Transcript Statistical Methods for Assessment of Individual/Population Bioequivalence Shein-Chung Chow, Ph.D. Biostatistics and Clinical Data Management Millennium Pharmaceuticals, Inc. Cambridge, MA 02139 Presented at ASA Boston Chapter December 2, 2003

Statistical Methods for
Assessment of
Individual/Population
Bioequivalence
Shein-Chung Chow, Ph.D.
Biostatistics and Clinical Data Management
Millennium Pharmaceuticals, Inc.
Cambridge, MA 02139
Presented at ASA Boston Chapter
December 2, 2003
Outline
 Background
– What and Why?
– History
 Conduct of Bioequivalence Trials
 Drug Interchangeability
– Population Bioequivalence
– Individual Bioequivalence
 Recent Development
 Summary
What and Why?
 What?
– Bioavailability is defined as the rate and extent to
which the active drug ingredient is absorbed and
becomes available at the site of drug action
– Two drug products are said to be bioequivalent if they
are pharmaceutical equivalent or pharmaceutical
alternatives, and if their rates and extents of absorption
do not show a significant difference.
What and Why?
 New Drugs
– Drug discovery, formulation, laboratory development,
animal studies, clinical development, etc.
– IND, NDA, IRB, Advisory Committee
– The process is lengthy & costly
 Generic Drugs
– ANDA
– The US FDA was authorized to approve generic drugs via
the evaluation of bioequivalence trials in 1984
What and Why?
Fundamental Bioequivalence
Assumption
When a generic drug is claimed bioequivalent to
a brand-name drug, it is assumed that they are
therapeutically equivalent.
History
 1938-1962
– Generic copies of approved drug products could be
approved by an ANDA which includes the information
of formulation, manufacturing and quality control
procedures, and labeling.
 1975
– Regulations were established.
 1977
– Regulations were finalized and became effective
(21 CFR 320).
History
 1977-1980
– Several decision rules were proposed: 75/75, 80/120,
and 20% rules
 1984
– The Drug Price Competition and Patent Term
Restoration Act
 1986
– FDA Hearing on bioequivalence issues of solid dosage
form
History
 1992
– FDA issued a guidance on statistical procedure
– Chow and Liu published the first BA/BE book
– FDA Core Committee raised the issue of switchability
 1993
– Generic Drug Advisory Committee Meeting discussed
individual bioequivalence
 1994
– DIA BA/BE Symposium held in Rockville, Maryland
History
 1995
– Generic Drug Advisory Committee Meeting
– International Workshop (Canada, US, and Germany)
held in Germany
– SUPAC-IR
 1996
– FDA Individual BE Working Group/PhRMA/Generic
Trade Association
– FIP BioInternational’96, Tokyo, Japan
History
 1997
– DIA Hilton Head Meeting
– Draft guidance on PBE/IBE circulated for comments
 1998
– AAPS annual meeting
 1999
– Revised draft guidance on PBE/IBE issued
– FDA guidance on in vitro bioequivalence testing
– Chow & Liu’s BA/BE book revision
History
 2000
– AAPS annual meeting
– FDA guidance on Bioavailability and Bioequivalence Studies for
Orally Administered Drug Products - General Considerations
(October, 2000)
– FDA guidance on Statistical Approaches to Establishing
Bioequivalence (January, 2001)
 2001
– FDA guidance on Statistical Approaches to Establishing
Bioequivalence (January, 2001)
 2002
– FDA draft guidance on Bioavailability and Bioequivalence Studies
for Orally Administered Drug Products – General Considerations
(July, 2002)
Current Regulations
 Most regulatory agencies including the U.S. Food
and Drug Administration (FDA) require evidence
of bioequivalence in average bioavailabilities
between drug products.
– This type of bioequivalence is referred to as ABE.
 Based on the 2001 FDA guidance, bioequivalence
may be established via population and individual
bioequivalence provided that the observed ratio of
geometric means is within the bioequivalence
limits of 80% and 125%.
Current Regulation - ABE
 Bioequivalence is concluded if the average
bioavailability of test product is within 20% of
that of the reference product with 90% assurance
(raw data), or
 Bioequivalence is claimed if the ratio of average
bioavailabilities between test and reference
products is within (80%, 125%) with 90%
assurance (log-transformed data).
Standard Two-sequence, Two period Crossover Design
PERIOD
Subjects
R
A
N
D
O
M
I
Z
A
T
I
O
N
II
I
Sequence 1
Reference
Sequence 2
Test
W
A
S
H
O
U
T
Test
Reference
Conduct of Bioequivalence Trials
 Number of Subjects - ABE
– Pivotal fasting studies: 24-36 subjects
– Limited food studies: minimum of 12 subjects
– Liu, J.P. and Chow, S.C. (1992). J. Pharmacokin. Biopharm.,
20, 101-104.
Difference in Means
Power
80%
CV
20
22
24
26
28
30
0%
20
24
28
32
36
40
5%
24
28
34
40
46
52
10%
52
62
74
86
100
114
15%
200
242
288
336
390
448
Conduct of Bioequivalence Trials
 Washout
– 5.5 half-lives for IR products
– 8.5 half-lives for CR products
 Blood Sampling
– More sampling around Cmax
– Sampling at least three half-lives
Statistical Methods - ABE
 Confidence Interval
–
–
–
–
The classical (shortest) confidence interval
Westlake’s symmetric
Fieller’s theorem
Chow and Shao’s confidence region
 Interval Hypotheses Testing
– Shuirmann’s two one-sided tests procedure
Current Regulations - ABE
 A generic drug can be used as a substitute for the
brand-name drug if it has been shown to be
bioequivalent to the brand-name drug.
 Current regulations do not indicate that two
generic copies of the same brand-name drug can
be used interchangeably, even though they are
bioequivalent to the same brand-name drug.
 Bioequivalence between generic copies of a
brand-name drug is not required.
Safety Concern
Generic
#1
Generic
#K
?
Generic
#5
Generic
#2
Brand-name
Generic
#4
Generic
#3
Safety Concern
Generic Drugs
They’re cheaper, but do they work as well?
Safety Concern
 Generic and brand-name drugs do exactly the same thing
and are completely interchangeable.
- D. McLean
Deputy Associate Commissioner for Public Affairs
U.S. Food and Drug Administration
 I would hesitate to substitute a generic for a brand-name
drug for those patients who have been on the drug for
years. However, I would not hesitate to suggest a doctor
start a new patient on the generic version.
- A. Di Cello
Executive Director
Pennsylvania Pharmacists Association
Drug Interchangeability
 Drug Prescribability
– Brand-name vs. its generic copies
– Generic copies vs. generic copies
 Drug Switchability
– Brand-name vs. its generic copies
– Generic copies vs. generic copies
 Current regulation for ABE does not guarantee
drug prescribability and drug switchability
Limitations of ABE





