- On 29 Sep 2004 at 05:08:32, kanimozhi A (kani_bio01.-a-.yahoo.co.in) sent the message
Sir/Madam,

Back to the Top

I have a doubt in interpretation of the bioequivalence results.

In a bioequivalence trial if the 90% confidence interval and the

ratios are with in the acceptance limits of bioequivalence (80-125%).

But in PROC GLM for all the three parameters i.e. Cmax AUC0-t and AUC

0-inf is significant by formulation wise, so can we conclude that the

two formulations are bioequivalent or not.

Thanks and regards,

kanimozhi.A - On 29 Sep 2004 at 05:55:38, Priti Pandey (priti_pandey.-a-.yahoo.com) sent the message

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Dear Kanimozhi,

Bioequivalence result depends only on 90% CI. If your defined

regulatory (80%-125% for most regulatories) criteria meets then you can

conclude bioequivalence. PROC GLM gives us "error" term to calculate

90% CI.

Hope this will be helpfull to you.

Regards

Priti - On 29 Sep 2004 at 13:48:32, Helmut_Schutz (helmut.schuetz.-at-.bebac.at) sent the message

Back to the Top

Dear kanimozhi A,

don't worry about about significant results, we were testing them

almost more than two decades ago ;-)

In BE assessment we are only interested in rejecting the

null-hypothesis of inequivalence by means of interval inclusion (given for bioavailability ratios):

null hypothesis [=B5(test) and =B5(reference) are not equivalent]

H0: =B5(test)/=B5(reference)theta2

alternative hypothesis [=B5(test) and =B5(reference) are equivalent]

H1: theta1<=B5(test)/=B5(reference)The interval [theta1,theta2] denotes the acceptance ranges for any

given parameter, where a beta-risk of 0.2 leads to theta1(1-beta0.8)

and theta21/theta11.25.

Best regards,

Helmut

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html - On 30 Sep 2004 at 11:22:58, Helmut_Schutz (helmut.schuetz.aaa.bebac.at) sent the message

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Dear kanimozhi A,

since yesterday's mail showed up in some strange coding, I will give it a second try:

null hypothesis [mu(T) and mu(R) are not equivalent]

H0: mu(T)/mu(R)theta2

alternative hypothesis [mu(T) and mu(R) are equivalent]

H1: theta1The interval [theta1,theta2] denotes the acceptance ranges for any

given parameter, where a beta-risk of 0.2 leads to

theta1(1-beta)0.8,

and

theta21/theta11.25.

Best regards,

Helmut

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html

[Still looks strange to me but this is what arrived for distribution - db] - On 30 Sep 2004 at 14:32:07, Angusmdmclean.at.aol.com sent the message
September 30, 2004:

Back to the Top

Helmut; thank you for outlining the essence of statistical tests for

bioequivalence and indeed bioinequivalence. This is indeed useful

material. Please

could you add the definitions of all the symbols and letters in the

equations, since this will significantly aid comprehension of the

letters and symbols

in your presentation and eliminate confusion.

thank you

Angus McLean Ph.D.

8125 Langport Terrace,

Suite 100,

Gaithersburg,

MD 20877

301-869-1009

301-869-5737

BioPharm Global

(http://home.comcast.net/~angusmdmclean/BGWEBSITE/home.html) - On 1 Oct 2004 at 08:55:57, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message

Back to the Top

Dear Helmut Schutz,

You wrote:

> The interval [theta1,theta2] denotes the acceptance ranges for any

> given parameter, where a beta-risk of 0.2 leads to

> theta1(1-beta)0.8,

> and

> theta21/theta11.25.

Perhaps I am wrong, but in my opinion, the values 0.8 and 1.25 are

defined

as the acceptable range for the AUC-ratio, with a probability of 95%

(alpha

0.05 'consumers' risk'), and this has nothing to do with the

beta-risk

('manufacturers' risk'). A beta of 0.2 implies that, given that the true

AUC-ratio is 1, the chance of concluding bioequivalence is 80%. The

sample

size is chosen to achieve this.

