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 ChapterDecember 2, 2003

Background– What and Why?– History

Conduct of Bioequivalence Trials Drug Interchangeability

– Population Bioequivalence– Individual Bioequivalence

Recent Development Summary

Outline

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1997– DIA Hilton Head Meeting– Draft guidance on PBE/IBE circulated for comments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

RANDOMIZATION

Subjects

Sequence 1

Sequence 2

PERIOD

Reference

Test

Test

Reference

I II

WASHOUT

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.

Conduct of Bioequivalence Trials

CV202224262830

Power80%

0% 5% 10% 15% 20 24 52 200 24 28 62 242 28 34 74 288 32 40 86 336 36 46 100 390 40 52 114 448

Difference in Means

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

Brand-nameGeneric

#2

Generic#3

Generic#4

Generic#5

?

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

NotationsT = mean of the test product

R = 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

2 2 2 2

2 20

( ) ( )

max( , )T R D WT WR

IWR W

2

20

(ln1.25)I

W

Where

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 WR

2, WT2, and D

2.

The standard 2 x 2 crossover design is not appropriate. FDA recommends a replicated design be used

TRTRRTRT

TRTRTR

(recommended)

(possible alternative)

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.

2 ' 2

' 2

2 ' 2

20

( ) ( )

( ) / 2

( ) ( )

R T R R

R R

R T R R

E y y E y y

E y y

E y y E y y

20

' 2 20( ) / 2R RE y y

' 2 20( ) / 2R RE y y

'Ry

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

.

PBE

IBE

'RyRyTy

Ty Ry 'Ry

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

' 2( ) 2R RE y y

2 2 2

2 20

( )

max{ , }T R TT TR

TR

2 2 2 2

2 20

( ) ( )

max{ , }T R D WT WR

WR

'Ry

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.

0 : IBEH 0 : IBEH

IBE

Assessment of IBE

Testing versus is equivalent

to testing the following hypotheses

versus

where

0 : IBEH 0 : IBEH

0 : 0H 0 : 0H

2 2 2 2 2 20( ) max{ , }.T R D WT WR IBE WR

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.

1 ... m

2 21 1 1ˆ ˆ... ... ,m m mL S L S

ˆi i 2iS

ˆi

ˆi

Assessment of IBE

Hyslop, Hsuan, and Holder (2000) considered the

following decomposition of

where

Note that

2 2 2 2 2 20.5,0.5 00.5 1.5 max{ , }WT WR IBE WR

2 2 2 2,a b D WT WRa b

2 2 2 2 2 20max{ , }D WT WR IBE WR

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.

( )T R 20.5,0.5 2

WT 2WR

Assessment of IBE

Let

and Zjk and be the sample mean and sample variance

based on Zijk

11 11 21 31 41

21 11 31

31 21 41

12 12 22 32 42

22 22 42

32 12 32

( ) 2

( ) 2

i i i i i

i i i

i i i

i i i i i

i i i

i i i

Z y y y y

Z y y

Z y y

Z y y y y

Z y y

Z y y

2jkS

Assessment of IBE

, , , and are independent.

1 2

1 2

1 2

20.5,0.511 12 1 1

2 22 20.5,0.5 22 1 11 2 12

0.5,0.51 2 1 2

2 22 222 1 21 2 22

1 2 1 2

2 22 1 31 2 32

1 2

ˆ ~ [ , ( )]2 4

( 1) ( 1)ˆ ~

2 2

( 1) ( 1)ˆ ~

2( 2) 2

( 1) ( 1)ˆ ~

2( 2)

n n

n n

WT n nWT

WRWR

Z ZN

n S n S

n n n n

n S n S

n n n n

n S n S

n n

1 2

2 22

1 2 2n n

n n

20.5,0.5 2ˆWT 2ˆWR

Assessment of IBE

An approximate 95% upper confidence bound for is

2 2 2 20.5,0.5

ˆˆ ˆ ˆ ˆ0.5 (1.5 )U WT IBE WR U

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

20.5,0.5

1 2 1 2

1 2

1 2

1 2

ˆ 2 2 21 11 0.95, 2 2

4 21 22 0.5,0.5 2

0.05, 2

2 4 21 23 2

0.05, 2

2 4 21 24 2

0.05, 2

ˆ ˆ[( ) ]

2ˆ ( 1)

2ˆ0.5 ( 1)

2ˆ(1.5 ) ( 1)

n n n n

n n

WTn n

IBE WRn n

U t

n nU

n nU

n nU

2,a b (100 )a th

Assessment of IBE

Testing for versus

If , then reject H0.

2 20 0: WRH 2 2

1 0: WRH

1 2

221 202

0.05, 2

ˆ ( 2)WR

n n

n n

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.

FDA’s Approach to Establishing PBE

Lineaized PBE criterion

where

and are not mutually independent

although is independent of

2 2 2 2 20max{ , }TT TR PBE TR

T R

2ˆ ˆ, TT 2ˆTR

2 2 2 2 21 2ˆ ˆ( , ) 2 /( 2)TT TR BT BRCov n n

2 2ˆ ˆ( , )TT TR

FDA’s Approach to Establishing PBE

The asymptotic size of FDA’s approach is given by

where

and if and if .

0.05

2 2 2 21 2 /BT BR

z

a

2 2 2 2 2 4 2 42 ( 0.5 0.5 ) 0.25 0.25D WT WR WT WRa

2 2 2 2 2 2 2( 0.5 ) ( 0.5 )BT WT BR WRa

1 PBEa 2 20TR 1a 2 2

0TR

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.)

2 2 2 2 2 20.5,0.5 00.5 1.5 max{ , }WT WR IBE WR

2 2 2 2 2 2 20.5,1 1,0.5 00.5( ) 0.25 1.75 max{ , }WT WR IBE WR

2 2 2 2 21,0.5 01.5 max{ , }WR IBE WR

2WT

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

2WR 2

D

2 20.5,0.5 1,0.54 / 3

2 2 20.5 .D WR 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 Infor

mation 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 Statisti

cs 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 tab

lets guideline. Drug Information Journal, 30, 881-889. Chow, S. C. (1999). Individual bioequivalence - a review of FDA draft guidance. D

rug Information Journal, 33, 435-444. Wang, H., Shao, J., and Chow, S.C. (2001). On FDA’s statistical approach to establi

shing population bioequivalence. Unpublished manuscript.

Selected References

Books Chow, S.C. and Liu, J.P. (1998). Design and Analysis of Bioavailability and Bioequivale

nce 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 Researc

h, Marcel Dekker, Inc., New York, New York.

Original Articles Shao, J., Chow, S. C., and Wang, B. (2000). Bootstrap methods for individual bioequiva

lence. 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, 2

2, 55-68 . Chow, S.C., Shao, J., and Wang, H. (2003). Statistical tests for population bioequivalenc

e. Statistica Sinica, 13, 539-554.

Thank you