Focuses only on population average
Ignores distribution of the metric
Ignores subject-by-formulation interaction
Does not address the right question
Comments
– One size fits all BE criteria
– Clinical evidence
– Post-approval process validation/control
Drug Prescribability
 The physician’s choice for prescribing an appropriate drug
for his/her patients between the brand-name drug and its
generic copies
 Population Bioequivalence (PBE)
– Anderson and Hauck (1990)
– Chow and Liu (1992)
 Post-approval meta-analysis for BE review
– Chow and Liu (1997)
– Chow and Shao (1999)
Drug Switchability
 The switch from a drug (e.g., a brand-name drug or its
generic copies) to another (e.g., a generic copy) within the
same patient whose concentration of the drug has been
titrated to a steady, efficacious and safe level
 Individual Bioequivalence (IBE)
–
–
–
–
Anderson and Hauck (1990)
Schall and Luus (1993)
Holder and Hsuan (1993)
Esinhart and Chinchilli (1994)
 Post-approval meta-analysis for BE review
– Chow and Liu (1997)
– Chow and Shao (1999)
Type of Bioequivalence
 Average Bioequivalence (ABE)
– Current regulatory requirement
 Population Bioequivalence (PBE)
– Prescribability
 Individual Bioequivalence (IBE)
– Switchability
Ideal IBE/PBE Criteria
Chen, M.L. (1997). Individual Bioequivalence - A
Regulatory Update. Journal of Biopharmaceutical
Statistics, 7, 5-11.
 Should take into consideration for both average
and variance
 Should be able to assume switchability
 Should encourage or reward formulations that reduce
within subject variability
 Should have a statistically valid method that controls
consumer’s risk at the level of 5%
Ideal IBE/PBE Criteria
 Should be able to estimate appropriate sample size for the
study in order to meet the criteria
 The software application for the statistical method should
be user-friendly
 Should provide interpretability for scientists
and clinicians
 Statistical methods should permit the possibility of
sequence and period effect, as well as missing data.
IBE/PBE Criteria
 Notations
mT = mean of the test product
mR = mean of the reference product
sWT2 = within-subject variability for the test product
sWR2 = within-subject variability for the reference product
sD2 = variability due to the subject-by-formulation interaction
FDA’s Recommendation





