- On 14 Dec 1999 at 23:12:07, david_william.tudor.-a-.pharma.Novartis.com sent the message

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Dear PharmPK group,

I know I am asking a question that has been discussed ad nauseam, but

nevertheless, I am interested in your opinions about the statistical

presentation of the tmax results of pk-studies. As we all know, concentration

measurements are taken only at pre-determined (fixed) time points and are thus

not continuous random variables in a proper sense. Obviously, the

data observed

are not normally distributed, so it is not particularly elegant to report means

and standard deviations. What do you suggest ? Medians, Modes,

other ? Thanks

for your responses.

David Tudor - On 15 Dec 1999 at 21:24:54, David_Bourne (david.-at-.boomer.org) sent the message

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[Two replies - db]

Date: Wed, 15 Dec 1999 09:18:26 +0200

From: Andrew Volosov

X-Accept-Language: en,pdf

To: PharmPK.at.boomer.org

Subject: Re: PharmPK Statistical description of tmax

Dear David,

You might find useful the method we published a couple of years ago.

This method

deals with the case when tmax cannot be properly determined by simple

observation.

The strong side of the method is that it utilizes all data points you

have. The

drawback is that it can be used only when your data fits the Bateman "kit-kat"

equation. We have applied this method in several studies quite successfully.

The reference is:

"Use of Mean Residence Time to Determine the Magnitude of Difference

Between Rate

Constants and to Calculate tmax in the Bateman Equation". Biopharm.

Drug Dispos.

20: 3-9 (1999).

Andrew Volosov

The Hebrew University of Jerusalem

School of Pharmacy

volosov.-a-.md2.huji.ac.il

---

Date: Wed, 15 Dec 1999 03:33:19 -0700 (MST)

X-Sender: ml11439.at.pop.goodnet.com

To: PharmPK.-at-.boomer.org

From: ml11439.aaa.goodnet.com (Michael J. Leibold)

Subject: Re: PharmPK Statistical description of tmax

David,

W.W.Daniel, the author of "Biostatistics", also has published a

statistics book: "Applied Nonparametric Statistics", PWS Kent, Boston 1990.

In nonparametric estimates of central tendency the median rather than the

mean is the location parameter for central tendency. Nonparametric

methods for estimating a population median include the Sign test and

the Wilcoxan Signed-ranks test. Other nonparametric methods are also

available for comparing test groups, similar to parametric analysis

of variance.(1)

A Chi-Sqaure goodness of fit test can be used to determine if the

distribution of a sample of variables is normal, log-normal or fits

another probability distribution(3). That is, to test for deviation from

a normal distibution and the need for nonparametric statistical analysis.

The nonparametric methods can also be used in when the samples fit a

normal distribution, and are proposed to have the same statistical power

as the parametric methods in this case(2).

Also:NPML

Also, there are advanced methods of nonparametric estimation such

as the the "Nonparametric Maximum Likelihood Method". For this method,

computer software has been developed which renders a nonparametric

maximum likelihood estimate of the distribution of parameters without

any prior assumptions of a normal distribution. The kinetic parameters

and distributions obtained with this method can then be used in Bayesian

regression programs for dose optimization.(4)

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com

References:

1) Daniel, W.W., Applied Nonparametic Statistics, PWS Kent, Boston 1990

2) Glantz, S.A., Primer of Biostatistics, McGraw Hill, New York 1997

3) Dowdy, S., Wearden, S., Statistic for Research, Wiley Interscience,

New York 1983

4) Taright, N., et al., Nonparamettic Estimation of Population Characteristics

in the kinetics of lithium......., Ther Drug Monitoring 1994;16(3):258-269 - On 16 Dec 1999 at 22:32:03, David_Bourne (david.-a-.boomer.org) sent the message

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[Two replies - db]

Reply-To: lesassays.at.ukneqasaa.win-uk.net (Les White)

To: PharmPK.-at-.boomer.org

Date: Thu, 16 Dec 1999 12:37:15

Subject: Re: PharmPK Statistical description of tmax

From: lesassays.aaa.ukneqasaa.win-uk.net (Les White)

both if they are very different

---

X-Sender: flerner.-at-.mail.intramed.net.ar

Date: Thu, 16 Dec 1999 17:57:21 -0300

To: PharmPK.aaa.boomer.org

From: Federico Ezequiel Lerner

Subject: Re: PharmPK Statistical description of tmax

Dear all:

A few month ago we proposed to analyses the normal distribution of Tmax an

other Pk parameters and describe those according to the results. See: J.