Best regards,

Hans Proost

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.-at-.farm.rug.nl - On 1 Oct 2004 at 09:31:53, "Dowling, Thomas" (tdowling.at.rx.umaryland.edu) sent the message

Back to the Top

I was wondering if someone could share their experiences in terms of

calculating sample size for BE studies? Since we rarely know the

intra-subject variability of Cmax and AUC for either the reference or

test drug, what is the most common approach?

Bests,

Tom

[Try searching at

http://www.boomer.org/cgi-bin/htsearch?

method='and'&sort='score'&words=sample%20size&restrict=http://

www.boomer.org/pkin/ - db] - On 1 Oct 2004 at 10:43:45, "Lee, Jang-Ik" (LEEJANG.-at-.cder.fda.gov) sent the message

Back to the Top

Tom,

Personally, I have used PASS in determining sample size for BE studies.

Even though you do not know the variability, you can play around with

assumptions (e.g., CV = 10%, 20%, 30%; and power = 0.8, 0.9....). PASS

gives you estimated sample size in each combination of assumption.

I hope this helps. Best regards.

Ike.

Jang-Ik Lee, Pharm.D., Ph.D.

Clinical Pharmacology Reviewer

Office of Clinical Pharmacology and Biopharmaceutics

Center for Drug Evaluation and Research

U.S. Food and Drug Administration

9201 Corporate Blvd, HFD-880, Rockville, MD 20850

Phone: 301-827-2492 Fax: 301-827-2579

[http://www.dataxiom.com/products/Pass/ or

http://www.ncss.com/pass.html ? - db] - On 1 Oct 2004 at 16:52:23, fabrice_nollevaux.aaa.sgs.com sent the message

Back to the Top

Dear Thomas,

Unfortunately, you should have a previous estimation of the

intra-subject

variability to be able to calculate the required sample size.

The compounds concerned by bioequivalence being generally quite "old",

this information can be found or derived either from the litterature or

from previous studies performed with the reference formulation.

If this is not the case, I am afraid you need a pilot study with a few

subjects in order to get this estimation.

But then, be careful that the estimate of variability obtained wihtin a

limited number of subjects will carry out a large uncertainty, so you

would have to use a conservative approach in further sample size

estimation (e.g. based on the upper 95%CI of the estimated intra-CV).

Hope this helps,

Fabrice

Fabrice Nollevaux,

Senior Biostatistician

SGS Life Sciences - Wavre - Belgium

http://www.sgs.com/life_sciences - On 1 Oct 2004 at 19:45:20, "Jadhav, Pravin *" (JadhavP.at.cder.fda.gov) sent the message

Back to the Top

Hi Hans and Helmut,

I think, there are two issues here.

1. BE limit: (0.8 - 1.25): In that sense, Helmut's logic makes sense.

The

given logic

> theta1=(1-beta)=0.8,

> and

> theta2=1/theta1=1.25.

makes sure that the intervals are symmetric around 1 (20% on both

sides, the

increase from 100 TO 120 is only 16.67%). This limit is *recommended*

by the

agency. I don't see any relation with "consumers' risk" (alpha) or

"manufacturers' risk" (beta). (or is it?) I see it as an expectation

that if

the ratio of some relevant quantity (e.g. log transformed AUC) for two

products is within 20%, these two products will be equivalent.

This was a result of Hatch-Waxman Act of 1984 where an assumption was

made

that

duplicates of pioneer drugs would be the same as the innovator's drug. A

second assumption was that bioequivalence data was an effective

surrogate

for safety and effectiveness. There is some controversy about these

assumptions, but this is what the law was about. Twenty percent was

considered as a fairly good margin, and many medical professionals

believed

that for drugs that have a wide therapeutic index, twenty percent is not

important at all.

Overview of Hatch-Waxman:

http://www.oblon.com/Pub/display.php?hatchwax.html

2. Confidence intervals: Now, we are going to have some variability in

the

estimate. So C.I.s are relied upon to get an idea of the uncertainty in

the

estimation. However, should it be 95% C.I. or 90% C.I.? is not

mentioned in

the BA/BE guidance.

In other words: if the C.I., a measure of uncertainty, falls within the

set

BE limit(one could set it to 10%, 20% or 50%), it is reasonable to

assume

equivalency. Also, it should be noted that these analyses are performed

on

log-transformed data.

Am I making sense here?

