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					 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
              R
                                      I                    II
              A
              N       Sequence 1                W         Test
                                   Reference
              D                                 A
Subjects      O                                 S
              M                                 H
              I                                 O
              Z       Sequence 2     Test               Reference
                                                U
              A                                 T
              T
              I
              O
              N
  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      CV      0%     5%     10%     15%
            80%       20      20     24      52     200
                      22      24     28      62     242
                      24      28     34      74     288
                      26      32     40      86     336
                      28      36     46     100     390
                      30      40     52     114     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                Generic
             #K                     #1

                                              ?

Generic                                           Generic
  #5
                     Brand-name                     #2




          Generic                   Generic
            #4                        #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
  WT2 = within-subject variability for the test product
  WR2 = within-subject variability for the reference product
  D2 = 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  m R )    (   )
           2     2      2       2
                 D      WT
                            I WR

        max( ,  W 0 )
                 2
                 WR
                   2


Where
               (ln1.25)   2
        I 
                      2
                       W0
     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)
     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 WR2, WT2, and D2.
 The standard 2 x 2 crossover design is not appropriate.
 FDA recommends a replicated design be used
  TRTR
            (recommended)
  RTRT
  TRT
  RTR       (possible alternative)
        General Approaches for IBE/PBE
Let yT be the PK response from the test formulation,
         '
yR and y R be two identically distributed PK responses
from the reference formulation, and

        E ( yR  yT ) 2  E ( yR  yR ) 2
                                     '

                                            if E ( yR  yR ) 2 / 2   02
                                                          '

               E ( yR  yR ) 2 / 2
                            '

     
        E ( yR  yT ) 2  E ( yR  yR ) 2
                                     '

                                             if   E ( yR  yR ) 2 / 2   02
                                                            '
       
                       02



where  02 is a given constant.
       General Approaches for IBE/PBE

 If yT , y R , and y R are independent observations from
                      '



  different subjects, then the two formulations are
  population bioequivalence when        PBE .
                      '
 If yT , y R , and y 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 - y R
 E ( yR  yR )2 2 is the within-subject variance of the
            '



    reference formulation

           ( mT  m R ) 2   TT   TR
                              2      2
                                        for PBE
                max{ 0 ,  TR }
                          2    2


          ( mT  m R ) 2   D  ( WT   WR )
                             2      2      2
                                              for IBE
                    max{ 0 ,  WR }
                              2   2
                         Assessment of IBE
 Hypotheses Testing
           H 0 :    IBE versus H 0 :    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 H :        versus H :    is equivalent
           0        IBE         0       IBE

 to testing the following hypotheses

          H0 :   0       versus      H0 :   0
where

   ( mT  m R )    
                2      2
                       D
                             2
                             WT      2
                                       WR     IBE max{ , }.
                                                        2
                                                        0
                                                            2
                                                            WR
                          Assessment of IBE

 If    1  ...   m , then an approximate upper confidence
  bound can be obtained as
                    ˆ1  ...  ˆm  L1S12  ...  Lm Sm ,
                                                        2


  where ˆi is an unbiased estimator of  i ,                      S i2   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   0.5,0.5  0.5WT  1.5WR  IBE max{ 02 ,WR}
                  2             2        2                    2


 where
       a,b   D  aWT  bWR
        2       2     2      2



 Note that
         2   D   WT   WR   IBE max{ 0 , WR }
                  2     2      2                2    2
                   Assessment of IBE

The reason to decompose  as suggested by Hyslop,
Hsuan and Holder (2000) is because independent unbiased
estimator of ( mT  m R ) ,    0.5,0.5 ,  WT
                                2           2
                                                 and  WR can be
                                                       2


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 2 be the sample mean and sample variance
              jk
based on Zijk
                         Assessment of IBE

    ˆ  Z11  Z12 ~ N [ ,  0.5,0.5 ( 1  1 )]
                                    2

                                      n1  n2
            2                 4
                 (n1  1) S11  (n2  1) S12  0.5,0.5  n1  n2  2
                            2              2           2       2