Clin Pharmacol 1999; 39: 1053-1061 and also Ther Drug monit 1999; 21: 200-207

regards

Federico Lerner, MD - On 17 Dec 1999 at 19:48:48, "Jia, Xinwei [JANUS]" (XJia.-at-.JANUS.JNJ.com) sent the message

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In nature, the observed data of Tmax better be described as from a discrete

uniform distribution. Even though, it may not be as that accurate. Consider

this: the likelihood of very large (i.e., towards the end portion of the

scheduled plasma sampling times) Tmax value usually is very small. I would

prefer using Median, Mode, Maximum, and Minimum measures. If there is a

need for confidence interval calculation, I would prefer using nonparametric

approach.

Xinwei Jia

Biostatistics

Janssen Research Foundation - On 27 Dec 1999 at 19:23:10, "Osama Ziada" (oziada.at.hotmail.com) sent the message

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Hi colleagues

in BIO-EQUIVALENCE STUDIES

I'll appreciate if anyone explain to me the significance and the

limit of tmax ,in case of comparing two oral products e.g tablets

for AUC I know that the two products are considered bioequivalant if

the AUC as well as C-max are from 80% -120% from the reference

product , this is according to FDA

Please correct me if this not right.

Also what can be happen if the new product absorption is improved to

be far better than the original reference product. i.e more than 120%

,should this considered NON equivalent ??

thanks

Osama Ziada

Julphar - On 28 Dec 1999 at 16:52:12, Art Straughn (ASTRAUGHN.-a-.utmem1.utmem.edu) sent the message

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To: Osama Ziada

Your inquiry concerning bioavailability/bioequivalence indicates that you have

not yet reviewed the FDA's guidances on the subject which can be found at

http://www.fda.gov/cder/guidance/index/htm. In contradiction to what you stated

you knew, the FDA does not consider two products bioequivalent if the Cmax and

AUC are within 80-120%. What they do require is that the 90% confidence

interval for the ln transformed metrics must be within 80-125%. This is very

different than the average AUC and Cmax (I assume you meant average) of the

test formulation being within 80-120% of the reference. This is a perception

that many people have and it must be made clear that if a formulation passes

confidence intervals it is highly unlikely that the mean differences are more

than 10%, and in most cases they will be within 5%. Next, if a test

formulation is "better" than the reference (for example: CI's for AUC are 110%

to 140%, it is not bioequivalent and that's that. This does not mean that a

firm cannot market this "better" formulation, but it will not be approvable as

therapeutically equivalent. It must undergo further clinical testing for safety

and efficacy. Finally, although the FDA is not currently requiring Tmax's to

pass some specified criteria, they must be reported, and the draft guidances do

address some of the issues associated with how they will deal with Tmax in the

future. Go to the web.

Art Straughn

Memphis - On 28 Dec 1999 at 23:17:23, GOBBURUJ.aaa.cder.fda.gov sent the message

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Hello,

You can find relevant guidance on BE studies at :

http://www.fda.gov/cder/guidance/index.htm

These are my personal views and not necessarily of the agency:

I think the pharmacodynamic implications of the test/reference ratio

being greater than 125% (or < 80%) are more meaningful before deeming

some test formulation inequivalent to a reference. A concentration -

effect model should help you in translating the PK differences into PD

differences.