Pravin

PS: Please note that these are my personal views and understanding of

the

topic.

Pravin Jadhav

Graduate student

Department of Pharmaceutics

MCV/VCU - On 2 Oct 2004 at 12:15:10, helmut.schuetz.aaa.bebac.at sent the message

Back to the Top

Dear Angus, dear Hans,

just another try:

null hypothesis [mu(T) and mu(R) are not equivalent]

H0: mu(T)/mu(R)theta2

alternative hypothesis [mu(T) and mu(R) are equivalent]

H1: theta1The interval [theta1,theta2] denotes the acceptance range for any given

parameter,

where an acceptable deviation of 0.20 leads to

theta1 (1-AD) 0.80,

and

theta21/theta11.25.

H0 : null hypothesis (inequivalence)

H1 : alternative hypothesis (equivalence)

mu : expected mean

T : test formulation

R : reference formulation

theta1: lower goalpost (acceptance limit)

theta2: upper goalpost (acceptance limit)

AD : acceptable deviation of T from R

(generally 0.20, may be extended [e.g. to 0.25] in some

legislations

[EU,AUS,NZ,TR,MAL,RC; recommended by WHO] based on

safety/efficacy

of the drug)

BE : bioequivalence

BA : bioavailability

Since the expected (population) means mu(T) and mu(R) are unknown, they

are

estimated from their sample means x_(T) and x_(R) by means of confidence

intervals.

Two types of error must be observed:

alpha : error type I, risk I

In BE patient's risk to be treated with an _inequivalent_

formulation, which was (erroneously) claimed to be equivalent.

Generally set to <0.05 (0.025 in Brazil for narrow therapeutic

range drugs).

Since a given patient can only show BA _either_ below _or_ above

the stated AD, the risk for the population becomes _2*alpha_

(and

therefore we are building a >90% confidence interval)

beta : error type II, risk II

In BE producer's risk for an equivalent formulation

[mu(T)/mu(R)1]

to be declared inequivalent (the chance to fail to show BE).

Both errors are used in sample size estimation, where beta generally is

set

within 0.10-0.20 (power1-beta80%-90%). Sample sizes corresponding to

power <70% or >90% will raise ethical issues (either unecessary

tratment of

subjects with a rather low chance to show BE, or probable cause for

'forced' BE).

Best regards,

Helmut

P.S.: Thanks to Hans, who corrected my first sloppy mail.

P.P.S.: .-at-.David:

Previous mails were produced as 'plain text' by Mozilla 1.7.1

This time I give it a trial with a web-mail application

SquirrelMail 1.2.10...

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html - On 3 Oct 2004 at 13:46:18, =?ISO-8859-1?Q?Helmut_Schutz?= (helmut.schuetz.-at-.bebac.at) sent the message

Back to the Top

Hi Pravin,

> However, should it be 95% C.I. or 90% C.I.? is not mentioned in the

BA/BE guidance.

Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];

Guidance for Industry: Statistical Approaches to Establishing

Bioequivalence.

http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)

states at B. Statistics:

[...] average bioequivalence and involves the calculation of a 90%

confidence

interval for the ratio of the averages (population geometric means) of

the measures for the T and are products. To establish BE, the calculated

confidence interval should fall within a BE limit, usually 80-125% for

the ratio of the product averages.

IMHO 90% CI is applied worldwide, with the exception of Brazil

(ANVISA), where a 95% CI is required for BE of narrow therapeutic range

drugs.

Regards,

Helmut

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html - On 4 Oct 2004 at 03:14:41, vardhini kirthivas (vardhinikirthivas.-at-.yahoo.com) sent the message
Hi.,

Back to the Top

Is it possible to estimate the sample size for Pivotal BE Studies from the results of Pilot BE studies.

Can some one explain how?

Regards

Vardhini - On 4 Oct 2004 at 09:47:29, "Kurnik, Daniel" (daniel.kurnik.-at-.Vanderbilt.Edu) sent the message

Back to the Top

Hi Helmut,

can I ask: why is

theta2 = 1/theta1,

and not

theta2= (1+AD) = 1.2 ?

