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?HistoryConduct of Bioequivalence TrialsDrug InterchangeabilityPopulation BioequivalenceIndividual BioequivalenceRecent DevelopmentSummary
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 actionTwo 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 CommitteeThe process is lengthy & costlyGeneric DrugsANDAThe 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 aretherapeutically equivalent.
6 HistoryGeneric copies of approved drug products could be approved by an ANDA which includes the information of formulation, manufacturing and quality control procedures, and labeling.1975Regulations were established.1977Regulations were finalized and became effective(21 CFR 320).
7 HistorySeveral decision rules were proposed: 75/75, 80/120, and 20% rules1984The Drug Price Competition and Patent Term Restoration Act1986FDA 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 bookFDA Core Committee raised the issue of switchability1993Generic Drug Advisory Committee Meeting discussed individual bioequivalence1994DIA BA/BE Symposium held in Rockville, Maryland
9 History 1995 1996 Generic Drug Advisory Committee Meeting International Workshop (Canada, US, and Germany) held in GermanySUPAC-IR1996FDA Individual BE Working Group/PhRMA/Generic Trade AssociationFIP BioInternational’96, Tokyo, Japan
10 History 1997 1998 1999 DIA Hilton Head Meeting Draft guidance on PBE/IBE circulated for comments1998AAPS annual meeting1999Revised draft guidance on PBE/IBE issuedFDA guidance on in vitro bioequivalence testingChow & 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)20012002FDA draft guidance on Bioavailability and Bioequivalence Studies for Orally Administered Drug Products – General Considerations (July, 2002)
12 Current RegulationsMost 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), orBioequivalence 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 ZATIO NIIIW A SHO U TSequence 1ReferenceTestSubjectsSequence 2TestReference
15 Conduct of Bioequivalence Trials Number of Subjects - ABEPivotal fasting studies: subjectsLimited food studies: minimum of 12 subjectsLiu, J.P. and Chow, S.C. (1992). J. Pharmacokin. Biopharm., 20,0% 5% % %Difference in MeansPower 80%CV2830
16 Conduct of Bioequivalence Trials Washout5.5 half-lives for IR products8.5 half-lives for CR productsBlood SamplingMore sampling around CmaxSampling at least three half-lives
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.
20 Generic Drugs Safety Concern They’re cheaper, but do they work as well?
21 Safety ConcernGeneric and brand-name drugs do exactly the same thing and are completely interchangeable.- D. McLeanDeputy Associate Commissioner for Public AffairsU.S. Food and Drug AdministrationI 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 CelloExecutive DirectorPennsylvania Pharmacists Association
22 Drug Interchangeability Drug PrescribabilityBrand-name vs. its generic copiesGeneric copies vs. generic copiesDrug SwitchabilityCurrent regulation for ABE does not guarantee drug prescribability and drug switchability
23 Limitations of ABE Focuses only on population average Ignores distribution of the metricIgnores subject-by-formulation interactionDoes not address the right questionCommentsOne size fits all BE criteriaClinical evidencePost-approval process validation/control
24 Drug PrescribabilityThe physician’s choice for prescribing an appropriate drug for his/her patients between the brand-name drug and its generic copiesPopulation Bioequivalence (PBE)Anderson and Hauck (1990)Chow and Liu (1992)Post-approval meta-analysis for BE reviewChow and Liu (1997)Chow and Shao (1999)
25 Drug SwitchabilityThe 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 levelIndividual Bioequivalence (IBE)Anderson and Hauck (1990)Schall and Luus (1993)Holder and Hsuan (1993)Esinhart and Chinchilli (1994)Post-approval meta-analysis for BE reviewChow and Liu (1997)Chow and Shao (1999)
26 Type of Bioequivalence Average Bioequivalence (ABE)Current regulatory requirementPopulation Bioequivalence (PBE)PrescribabilityIndividual 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 varianceShould be able to assume switchabilityShould encourage or reward formulations that reduce within subject variabilityShould 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 criteriaThe software application for the statistical method should be user-friendlyShould provide interpretability for scientists and cliniciansStatistical 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 productsWT2 = within-subject variability for the test productsWR2 = within-subject variability for the reference productsD2 = variability due to the subject-by-formulation interaction
32 Comments on IBE Criterion It is a non-linear function of means and variance componentsThe selection of weights lack of scientific and statistical justificationThe determination of bioequivalence limit is subjectiveIBE 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 interactionMasking effect for distributions of individual componentsOffsetting effectBias versus intrasubject variabilityTwo-stage test procedure
34 Offsetting Effect One actual data set from the US FDA Four-sequence, four-period crossover designN=22 subjectsAverage BioequivalenceThe ratio of average AUC is with a C.I. of (1.025, 1.280)Individual BioequivalenceThe 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 EffectThe 14% increase in the average is offset by a 48% reduction in the variabilityWe may conclude IBE even though the distributions of PK responses are totally different.
36 Study Design for IBEThe 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 usedTRTR RTRTTRT 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 responsesfrom the reference formulation, andifwhere is a given constant.
38 General Approaches for IBE/PBE If , , and are independent observations fromdifferent subjects, then the two formulations arepopulation bioequivalence when If , , and are from the same subject, then thetwo formulations are individual bioequivalence when.
39 General Approaches for IBE/PBE is a measure of the relative difference between themean squared errors of yR- yT and yR - is the within-subject variance of thereference formulationfor PBEfor IBE
40 Assessment of IBE Hypotheses Testing versus IBE is claimed if a 95% confidence upper bound of isless than and the observed ratio of geometric meansis within bioequivalence limits of 80% and 125%. References1. FDA (1999). In Vivo Bioequivalence Studies Based on Population and IndividualBioequivalence Approaches. Food and Drug Administration, Rockville, Maryland,August, 1999.2. FDA (2001). Guidance for Industry: Statistical Approaches to EstablishingBioequivalence. Food and Drug Administration, Rockville, Maryland, January, 2001.
41 Assessment of IBE Testing versus is equivalent to testing the following hypothesesversuswhere
42 Assessment of IBE If , then an approximate upper confidence bound can be obtained aswhere is an unbiased estimator of , is anestimator 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 ofwhere Note that
44 Assessment of IBEThe 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 IBELetand Zjk and be the sample mean and sample variancebased on Zijk
47 Assessment of IBEAn 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 IBETesting for versusIf , 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.ReferenceWang, 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 criterionwhereand are not mutually independentalthough is independent of
52 FDA’s Approach to Establishing PBE The asymptotic size of FDA’s approach is given bywhereand 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 DevelopmentThe 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 designThe 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 DesignIBE (Chow, Shao, and Wang, 2002)2x4 Crossover DesignIBE (Hyslop, Hsuan, and Holder, 2000)Extra-reference 2x3 and 3x2 Designs and Other DesignsChow 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, 1995Chow, S.C. (Ed.) Special issue on Bioavailability and Bioequivalence of Journal of Biopharmaceutical Statistics, Vol. 7, No. 1, 1997Chow, 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 GuidancesChow, 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 ArticlesShao, 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,