Regards,

Joga

Joga Gobburu,

Pharmacometrics,

CDER, FDA - On 28 Dec 1999 at 23:59:47, David_Bourne (david.-at-.boomer.org) sent the message

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[A few replies - db]

Date: Tue, 28 Dec 1999 00:44:56 -0700 (MST)

X-Sender: ml11439.-a-.pop.goodnet.com

To: PharmPK.-at-.boomer.org

From: ml11439.-a-.goodnet.com (Michael J. Leibold)

Subject: Re: PharmPK Re: Statistical description of tmax

Hello Osama,

Tmax is related to Ka according as follows:

Tmax= [1/(Ka-Ke)][Ln(Ka/Ke)]

A decrease in Ka or rate of absorption would not change the AUC, which

is determined by F, Xo, Vd and Ke. Bioeqivalence studies standardize the

other parameters in this equation so that AUC is effected principally by

F or bioavailability.

Cmax should decrease as the Tmax increases according to the following

equation:

Cmax= [FXo/V]e-KeTmax

The Tmax or Cmax should be useful in comparing the rate of absorption of

different oral products. But, I think that F is the most important factor

in comparing bioequivalence, and I think that this is what the FDA uses.

Mike Leibold, PharmD, RPH

ML11439.-a-.goodnet.com

---

From: HARRY.MAGER.HM.aaa.bayer-ag.de

To: " - *PharmPK.aaa.boomer.org"

Subject: Antwort: PharmPK Re: Statistical description of tmax

Date: Tue, 28 Dec 1999 08:57:44 +0100

Due to the logarithmic transformation, the confidence intervals should be

within 80% to about 125%.

Testing for equivalence does not involve inferiority/superiority. Accordingly,

when one out of two formulations turns out to be superior in terms of a

pharmacokinetic parameter, the two formulations are not equivalent. However,

you can always test the hypothesis equivalent or superior versus inferior.

Best regards and have a great 2000.

---

X-Sender: denucci.-at-.mailhost.dglnet.com.br

Date: Tue, 28 Dec 1999 10:02:21 -0300

To: PharmPK.at.boomer.org

From: Gilberto de Nucci

Subject: Re: PharmPK Re: Statistical description of tmax

Dear Osamar

Please note that 80-125% is the range accepted by the FDA for both AUC and

Cmax

Regards

Gilberto De Nucci

---

From: Thomas.Senderovitz.aaa.ferring.com

To: PharmPK.aaa.boomer.org

Subject: RE: PharmPK Re: Statistical description of tmax

Date: Tue, 28 Dec 1999 14:56:18 +0100

Dear Osama,

To answer your last question first: Yes, if the AUC of the test

product is outside the 90% CI for the ratio of the means, then the

two products are NOT bioequivalent. If you are not able to establish

bioequivalence, then therapeutic equivalence might be established,

although this is considerable more difficult - you need to show

equivalence of clinical efficacy and safety!

tmax should preferably be described my nonparametric methods (in

accordance to guidelines), and hence median and range as descriptive

statistics are appropriate. For comparison between test and reference

product with respect to tmax, a nonparametric test can be used, and

guidelines do not state level of significance (but i guess 5% would

be the usual).

Hope this helps.

Thomas Senderovitz - On 29 Dec 1999 at 20:46:29, David_Bourne (david.aaa.boomer.org) sent the message

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[A few replies - db --- Happy New Year everyone!]

Date: Wed, 29 Dec 1999 01:45:49 -0700 (MST)

X-Sender: ml11439.aaa.pop.goodnet.com

To: PharmPK.-at-.boomer.org

From: ml11439.-a-.goodnet.com (Michael J. Leibold)

Subject: Re: PharmPK Statistical description of tmax

Hello David,

I further considered your question regarding statistical treatment

of pharmacokinetic data:

I checked the FDA CDER site and found that the FDA uses parametric

analysis of log-transformed data for AUC and Cmax. This is in reference to

your question regarding the statistical analysis of Cmax data (or Tmax data)

using nonparametric methods. That is, a log-normal distribution is

assumed for AUC and Cmax data for a parametric analysis of the data. So, if

your data does not appear normally distributed, try looking at the log-

transformed data (log10 or ln).

