warfarin sodium clathrate (Taro Phar-
maceutical Industries, Ltd., Lot No. 780049, manufac-
a. DuPont Merck letter (Richard S. Levy, MD, Vice President,
Worldwide Regulatory Affairs) to the Food and Drug Administration
(Janet Woodcock, MD, Director, and Roger S. Williams, MD, Deputy
Director for Pharmaceutical Science, Center for Drug Evaluation and
Research), June 18, 1997.
Pharmacokinetic and statistical analysis. The fol-
lowing pharmacokinetic parameters were calculated
for each subject who completed the study (n = 23) and
827
J Clin Pharmacol 2000;40: 826-835
·

A CASE FOR WARFARIN
formulation (2 mg and 10 mg Coumadin® tablets,
for each treatment using standard noncompartmental
methods: AUC0-t, AUC0-inf, Cmax, tmax, Kel, and t1/2. Using
the general linear models procedure (SAS Institute,
Cary, NC), ANOVA was performed on tmax, Kel, and t1/2
and on ln-transformed AUC0-t, AUC0-inf, and Cmax at the
alpha level of 0.05. Fixed effects considered in ANOVA
included sequence, subject within sequence, period,
and treatment. Intra- and intersubject coefficients of
variation (CV%) were estimated from the ANOVA. Ra-
tio of means test/reference (T/R) and 90% geometric
confidence interval for the ratio of means, based on the
least squares means from the ANOVA of the ln-
DuPont Pharma, USA, Lot Nos. ELD242A, expiration
date 02/00, and ELB085B, expiration date 01/00,
respectively).
These two studies used the standard two-way cross-
over bioequivalence study design. The sampling times
were similar to the times used for the current repli-
cate-design study, with up to 20 blood samples taken
for measuring plasma concentrations of warfarin. The
plasma samples were analyzed by a validated and spe-
cific HLPC method. ANOVA statistical analysis was
performedtocomparethetestandreferenceproducts.
Table I summarizes the pharmacokinetic parameters
of warfarin in normal subjects who received a single
dose of 2 and 10 mg warfarin in two different bioequi-
valence studies. These data showed bioequivalence be-
tween the brand and generic products and reproduc-
ible pharmacokinetic parameters with remarkably low
intersubject variabilities, which is characteristic of
warfarin in normal subjects. There was no statistically
significant difference between the pharmacokinetic pa-
rameters for the brand and generic products, with a rel-
atively narrow 90% confidence interval (CI).
Table II summarizes the pharmacokinetic parame-
ters of warfarin in 23 fasted volunteers after a single 5
mg dose of warfarin sodium. Each subject received the
test or reference product on two different occasions in a
four-way replicate-design study. The results compare
the average pharmacokinetic values obtained for the
two doses of test and reference products by either
pooled data or Liu’s method.1 Figure 1 depicts the
mean warfarin plasma concentrations over two admin-
istrations of the test and reference formulations’ aver-
age, whereas Figure 2 depicts mean warfarin plasma
concentrations for both the test (Figure 2a) and refer-
ence (Figure 2b) formulations, respectively. The
ANOVA results show bioequivalence by the standard
average analyses test in a similar fashion to that con-
ducted by a two-way crossover design study. Average
bioequivalence was also determined using data from
all four periods, using Liu’s method for a repli-
cate-design study (Table II). Again, bioequivalence was
demonstrated with a similar confidence interval for
both AUC and Cmax, similar to those seen by the earlier
standard two-way bioequivalence studies conducted
for the 2 and 10 mg tablets (Table I).
transformed data, were calculated for AUC0-t, AUC0-inf
,
and Cmax. The replicate study design made it possi-
ble to determine both average and individual
bioequivalence.
Average bioequivalence analysis was conducted us-
ing two methods: (1) pooled analysis using the plasma
concentrations, averaged over two administrations of
both the test and reference administrations, and (2)
comparison of two administrations of test (T1, T2) and
reference formulations (R1, R2) over four periods ac-
cording to the method described by Liu.1 Fixed effects
in the ANOVA, for this method, included sequence,
subject (sequence), period, treatment, and subject-by-
formulation (S•F) interaction.
Statistical analysis using individual bioequivalence
methods was conducted as described in two Food and
Drug Administration (FDA) draft guidances:2,3 (1) re-
stricted maximum likelihood (REML) method using
PROC MIXED and confidence intervals estimated by
bootstrap and (2) method of moments (see appendix).
Both methods were conducted on ln-transformed
AUC0-t, AUC0-inf, and Cmax. These two methods are based
on one-sided test aggregate criteria. As such, the 95%
upper bound is used to establish whether bioequiva-
lence is met. For each method, the analysis was con-
ducted using both constant and reference scaling.
Regression analyses were performed between for-
mulations and within formulations for Cmax, AUC0-inf
,
and plasma concentrations.
RESULTS
In unpublished single-dose studies in fasted normal
subjects, it was shown that by using the classical
two-way crossover bioequivalence study design, the
generic formulation of 2 and 10 mg warfarin sodium
tablets (Taro Pharmaceutical Industries, Ltd., Lot Nos.
Taro 780100, manufactured 09/97 [2 mg strength] and
780060 manufactured 04/97 [10 mg strength], respec-
tively) was bioequivalent to the respective U.S.-brand
Individual bioequivalence was calculated using the
two methods proposed in the FDA draft guidance.2,3 Ta-
ble III shows parameter estimates calculated using the
REML method. The confidence interval for Cmax and
AUC was similar to those calculated by average
bioequivalence methods. Again, bioequivalence is
clearly demonstrated with no meaningful subject-by-
DRUG DEVELO PMENT
828