Aggregate criterion
Moment-based approach
Scaling method
Weighing factors
One-sided test
IBE Criterion
(mT  mR )  s  (s  s )
 I
2
max(s , s W 0 )
2
Where
I 
2
D
2
WR
2
WT
(ln1.25)  
2
s
2
W0
2
WR
Comments on IBE Criterion
 It is a non-linear function of means and variance
components
 The selection of weights lack of scientific and
statistical justification
 The determination of bioequivalence limit is
subjective
 IBE criteria may lead to a negative value (overcorrected)
Comments on IBE Criterion
 Aggregate criteria cannot isolate the effects due to
average intrasubject variability and variability due
to the subject-by-formulation interaction
 Masking effect for distributions of individual
components
 Offsetting effect
– Bias versus intrasubject variability
 Two-stage test procedure
Offsetting Effect




One actual data set from the US FDA
Four-sequence, four-period crossover design
N=22 subjects
Average Bioequivalence
– The ratio of average AUC is 1.144 with a C.I. of (1.025, 1.280)
 Individual Bioequivalence
– The upper bound of the 90% confidence interval based on
2000 bootstrap samples is 1.312, which is less than IBE limit.
– The ratio of intrasubject standard deviation between the test
and reference formulation is 0.52.
Offsetting Effect
 The 14% increase in the average is offset by a
48% reduction in the variability
 We may conclude IBE even though the
distributions of PK responses are totally different.
Study Design for IBE
 The IBE criteria recommended by the FDA involves
the estimation of sWR2, sWT2, and sD2.
 The standard 2 x 2 crossover design is not appropriate.
 FDA recommends a replicated design be used
TRTR
RTRT
(recommended)
TRT
RTR
(possible alternative)
General Approaches for IBE/PBE
Let yT be the PK response from the test formulation,
yR and yR' be two identically distributed PK responses
from the reference formulation, and
 E ( yR  yT ) 2  E ( yR  yR' ) 2

' 2
E
(
y

y

R
R) / 2
 
2
' 2
 E ( yR  yT )  E ( yR  yR )
2

s
0

where s 02 is a given constant.
if E( yR  yR' )2 / 2  s 02
' 2
2
E
(
y

y
)
/
2

s
if
R
R
0
General Approaches for IBE/PBE
 If yT , yR , and yR' are independent observations from
different subjects, then the two formulations are
population bioequivalence when
   PBE .
'
y
y
y
 If T , R , and R are from the same subject, then the
two formulations are individual bioequivalence when
   IBE
.
General Approaches for IBE/PBE
  is a measure of the relative difference between the
mean squared errors of yR- yT and yR - yR'
 E( yR  yR' )2 2 is the within-subject variance of the
reference formulation


2
2
( mT  m R ) 2  s TT
 s TR
 
2
for PBE
max{s 02 , s TR
}
2
2
( mT  mR )2  s D2  (s WT
 s WR
)
for IBE
 
2
2
max{s 0 , s WR }
Assessment of IBE
 Hypotheses Testing
H0 :    IBE versus H0 :    IBE
 IBE is claimed if a 95% confidence upper bound of  is
less than  IBE and the observed ratio of geometric means
is within bioequivalence limits of 80% and 125%.
 References
1. FDA (1999). In Vivo Bioequivalence Studies Based on Population and Individual
Bioequivalence Approaches. Food and Drug Administration, Rockville, Maryland,
August, 1999.
2. FDA (2001). Guidance for Industry: Statistical Approaches to Establishing
Bioequivalence. Food and Drug Administration, Rockville, Maryland, January, 2001.
Assessment of IBE
 Testing
H0 :    IBE versus H0 :    IBE is equivalent
to testing the following hypotheses
H0 :   0
versus
H0 :   0
where
  (mT  mR )  s  s  s  IBE max{s ,s }.
2
2
D
2
WT
2
WR
2
0
2
WR
Assessment of IBE
 If    1  ...   m , then an approximate upper confidence
bound can be obtained as
ˆ1  ...  ˆm  L1S12  ...  Lm Sm2 ,
where ˆi is an unbiased estimator of  i , Si2 is an
estimator of the variance of ˆi , and Lm are some constants.
 Note that ˆi are independent.
 References
- Howe, W.G. (1974). JASA, 69, 789-794.
- Graybill, F. and Wang, C.M. (1980). JASA, 75, 869-873.
- Hyslop, T., Hsuan, F., and Holder, D. (2000). Statistics in Medicine, 19, 2885-2897.
Assessment of IBE
 Hyslop, Hsuan, and Holder (2000) considered the
following decomposition of 
2
2
2
2
   2  s 0.5,0.5
 0.5sWT
 1.5sWR
 IBE max{s 02 ,sWR
}
where
2
2
s a2,b  s D2  asWT
 bsWR
 Note that
2
2
2
   2  s D2  sWT
 sWR
  IBE max{s 02 ,sWR
}
Assessment of IBE
The reason to decompose  as suggested by Hyslop,
Hsuan and Holder (2000) is because independent unbiased
estimator of (mT  mR ) ,
2
2
, sWT
s 0.5,0.5
2
and s WR
can be
derived under the 2  4 crossover design, recommended
in the 2001 FDA guidance.
Assessment of IBE
Let
Z i11  ( yi11  yi 21  yi 31  yi 41 ) 2
Z i 21  yi11  yi 31
Z i 31  yi 21  yi 41
Z i12  ( yi12  yi 22  yi 32  yi 42 ) 2
Z i 22  yi 22  yi 42
Z i 32  yi12  yi 32
and Zjk and S 2jk be the sample mean and sample variance
based on Zijk
Assessment of IBE
s 0.5,0.5 1 1
Z11  Z12
ˆ