Daniel - On 5 Oct 2004 at 09:14:31, "Mitesh Gandhi" (miteshgandhi.aaa.alembic.co.in) sent the message

Back to the Top

Dear vardhini

One of the objective of carrying our pilot BE study is to get idea of

sample

size for pivotal trial. From pilot study, you will get intra CV%, T/R

ratio. and from this you can have estimate of sample size to generate

80%

power.

For detail, you can refer Pharamceutical statistics by Bolton.

Hope, this will help you at somewhat extent.

Regards

Mitesh - On 6 Oct 2004 at 12:13:55, Helmut_Schutz (helmut.schuetz.-a-.bebac.at) sent the message

Back to the Top

Dear Daniel,

you wrote:

why is

theta2 = 1/theta1,

and not

theta2= (1+AD) = 1.2 ?

The statistical model for AUC and Cmax is multiplicative, not additive.

If we assume no carryover (sufficient washout period, verified by taking

a predose sample in each treatment period) it is given with:

X(ijk) = mu * pi(k) * Phi(l) *s(ik) * e(ijk)

where

Xijk: log-transformed response of j-th subject [j=1,_,n(i)] in i-th

sequence [i=1,2] and k-th period [k=1,2]

mu: global mean, mu(l): expected formulation means [l=1,2:

mu(1)=mu(test), mu(2)=mu(ref.),

pi(k): fixed period effects,

Phi(l): fixed formulation effects [l=1,2: Phi(1)=Phi(test),

Phi(2)=Phi(ref.)]

s(ik): random subject effect,

e(ijk): random error.

Main Assumptions:

a) All ln{s(ik)} and ln{e(ijk)} are independently and normally

distributed about unity with variances sigma(Z)(s) and sigma(Z)(e).

b) All observations made on different subjects are independent.

The assumption of a multiplicative model is based on:

1) pharmacokinetic grounds

from

[F(test) * AUC(test)] / [D(test) * CL(test)] , [F(ref.) * AUC(ref.)] /

[D(ref.) * CL(ref.)]

assuming

c) D(test) = D(ref.) and

d) CL(test) = CL(ref.)

we are apble to calculate

F(rel.) = BA = AUC(test.) / AUC (ref.)

2) analytical grounds

Serial dilutions used in the preparation of calibration curves lead

according to the law of error propagation to a multiplicative error

model

Therefore we log-transform AUC and Cmax. In the logarithmic scale

equidistance is given by [x,1/x] --> [0.9/1.11], [0.80/1.25],

[0.75/1.33]...

Some remarks on assumptions:

ad a) According to Good Statistical Practice this can (and should) be

tested (1). If rejected, one should opt for a nonparametric method.

Funny enough FDA is against this procedure (2).

ad b) Speaks aginst the inclusion of twins in BE-studies ;-)

ad c) Dose correction according to actual content may be reasonable

(also recommended in some guidelines [Canada, WHO])

ad d) In a 2x2 crossover it is impossible to separate inter-occassion

variability from inter-treatment variability, therefore we rely on this

assumption. A replicate design would be needed to separate these

effects. For highly variable drugs/drug products the use of AUC*k(el)

instead of AUC _may_ help (3).

(1) Jones, B. and M.G. Kenward;

Design and Analysis of Cross-Over Trials.

2nd Edition, Chapman & Hall, Boca Raton, London, New York, Washington,

D.C. (2003)

"No analysis is complete until the assumptions that have been made in

the modeling have been checked. Among the assumptions are that the

repeated measurements on each subject are independent, normally

distributed random variables with equal variances. Perhaps the most

important advantage of formally fitting a linear model is that

diagnostic information on the validity of the assumed model can be

obtained. These assumptions can be most easily checked by analyzing the

residuals."

(2) Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];

Guidance for Industry: Statistical Approaches to Establishing

Bioequivalence.

http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)

"The limited sample size in a typical BE study precludes a reliable

determination of the distribution of the data set. Sponsors and/or

applicants are not encouraged to test for normality of error

distribution after log-transformation [...].

(3) H.Y. Abdalah;

An Area Correction Method To Reduce Intrasubject Variability In

Bioequivalence Studies.