YACOBI ET AL
Table I Summary of Pharmacokinetic Parameters of Warfarin in Fasted Volunteers Investigated in
Two Separate Studies after Single 2 mg and 10 mg Tablets and Results of Statistical Analyses
Mean Values (CV%)
Parametersa
Test Product
Reference Product
Ratio
90% CI
Study 1, 2 mg (n = 35)
AUC0-∞ (µg•h/ml)
Cmax (µg/ml)
tmax (h)
18.7 (23)
0.456 (16)
0.81 (60)
68.0 (18)
18.8 (23)
0.481 (17)
0.30 (72)
66.7 (15)
1
97-102
91-99
0.95
1.01
1.02
t1/2 (h)
Study 2, 10 mg (n = 34)
AUC0-∞ (µg•h/ml)
Cmax (µg/ml)
tmax (h)
44.5 (24)
1.05 (17)
1.22 (69)
45.4 (24)
45.2 (23)
1.12 (19)
1.08 (60)
47.8 (20)
0.98
0.94
1.13
0.95
96-101
89-99
t1/2 (h)
a. Determined from the ANOVA model that included treatment, period, sequence, group, group treatment, period (group), sequence group, and subject (se-
quence group) as fixed effects or interaction terms.
Table II Summary of Average Pharmacokinetic Parameters of Warfarin in 23 Fasted
Volunteers after a Single 5 mg dose and the Results of Statistical Analyses
Mean Values (CV%)
Parametersa
Test Product (T)
Reference Product (R)
Ratio T/R
90% CI
Pooled data (N = 23)
AUC0-∞ (µg•h/ml)
Cmax (µg/ml)
tmax (h)
27.0
0.585 (19)
0.99 (81)
(22)
26.3
0.607 (19)
0.67 (36)
(20)
1.03
0.962
1.48
1.04
100-107
92-101
t1/2 (h)
66.4
(18)
64.0
(17)
Liu’s method (N = 46)
AUC0-∞ (µg•h/ml)
Cmax (µg/ml)
tmax (h)
27.0
0.606 (20)
(22)
26.3
0.625 (20)
(22)
1.03
0.970
—
100-106
93-101
—
—
—
—
t1/2 (h)
—
—
Each subject received T and R each at two different occasions in a four-way replicate-design study, and the results are shown for (1) comparison of average T and
1
2
1
T to average R and R (pooled data) and (2) comparison of all plasma concentrations by Liu’s method (N= 46), which compares T and T versus R and R ad-
2
1
2
1
2
1
ministrations. Results are determined from the ANOVA model that included sequence, subject (sequence), period, and treatment as terms for the pooled data.
UsingLiu’smethod, ANOVAwascalculatedusingfixedeffects:sequence, subject(sequence), period, treatment, andsubject-by-formulation(S•F) interaction.
formulation (S•F) interaction and remarkably limited
intrasubject variability compared to intersubject vari-
ability. Overall, these data indicate bioequivalence be-
tween two different warfarin sodium tablet products,
and intrasubject variability is limited when the same
lot of the same product is administered to the same sub-
jects on two separate occasions.
Table IV summarizes the statistical criteria for esti-
mating individual bioequivalence criteria using REML
and the method of moments using both constant and
scaled criteria. Using constant scaling, bioequivalence
was demonstrated with both methods. However, when
scaled to reference, bioequivalence was demonstrated
for Cmax but not AUC, despite similar ratios. There was
comparable intrasubject variability, but there were no
subject-by-formulation interactions.
Figure 3 depicts the scatter plots of plasma concen-
tration (a total of 483 points) of warfarin after two ad-
ministrations of the test product (Figure 3a) and refer-
ence product (Figure 3b). The data show excellent
correlation between the two administrations of either
the test or the reference products, with relatively little
829
·J Clin Pharmacol 2000;40: 826-835