~ N [ ,
( n1  n2 )]
2
4
2
(n1  1) S112  (n2  1) S122 s 0.5,0.5  n1  n2  2

~
n1  n2  2
n1  n2  2
2
2
sˆ 0.5,0.5
2
2
s WT  n1  n2 2
(n1  1) S21
 (n2  1) S22

~
2(n1  n2  2)
n1  n2  2
2
2
sˆWT
2
2
sˆWR

(n1  1) S  (n2  1) S
2(n1  n2  2)
2
31
2
32
~
2
2
2
ˆ , ŝ 0.5,0.5
, sˆWT
, and sˆWR
2
2
s WR
 n2  n 2
1
2
n1  n2  2
are independent.
Assessment of IBE
An approximate 95% upper confidence bound for  is
2
2
2
ˆU  ˆ 2  sˆ 0.5,0.5
 0.5sˆWT
 (1.5   IBE )sˆWR
 U
Assessment of IBE
U is the sum of the following quantities:
U1  [( ˆ  t0.95, n1  n2  2
4
U 2  sˆ 0.5,0.5
(
2
sˆ 0.5,0.5
2
n1  n2  2

2
0.05, n1  n2  2
4
U 3  0.52 sˆWT
(
2
 0.05,
n n
4
U 4  (1.5   IBE ) 2 sˆ WR
(
2

1
n2
) 2  ˆ 2 ]2
 1) 2
n1  n2  2
1
1
n1
 1) 2
2
n1  n2  2
2
 0.05,
n n
1
2
 1) 2
2
where  is the (100a)th percentile of the chi-square
distribution with b degrees of freedom
2
a ,b
Assessment of IBE
2
H0 : sWR
 s 02 versus H1 : s
Testing for
2
sˆ WR
( n1  n2  2)
2

s
If
0 , then reject H0.
2
 0.05, n  n  2
1
2
2
WR
 s 02
FDA’s Approach to Establishing PBE
 The 2001 FDA guidance provides detailed statistical
method for assessment of PBE under the recommended
2x4 crossover design.
– Statistical procedure was derived following the method by Hyslop,
Hsuan, and Holder (2000) for IBE.
– Statistical validity of the method is questionable because the
method fails to meet the primary assumption of independence.
– The method is conservative with some undesirable properties.
 Reference
Wang, H., Shao, J., and Chow, S.C. (2001). On FDA’s statistical approach to
establishing population bioequivalence. Unpublished manuscript.
FDA’s Approach to Establishing PBE
 Lineaized PBE criterion
   2  s TT2  s TR2  PBE max{s 02 ,s TR2 }
where   mT  mR
2
2
 ˆ,sˆTT
and sˆ TR
are not mutually independent
2
2
2 2
2
ˆ
ˆ
Cov(s TT ,s TR )  2  s BTs BR /(n1  n2  2)
2
although ˆ is independent of (sˆTT2 ,sˆTR
)
FDA’s Approach to Establishing PBE
 The asymptotic size of FDA’s approach is given by

