Statistical Methods for Assessment of IndividualPopulation Bioequivalence SheinChung Chow, Ph'D' Bio

1
Statistical Methods for Assessment of
Individual/Population BioequivalenceShein-Chung
Chow, Ph.D.Biostatistics and Clinical Data
ManagementMillennium Pharmaceuticals,
Inc.Cambridge, MA 02139Presented at ASA Boston
ChapterDecember 2, 2003
2
Outline

• Background
• What and Why?
• History
• Conduct of Bioequivalence Trials
• Drug Interchangeability
• Population Bioequivalence
• Individual Bioequivalence
• Recent Development
• Summary

3
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.

4
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

5
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.

6
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).

7
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

8
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

9
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 BioInternational96, Tokyo, Japan

10
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 Lius BA/BE book revision

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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)

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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.

13
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).

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• Standard Two-sequence, Two period Crossover Design

PERIOD
II
I
Sequence 1
Test
Reference
Subjects
Sequence 2
Test
Reference
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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.

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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

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Statistical Methods - ABE

• Confidence Interval
• The classical (shortest) confidence interval
• Westlakes symmetric
• Fiellers theorem
• Chow and Shaos confidence region
• Interval Hypotheses Testing
• Shuirmanns two one-sided tests procedure

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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.

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Safety Concern
Generic 1
Generic K
?
Generic 5
Generic 2
Brand-name
Generic 3
Generic 4
20
Safety Concern

• Generic Drugs
• Theyre cheaper, but do they work as well?

21
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
  
  

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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

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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

24
Drug Prescribability

• The physicians 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)

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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)

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Type of Bioequivalence

• Average Bioequivalence (ABE)
• Current regulatory requirement
• Population Bioequivalence (PBE)
• Prescribability
• Individual Bioequivalence (IBE)
• Switchability

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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 consumers risk at the level of 5

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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.

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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-formulati
  on interaction

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FDAs Recommendation

• Aggregate criterion
• Moment-based approach
• Scaling method
• Weighing factors
• One-sided test

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IBE Criterion
Where
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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
  (over-corrected)

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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

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Offsetting Effect

• One actual data set from the US FDA
• Four-sequence, four-period crossover design
• N22 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.

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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.

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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
• TRTRRTRT
• TRTRTR

(recommended) (possible alternative)
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General Approaches for IBE/PBE
Let yT be the PK response from the test
formulation, yR and be two identically
distributed PK responses from the reference
formulation, and

if
if where is
a given constant.
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General Approaches for IBE/PBE
? If , , and are independent
observations from different subjects, then
the two formulations are population
bioequivalence when . ? If
, , and are from the same subject,
then the two formulations are individual
bioequivalence when .

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General Approaches for IBE/PBE
? is a measure of the relative difference
between the mean squared errors of yR- yT
and yR - ? is the
within-subject variance of the reference
formulation ?
for PBE ?

for IBE
40
Assessment of IBE
? Hypotheses Testing
versus ? IBE is claimed if a 95
confidence upper bound of is less than
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.
41
Assessment of IBE
? Testing versus
is equivalent to testing the
following hypotheses
versus where
42
Assessment of IBE
? If , then an
approximate upper confidence bound can be
obtained as where is an unbiased
estimator of , is an estimator of
the variance of , and Lm are some
constants. ? Note that 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.
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Assessment of IBE
? Hyslop, Hsuan, and Holder (2000) considered the
following decomposition of where ? Note
that
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Assessment of IBE
The reason to decompose as suggested by
Hyslop, Hsuan and Holder (2000) is because
independent unbiased estimator of
, , and can be
derived under the 2 4 crossover design,
recommended in the 2001 FDA guidance.
45
Assessment of IBE
Let and Zjk and be the sample
mean and sample variance based on Zijk
46
Assessment of IBE
, , , and are
independent.
47
Assessment of IBE
An approximate 95 upper confidence bound for
is
48
Assessment of IBE
U is the sum of the following quantities whe
re is the percentile of
the chi-square distribution with b degrees of
freedom
49
Assessment of IBE
Testing for
versus If
, then reject H0.
50
FDAs 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
  FDAs statistical approach to establishing
  population bioequivalence. Unpublished
  manuscript.

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FDAs Approach to Establishing PBE

• Lineaized PBE criterion
• where
• and are not mutually
  independent
• although is independent of

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FDAs Approach to Establishing PBE

• The asymptotic size of FDAs approach is given by
• where
• and if and
  if .

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Recent Development

• Assessment of IBE under various crossover designs
• (TRTR, RTRT) 2x4 design
• (TRT,RTR) 2x3 design
• (TRR,RTR) extra-reference 2x3 design
• (the confidence bound for is not
  required.)

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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 2x4 design when or is
  large.
• The variance of under the 2x4 design over
  the variance of under the extra-reference
  2x3 design is which is
  greater than 1 if and only if

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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)

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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
  FDAs statistical approach to establishing
  population bioequivalence. Unpublished
  manuscript.

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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.

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Thank you