A CASE FOR WARFARIN
Figure 1. Mean plasma con-
centrations of warfarin, aver-
aged over two administrations of
test and reference products, in
23 subjects.
Figure 2. Mean plasma con-
centrations of warfarin after two
administrations of test product
(a; top) and two administrations
of reference product (b; bottom)
in 23 subjects.
DRUG DEVELO PMENT
830

YACOBI ET AL
Table III Summary of Estimated Pharmacokinetic Parameters Using Restricted Maximum Likelihood Method
Intrasubject CV (%) (σw
)
Intersubject CV (%) (σB )
Parameters
Ratio Test/Reference S• F Interaction (σ D
)
Reference
Test
Reference
Test
90% CIa
AUC0-t
AUC0-∞
Cmax
1.03
1.03
0.97
0.059
0.062
0.014
6.7
7.3
13.7
5.5
7.5
11.1
18.4
19.9
15.4
18.8
20.3
16.9
100-106
100-106
93-100
Fixed effects included in the model: treatment, period, sequence, and period-by-sequence interaction.
a. The 90% confidence intervals are estimated from 2000 bootstrap samples.
Table IV Summary of Estimates for Individual Bioequivalence Statistics for the Restricted Maximum
Likelihood Method (REML) and the Method of Moments
95% Upper Bounds Confidence Limit for θ
Reference Scaled (σw2 = WR)
Constant Scaled (σw2 = 0.04)a
Parameters
REMLb
Momentb
REMLb
Momentb
AUC0-t
AUC0-∞
Cmax
3.03
3.34
0.478
0.00108
0.00394
–0.0346
0.280
0.351
0.138
–0.0896
–0.0850
–0.0966
a. Corresponds to an intrasubject CV of 20%.
b. Confidence limit obtained from 2000 bootstrap samples. For the REML method, bioequivalence is confirmed if the upper bound for θs is less than 2.495
2,3
(when ∈ = 0.05). For the procedure using method of moments, bioequivalence is confirmed if the upper bound for θ is a negative number.
I
scatter of the plasma concentrations around the unity
line. Figures 4 and 5 provide the comparison of indi-
vidual values of AUC and Cmax, respectively, between
test and reference products. In each case, there is a re-
markable reproducibility of pharmacokinetic parame-
ters of warfarin when the test and reference products,
or either the replicate administrations of the test prod-
uct and the reference product, are individually
compared.
during the absorption process(es). The latter assumes
that the absorption of a drug moiety in a subject may be
influenced by excipients and other nonactive ingredi-
ents in the product. As such, modified-release drug
products and those that demonstrate high intrasubject
variability in absorption of the drug moiety may poten-
tially benefit from individual bioequivalence testing.
In the past few years, there have been advocates for
testing the bioequivalence of pharmaceutical products
containing so-called narrow therapeutic index drugs,
such as warfarin, phenytoin, and carbamazepine. The
narrow therapeutic ratio is defined in the U.S. Code of
Federal Regulation at 21 CFR 320.33 (c)9 and has been
described previously.10 Although a draft guidance for
individual bioequivalence studies for all drugs has
been circulated, the FDA has not yet shown any indica-
tion of requiring separate bioequivalence criteria for
the so-called narrow therapeutic index drugsb in gen-
DISCUSSION
Individual bioequivalence study design to determine
bioequivalence between two products was initially
proposed by Anderson and Hauck,4,5 which is based on
a theoretical problem. The study design consists of rep-
licate administration of test and reference products in a
crossover study design fashion, and positive results
would assume switchability as well as prescribabil-
ity.5-8 This approach offers the opportunity to deter-
mine intrasubject variability in absorption of a drug
from a pharmaceutical product and determine the pos-
sibility of a subject-by-formulation (S•F) interaction
b. Food and Drug Administration letter (Roger L. Williams, MD,
Deputy Director for Pharmaceutical Science, Center for Drug Evalua-
tion and Research) to the National Association Boards of Pharmacy
(CarmenA. Catizone, ExecutiveDirector/Secretary), April16, 1997.
831
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·