z0.05

 1  2a  2s 2 s 2 / s 2
BT BR






where
2
2
4
4
s 2  2 2 (s D2  0.5sWT
 0.5sWR
)  0.25sWT
 0.25a2sWR
2
2
2
2 2
(s BT
 0.5sWT
)2  a2 (s BR
 0.5sWR
)
2
2
 s 02 .
 s 02 and a  1 if s TR
and a  1   PBE if s TR
Recent Development
 Assessment of IBE under various crossover designs
– (TRTR, RTRT): 2x4 design
2
2
2
2
   2  s 0.5,0.5
 0.5sWT
 1.5sWR
 IBE max{s 02 ,sWR
}
– (TRT,RTR): 2x3 design
2
2
2
2
2
   2  0.5(s 0.5,1
 s1,0.5
)  0.25sWT
 1.75sWR
  IBE max{s 02 ,sWR
}
– (TRR,RTR): extra-reference 2x3 design
2
2
2
   2  s1,0.5
 1.5sWR
 IBE max{s 02 ,sWR
}
2
(the confidence bound for sWT
is not required.)
Recent Development
 The extra-reference 2x3 design (TRR,RTR) requires the
construction of one fewer confidence bound than the 2x4
design.
 The extra-reference 2x3 design requires only 75% of the
observations in the 2x4 design
 The extra-reference 2x3 design is more efficient than the
2
2
2x4 design when s WR
or s D is large.
 The variance of ˆ under the 2x4 design over the variance
2
2
of ˆ under the extra-reference 2x3 design is 4s 0.5,0.5
/ 3s 1,0.5
2
2
which is greater than 1 if and only if s D2  0.5sWR
 s WT
.
Summary
 2x2 Standard Crossover Design
– ABE (Chow and Liu, 1999)
– PBE (Chow, Shao, and Wang, 2003)
 2x3 Crossover Design
– ABE (Chow and Liu, 1999)
– PBE (Chow, Shao, and Wang, 2003)
– IBE (Chow, Shao, and Wang, 2002)
 2x4 Crossover Design
– ABE (Chow and Liu, 1999)
– PBE (Chow, Shao, and Wang, 2003)
– IBE (Hyslop, Hsuan, and Holder, 2000)
 Extra-reference 2x3 and 3x2 Designs and Other Designs
– Chow and Shao (2002)
Selected References
Special Issues
 Chow, S.C. (Ed.) Special issue on Bioavailability and Bioequivalence of Drug
Information Journal, Vol. 29, No. 3, 1995
 Chow, S.C. (Ed.) Special issue on Bioavailability and Bioequivalence of
Journal of Biopharmaceutical Statistics, Vol. 7, No. 1, 1997
 Chow, S.C. and Liu, J.P. (Ed.) Special issue on Individual Bioequivalence of
Statistics in Medicine, Vol. 19, No. 20, October, 2000.
Review of FDA Guidances
 Chow, S. C. and Liu, J. P. (1994). Recent statistical development in
bioequivalence trials - a review of FDA guidance. Drug Information
Journal, 28, 851-864.
 Liu, J. P. and Chow, S. C. (1996). Statistical issues on FDA conjugated
estrogen tablets guideline. Drug Information Journal, 30, 881-889.
 Chow, S. C. (1999). Individual bioequivalence - a review of FDA draft
guidance. Drug Information Journal, 33, 435-444.
 Wang, H., Shao, J., and Chow, S.C. (2001). On FDA’s statistical approach to
establishing population bioequivalence. Unpublished manuscript.
Selected References
Books
 Chow, S.C. and Liu, J.P. (1998). Design and Analysis of Bioavailability and
Bioequivalence Studies, 2nd edition, Marcel Dekker, New York, New York.
 Chow, S.C. and Shao, J. (2002). Statistics in Drug Research, Marcel Dekker, New York,
New York.
 Chow, S.C., Shao, J., and Wang, H. (2003). Sample Size Calculation in Clinical
Research, Marcel Dekker, Inc., New York, New York.
Original Articles
 Shao, J., Chow, S. C., and Wang, B. (2000). Bootstrap methods for individual
bioequivalence. Statistics in Medicine, 19, 2741-2754.
 Chow, S.C., Shao, J., and Wang, H. (2002). Individual bioequivalence testing under 2x3
crossover designs. Statistics in Medicine, 21, 629-648.
 Chow, S.C. and Shao, J. (2002). In vitro bioequivalence testing. Statistics in Medicine,
22, 55-68 .
 Chow, S.C., Shao, J., and Wang, H. (2003). Statistical tests for population
bioequivalence. Statistica Sinica, 13, 539-554.
Thank
you