http://www.fda.gov/cder/guidance/index.htm

Average, Population, and Individual Approaches to Establishing

Bioequivalence [HTML] or [Acrobat] or [Word97] (Issued 8/1999, Posted

8/27/1999, Word and Acrobat version reposted 9/8/99)

From Web Site:

1. Average Bioequivalence

a. Overview

"Parametric (normal-theory) methods are recommended for the analysis of

log-transformed BE measures. For average BE using the criterion stated

in equations 2 or 3 above, the general approach is to construct a 90%

confidence interval for the quantity :T-:R and to reach a conclusion

of average BE if this confidence interval is contained in the interval

[-2A , 2A]. Due to the nature of normal-theory confidence intervals,

this is equivalent to carrying out two one-sided tests of hypothesis

at the 5% level of significance (Schuirmann 1987).

The 90% confidence interval for the difference in the means of the

log-transformed data should be calculated using methods appropriate to

the experimental design. The antilogs of the confidence limits obtained

constitute the 90% confidence interval for the ratio of the geometric

means between T and R product."

Mike Leibold, PharmD, RPH

ML111439.-a-.goodnet.com

---

Date: Wed, 29 Dec 1999 21:56:07 +1300

From: Nick Holford

X-Accept-Language: en

To: PharmPK.at.boomer.org

Subject: Re: PharmPK Re: Statistical description of tmax

> A decrease in Ka or rate of absorption would not change the AUC, which

> is determined by F, Xo, Vd and Ke.

AUC is determined by F, Dose and Clearance. Volume of distribution

does not influence AUC 0-inf.

CL = Vd * Ke is algebra not pharmacokinetics.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

---

X-Sender: walt.at.mail.simulations-plus.com

Date: Wed, 29 Dec 1999 12:25:46 -0800

To: PharmPK.aaa.boomer.org

From: Walt Woltosz

Subject: Re: PharmPK Re: Statistical description of tmax

I have always been impressed with the responses provided by certain members

of the PharmPK list server - especially those from Mike Leibold and Nick

Holford, but several others as well, so I do not mean to be critical here.

There are some hidden assumptions in some of the replies to this inquiry,

and they have been incorporated in other posts to this list server as well.

These assumptions may hold for some compounds, but could get you into

trouble for others.

I think it is very important to recognize that any analytical approach that

uses a single, constant value for Ka is a simplification that may work for

many compounds that have high solubility and permeability, but it can be

very misleading for those that are either low in permeability or

solubility, or both.

As a relative newcomer to this field, but with over 25 years' experience in

modeling and simulation, it has struck me as a bit strange that many

discussions seem to dwell on handling pharmacokinetics with higher order

models, while maintaining a constant Ka. If you're trying to

predict/estimate Cmax and Tmax, which are affected by the balance between

absorption and clearance pulling plasma concentration in opposite

directions, then you need to consider that for many compounds, absorption

rate is not a constant, but can vary with pH, local concentration, transit

times, saturation of transport mechanisms, dissolution rates, and other

factors. For such compounds, only an analysis that incorporates the

interactive effects of both pharmacokinetics and varying absorption rates

can hope to provide reasonable estimates.

Last year I visited a generic house to demonstrate GastroPlus(TM). Within

an hour, we showed by simulation that one of the company's generic

formulations would significantly overshoot Cmax compare to the original

formulation. (I found out later they had already learned this in clinical

trials, but they wanted to see what the prediction would show.) If the

company had used the simulation prior to going to clinical trials, they'd

have saved themselves considerable time and money. A simple constant Ka

model did not provide such a prediction.

Walt Woltosz

Chairman & CEO

Simulations Plus, Inc. (SIMU)

1220 W. Avenue J

Lancaster, CA 93534-2902

U.S.A.

http://www.simulations-plus.com

Phone: (661) 723-7723

FAX: (661) 723-5524

walt.-a-.simulations-plus.com

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