A CASE FOR WARFARIN
Figure 3. Scatter plot of plasma
concentrations of warfarin after
two administrations of test prod-
uct (a; top) and reference product
(b; bottom). The line of identity
represents an intercept of zero and
a slope of unity.
eral or for warfarin in particular.c It has been suggested
that the pharmaceutical industry should conduct repli-
cate-design studies and evaluate them with average
population and individual bioequivalence methods for
2 years to provide reliable and conclusive scientific
data on the most appropriate designs and analysis
methods.
The replicate-design study has been used to deter-
mine intrasubject variability of two digoxin capsule
products (reference vs. test) in normal volunteers.11
Interestingly, despite its potential, it was not proposed
or used to determine bioequivalence between these
two products. Recently, a randomized, single-dose,
c. Food and Drug Administration letter (Janet Woodcock, MD,
Director for Center for Drug Evaluation and Research) to DuPont
Merck denying a petition to establish individual bioequivalence test-
ing for narrow therapeutic index drugs. March 25, 1997.
DRUG DEVELO PMENT
832

YACOBI ET AL
Figure 4. Comparison of individ-
ual values of AUC0-inf between test
and reference products.
Figure 5. Comparison of individ-
ual values of Cmax between test and
reference products.
four-way crossover, replicate-design bioequivalence
study was conducted to compare two phenytoin sus-
pension products (reference vs. test) in 26 healthy sub-
jects.12 Also, in this study, it was shown that bio-
equivalence can be demonstrated by either the individ-
ual bioequivalence test or by the standard average
bioequivalence test, concluding that there is no need
for an individual bioequivalence design study to test
phenytoin suspension formulations.
The results of this study clearly indicate that bio-
equivalence was shown by either the standard average
bioequivalence method or an individual bioequi-
valence method. The power of the study was equally
strong, and the confidence interval characterizing bio-
equivalence was equally narrow for the two statistical
tests.
The uncomplicated absorption profile of warfarin
showed little variability within subject and between
subjects. Bioequivalence was well demonstrated and
consistent regardless of the method, except for the indi-
vidual bioequivalence test scaled to reference. In fact,
overall, the results for AUC and Cmax demonstrated sim-
ilar mean test/reference ratios around 100%, similar
intrasubject CV for reference and test formulations,
and no significant subject-by-formulation (S•F) inter-
action. However, individual bioequivalence criteria
failed for AUC when scaled to reference but not for
Cmax. This was caused by the lower intrasubject vari-
ance for AUC compared to Cmax. Scaled criteria depend
on the variability that affects the denominator (equa-
tion (1) in the appendix). The criteria for drugs with
low variability, therefore, may be inflated and may
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·