    0.5,0.5
    ˆ2                                      ~
                        n1  n2  2            n1  n2  2
            (n1  1) S 21  (n2  1) S 22  WT  n1  n2  2
                       2               2           2       2

    WT
    ˆ2                                  ~
                 2(n1  n2  2)            n1  n2  2
            (n1  1) S31  (n2  1) S32  WR  n1  n2  2
                      2              2            2        2

    WR
    ˆ2                                ~
                 2(n1  n2  2)          n1  n2  2

ˆ ,  0.5,0.5 ,  WT , and  WR
     ˆ2           ˆ2         ˆ2                are independent.
                 Assessment of IBE

An approximate 95% upper confidence bound for     is

ˆU  ˆ2   0.5,0.5  0.5WT  (1.5   IBE ) WR  U
             ˆ2            ˆ2                   ˆ2
                    Assessment of IBE
U is the sum of the following quantities:
              ˆ                           0.5 ,0.5                             ˆ
     U1  [(   t0.95, n1  n2  2                                      ) 2   2 ]2
                                          ˆ2
                                               2
                                                         1
                                                         n1        1
                                                                    n2

                         n1  n2  2
     U 2   0.5,0.5 (
            ˆ4                                  1) 2
                          0.05, n  n
                           2
                                 1   2   2

                            n1  n2  2
     U 3  0.52  WT (
                 ˆ4                                    1) 2
                             0.05, n  n
                              2
                                     1     2   2

                                            n1  n2  2
     U 4  (1.5   IBE ) 2  WR (
                             ˆ4                                           1) 2
                                             0.05, n  n
                                              2
                                                        1      2   2


where  is the (100a)th percentile of the chi-square
          2
          a ,b
distribution with b degrees of freedom
                       Assessment of IBE

Testing for       H 0 :  WR   02 versus H1 : 
                          2                          2
                                                    WR    0
                                                            2




    WR (n1  n2  2)
   ˆ2
If                      0 , then reject H0.
                          2

       0.05,n  n 2
         2
              1    2
    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   TT   TR   PBE max{ 02 , TR }
               2      2                      2


  where   mT  mR
 ˆ,  TT and  TR are not mutually independent
       ˆ2       ˆ2

    Cov( TT , TR )  2  2 BT BR /(n1  n2  2)
         ˆ2 ˆ2                2   2


  although ˆ is independent of ( TT ,  TR )
                                  ˆ2 ˆ2
    FDA’s Approach to Establishing PBE

 The asymptotic size of FDA’s approach is given by
                        z0.05             
                                         
               1  2a  2 2  2 /  2    
                            BT BR        
  where
     2 2 ( D  0.5 WT  0.5 WR )  0.25 WT  0.25a 2 WR
    2           2        2         2            4             4



           ( BT  0.5 WT ) 2  a 2 ( BR  0.5 WR ) 2
               2         2               2         2




  and a  1   PBE if  TR   02 and a  1 if  TR   02 .
                         2                        2
               Recent Development
 Assessment of IBE under various crossover designs
   – (TRTR, RTRT): 2x4 design
         2   0.5,0.5  0.5WT  1.5WR   IBE max{ 0 ,WR}
                  2             2        2                2   2



   – (TRT,RTR): 2x3 design
         2  0.5( 0.5,1  1,0.5 )  0.25WT  1.75WR   IBE max{ 0 , WR}
                      2        2              2         2                2    2



   – (TRR,RTR): extra-reference 2x3 design
         2  1,0.5  1.5WR   IBE max{ 0 , WR}
                 2           2                2    2




      (the confidence bound for  WT is not required.)
                                  2
              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  WR or  D is large.
                      2      2



 The variance of ˆ under the 2x4 design over the variance
  of ˆ under the extra-reference 2x3 design is 4 0.5,0.5 / 31,0.5
                                                      2         2


  which is greater than 1 if and only if  D  0.5 WR   WT .
                                           2        2      2
                            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.
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