J Pharm Pharmaceut Sci 1 (2), 60-65 (1998)

Best Regards

Helmut

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html - On 6 Oct 2004 at 12:13:55, Helmut_Schutz (helmut.schuetz.aaa.bebac.at) sent the message

Back to the Top

Dear Daniel,

you wrote:

why is

theta2 = 1/theta1,

and not

theta2= (1+AD) = 1.2 ?

The statistical model for AUC and Cmax is multiplicative, not additive.

If we assume no carryover (sufficient washout period, verified by taking

a predose sample in each treatment period) it is given with:

X(ijk) = mu * pi(k) * Phi(l) *s(ik) * e(ijk)

where

Xijk: log-transformed response of j-th subject [j=1,...,n(i)] in i-th

sequence [i=1,2] and k-th period [k=1,2]

mu: global mean, mu(l): expected formulation means [l=1,2:

mu(1)=mu(test), mu(2)=mu(ref.),

pi(k): fixed period effects,

Phi(l): fixed formulation effects [l=1,2: Phi(1)=Phi(test),

Phi(2)=Phi(ref.)]

s(ik): random subject effect,

e(ijk): random error.

Main Assumptions:

a) All ln{s(ik)} and ln{e(ijk)} are independently and normally

distributed about unity with variances sigma^2(s) and sigma^2(e).

b) All observations made on different subjects are independent.

The assumption of a multiplicative model is based on:

1) pharmacokinetic grounds

from

[F(test) * AUC(test)] / [D(test) * CL(test)] , [F(ref.) * AUC(ref.)] /

[D(ref.) * CL(ref.)]

assuming

c) D(test) = D(ref.) and

d) CL(test) = CL(ref.)

we are apble to calculate

F(rel.) = BA = AUC(test.) / AUC (ref.)

2) analytical grounds

Serial dilutions used in the preparation of calibration curves lead

according to the law of error propagation to a multiplicative error

model

Therefore we log-transform AUC and Cmax. In the logarithmic scale

equidistance is given by [x,1/x] --> [0.9/1.11], [0.80/1.25],

[0.75/1.33]...

Some remarks on assumptions:

ad a) According to Good Statistical Practice this can (and should) be

tested (1). If rejected, one should opt for a nonparametric method.

Funny enough FDA is against this procedure (2).

ad b) Speaks aginst the inclusion of twins in BE-studies ;-)

ad c) Dose correction according to actual content may be reasonable

(also recommended in some guidelines [Canada, WHO])

ad d) In a 2x2 crossover it is impossible to separate inter-occassion

variability from inter-treatment variability, therefore we rely on this

assumption. A replicate design would be needed to separate these

effects. For highly variable drugs/drug products the use of AUC*k(el)

instead of AUC _may_ help (3).

(1) Jones, B. and M.G. Kenward;

Design and Analysis of Cross-Over Trials.

2nd Edition, Chapman & Hall, Boca Raton, London, New York, Washington,

D.C. (2003)

"No analysis is complete until the assumptions that have been made in

the modeling have been checked. Among the assumptions are that the

repeated measurements on each subject are independent, normally

distributed random variables with equal variances. Perhaps the most

important advantage of formally fitting a linear model is that

diagnostic information on the validity of the assumed model can be

obtained. These assumptions can be most easily checked by analyzing the

residuals."

(2) Anonymous [FDA, Center for Drug Evaluation and Research (CDER)];

Guidance for Industry: Statistical Approaches to Establishing

Bioequivalence.

http://www.fda.gov/cder/guidance/3616fnl.pdf (January 2001)

"The limited sample size in a typical BE study precludes a reliable

determination of the distribution of the data set. Sponsors and/or

applicants are not encouraged to test for normality of error

distribution after log-transformation [...].

(3) H.Y. Abdalah;

An Area Correction Method To Reduce Intrasubject Variability In

Bioequivalence Studies.

J Pharm Pharmaceut Sci 1 (2), 60-65 (1998)

Best Regards

Helmut

--

Helmut Schutz

BEBAC

Consultancy Services for Bioequivalence and Bioavailability Studies

Neubaugasse 36/11

A-1070 Vienna/Austria

tel/fax +43 1 2311746

http://BEBAC.at http://forum.bebac.at

http://www.goldmark.org/netrants/no-word/attach.html

[Sorry, I caused a couple of errors in the first version - db]

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