A CASE FOR WARFARIN
even penalize formulations with lower variability. This
bound for θ is built using the nonparametric percentile
bootstrap confidence interval. Use of 2000 bootstrap
samples that preserve the number of subjects per se-
quence is recommended.
Another method described in the FDA guidance
uses method of moments to estimate means and vari-
ances of the individual bioequivalence criteria. Previ-
ously defined criteria (equations (1) and (2)) are
linearized in the following way.
case illustrates that scaling should only be used for
highly variable drugs but not for drugs with low vari-
ability such as warfarin, even if the drug is considered
to have a narrow therapeutic index.
The FDA’s proposed draft guidance2,3 will need
more research and more actual data before any possible
implementation. The results of this investigation
clearly show that the replicate-design study may not
apply across-the-board for all pharmaceutical prod-
ucts. Potentially, the primary beneficiary of such a
method may be the highly variable drugs for which ab-
sorption intrasubject variability of 30% or greater is
seen, and a large number of subjects are needed to
prove bioequivalence by the standard two-way cross-
over study. Also, controlled-release products, which by
design may show S•F interaction, may be suitable for
testing by replicate-design individual bioequivalence
studies, although actual data would be needed to con-
firm this approach.
Reference scaled:
η =(µT −µR )2 + σD2 + (σW2 T − σW2 R )−θI ⋅ σ2WR < 0
(3)
1
for σWR > σW 0
.
Constant scaled:
η2 =(µT −µR )2 + σD2 + (σW2 T − σW2 R )−θI ⋅ σ2WR <0
for σWR ≤ σW 0
(4)
.
Estimates of components of the linearized criteria de-
pend on the designs. We will assume a four-period de-
sign with equal replication of T and R in each of the se-
quences with an assumption of no (or equal) carryover
effect. Then, estimates of the linearized criteria are the
following:
APPENDIX
Methods Used for Individual
Bioequivalence Assessment
2
$
$
$
η =(µT −µR ) + MI + 0.5⋅ MT −(1.5 + θI )⋅ MR
The aggregate criteria for individual bioequivalence as-
sessment are the following.
1
for MR > σW 0
,
Reference scaled:
2
2
$
$
$
η2 =(µT −µR ) + MI + 0.5⋅ MT −1.5⋅ MR −θI ⋅ σW 0
for MR ≤ σW 0
(µT −µR )2 + σD2 + (σ2WT − σW2 R
)
)
.
(1)
(2)
θ =
≤θI for σWR > σW 0
.
σ2WR
MI, MT, and MR denote the variance estimates of Iij, Tij,
and Rij, respectively, pooling across sequences. Iij is the
difference between means over two administrations of
the test and the reference products for subject j within
sequence i. Tij is the difference between the two admin-
istrations of the test product for subject j within se-
quence i. Rij is the difference between the two adminis-
trations of the reference product for subject j within
sequence i.
These later statistics could be either positive (does
not conclude individual bioequivalence) or negative
(concludes individual bioequivalence). To test for indi-
vidual bioequivalence, the 95% upper confidence
bound of either reference-scaled or constant-scaled
linearized criterion should be computed. If the upper
bound were positive, we would not conclude individ-
ual bioequivalence; otherwise, we would conclude in-
dividual bioequivalence. The following table demon-
strates the computation for the upper confidence
bound for η1:
Constant scaled:
(µT −µR )2 + σD2 + (σ2WT − σW2 R
θ =
≤θI for σWR ≤ σW 0
,
σ2W 0
where µT = population average response of the test
formulation (ln-transformed data), µR = population
average response of the reference formulation (ln-
transformed data), σ2D = subject-by-formulation inter-
action variance component,σ2WT = within-subject vari-
ance of the test formulation,σ2WR = within-subject vari-
ance of the reference formulation, σ2W 0 = specified
constant within-subject variance (FDA’s draft guidance
recommends a value of 0.04),θI = BE limit (FDA’s draft
guidance recommends a value of 2.495).
The restricted maximum likelihood method (REML)
method uses the SAS procedure PROC MIXED to ob-
tain REML estimates of variance components and gen-
eralized least squares estimates of fixed effects in a
mixed-effects linear model. Also, 95% confidence
DRUG DEVELO PMENT
834

