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Statistical Methods for Assessment of Individual/Population Bioequivalence Shein-Chung Chow, Ph.D. Biostatistics and Clinical Data Management Millennium.

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Presentation on theme: "Statistical Methods for Assessment of Individual/Population Bioequivalence Shein-Chung Chow, Ph.D. Biostatistics and Clinical Data Management Millennium."— Presentation transcript:

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

2 Outline Background Conduct of Bioequivalence Trials
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 Generic 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 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 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 1993 1994 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 1996 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

10 History 1997 1998 1999 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

11 History 2000 2001 2002 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 2002 FDA draft guidance on Bioavailability and Bioequivalence Studies for Orally Administered Drug Products – General Considerations (July, 2002)

12 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).

14 Standard Two-sequence, Two period Crossover Design
R A N D O M I Z A T I O N I II W A S H O U T Sequence 1 Reference Test Subjects Sequence 2 Test Reference

15 Conduct of Bioequivalence Trials
Number of Subjects - ABE Pivotal fasting studies: subjects Limited food studies: minimum of 12 subjects Liu, J.P. and Chow, S.C. (1992). J. Pharmacokin. Biopharm., 20, 0% 5% % % Difference in Means Power 80% CV 28 30

16 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

17 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

18 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.

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

20 Generic Drugs Safety Concern
They’re 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

22 Drug Interchangeability
Drug Prescribability Brand-name vs. its generic copies Generic copies vs. generic copies Drug Switchability Current regulation for ABE does not guarantee drug prescribability and drug switchability

23 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 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)

25 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)

26 Type of Bioequivalence
Average Bioequivalence (ABE) Current regulatory requirement Population Bioequivalence (PBE) Prescribability Individual Bioequivalence (IBE) Switchability

27 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%

28 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.

29 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

30 FDA’s Recommendation Aggregate criterion Moment-based approach
Scaling method Weighing factors One-sided test

31 IBE Criterion Where

32 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)

33 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

34 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 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.

35 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.

36 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 TRT RTR (recommended) (possible alternative)

37 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 where is a given constant.

38 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 .

39 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, - Graybill, F. and Wang, C.M. (1980). JASA, 75, - Hyslop, T., Hsuan, F., and Holder, D. (2000). Statistics in Medicine, 19,

43 Assessment of IBE  Hyslop, Hsuan, and Holder (2000) considered the
following decomposition of where  Note that

44 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 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:
where 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 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.

51 FDA’s Approach to Establishing PBE
Lineaized PBE criterion where and are not mutually independent although is independent of

52 FDA’s Approach to Establishing PBE
The asymptotic size of FDA’s approach is given by where and if and if

53 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.)

54 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

55 Summary 2x2 Standard Crossover Design 2x3 Crossover Design
ABE (Chow and Liu, 1999) PBE (Chow, Shao, and Wang, 2003) 2x3 Crossover Design IBE (Chow, Shao, and Wang, 2002) 2x4 Crossover Design IBE (Hyslop, Hsuan, and Holder, 2000) Extra-reference 2x3 and 3x2 Designs and Other Designs Chow and Shao (2002)

56 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, Liu, J. P. and Chow, S. C. (1996). Statistical issues on FDA conjugated estrogen tablets guideline. Drug Information Journal, 30, Chow, S. C. (1999). Individual bioequivalence - a review of FDA draft guidance. Drug Information Journal, 33, Wang, H., Shao, J., and Chow, S.C. (2001). On FDA’s statistical approach to establishing population bioequivalence. Unpublished manuscript.

57 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, Chow, S.C., Shao, J., and Wang, H. (2002). Individual bioequivalence testing under 2x3 crossover designs. Statistics in Medicine, 21, Chow, S.C. and Shao, J. (2002). In vitro bioequivalence testing. Statistics in Medicine, 22, Chow, S.C., Shao, J., and Wang, H. (2003). Statistical tests for population bioequivalence. Statistica Sinica, 13,

58 Thank you


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