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
Back to the Top
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
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
Back to the Top
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]
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)
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
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]
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]
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
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
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
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
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
Back to the Top
Hi Helmut,
can I ask: why is
theta2 = 1/theta1,
and not
theta2= (1+AD) = 1.2 ?
Daniel
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
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
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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