YACOBI ET AL
Hq =
Eq =
Point Estimate
Uq =
3. Guidance for the Industry: Average, Population, and Individual
Approaches to Establishing Bioequivalence. Washington, DC: U.S.
Department of Health and Human Services, FDA, CDER, 1999.
Confidence Limit
(Hq – Eq)2
HD
=
4. Anderson S, Hauck WW: Consideration of individual bioequiva-
lence. J Pharmacokinet Biopharm 1990;18:259-273.
2
2
$



ED = ∆
UD
s


1
∆ + t1 − α , n −s
⋅
ni−1 ⋅MI
$






5. Hauck WW, Anderson S: Measuring switchability and pre-
scribability: when is average bioequivalence sufficient? J Pharma-
cokinet Biopharm 1994;22:551-564.
∑
s2




i = 1
(n − s)⋅ MI
HI =
EI = MI
UI
χ2α , n − s
6. Schall R, Williams R: Towards a practical strategy for assessing
individual bioequivalence. J Pharmacokinet Biopharm 1996;24:
133-149.
0.5⋅(n − s)⋅ MT
HT
HR
=
ET = 0.5 • MT
UT
χ2α , n − s
7. Vuorinen J, Turunen J: A Simple three-step procedure for paramet-
ric and non-parametric assessment of bioequivalence. Drug Inf J
1997;31:167-180.
−(1.5+ θI )⋅(n − s)⋅ MR
=
ER = –(1.5 + θI) • MR UR
χ12 − α , n − s
8. Chen L: Individual bioequivalence: a regulatory update. J Phar-
macokinet Biopharm 1997;7:5-11.
s
$
$
$
where n =
ni and ∆ = µ T − µ R . The upper confi-
∑
9. Criteria and evidence to assess actual or potential bioequivalence
problems, in: U.S. Code of Federal Regulations. 21 CFR 320.33 (C)
1977;206-207.
i = 1
dence bound is Hη
=
Eq
+
Uq .
∑
∑
1
10. Yacobi A, Zlotnick S, Colaizzi JL, Moros D, Masson E, Abolfathi Z,
LeBel M, Mehta R, Golander Y, Levitt B: A multiple-dose safety and
bioequivalence study of a narrow therapeutic index drug: a case for
carbamazepine. Clin Pharmacol Ther 1999;65:389-394.
The confidence limit for η2 is computed similarly,
adjusting the constants where appropriate.
11. Yacobi A, Stoll RG, Chao GC, Schwartz RA, Weidler DJ, Ayers JW,
Sakmar E, Hallmark M, Wagner JG: The assessment of the intra-
subject variability in digoxin absorption in man from two oral dosage
forms. J Clin Pharmacol 1981;21:301-310.
REFERENCES
1. Liu JP: Use of the repeated cross-over designs in assessing
bioequivalence. Statistics in Medicine 1995;14;1067-1078.
12. Schumaker RC, Metzler CM: The phenytoin trial is a case study of
individual bioequivalence. Drug Information J 1998;32:1063-1072.
2. Guidance for the Industry: In Vivo Bioequivalence Studies Based
on Population and Individual Bioequivalence Approaches. Wash-
ington, DC: U.S. Department of Health and Human Services, FDA,
CDER, 1997.
835
J Clin Pharmacol 2000;40: 826-835
·