- On 4 Jan 2006 at 11:58:35, "Shilpi Khan" (SKhan.-at-.cedracorp.com) sent the message

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Happy new year to all,

I have a question regarding dose linearity. In general, we examine, dose

linearity using a power model,

P = a * Dose^b

where P represents the dependent variable (Cmax, AUClast, AUCinf) and, a

and b are constants. A value of b~1 indicates linearity.

(To perform this simple regression in SAS, we use PROC REG on log

transformed data. The value of slope is 'b' and the exponentiation of

the intercept is 'a')

Do you have any comment or suggestion on this model?

Thanks in advance,

Shilpi

Shilpi Khan, M.S.

Staff Scientist/Biostatistician

CEDRA Corporation

Austin, TX 78754 - On 4 Jan 2006 at 13:30:11, dan combs (dan_combs.at.comcast.net) sent the message

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Shilpi:

Here is a reference for the method you mentioned. One can use SAS

Proc Mixed or the WinNonlin Linear Mixed Effects modelling feature.

Excel power curve plots give the same 'a' and 'b' parameter estimates

but does not compute confidence intervals, which are needed for the

assessment.

BP Smith, FR Vandenhende, KA DeSante, NA Farid, PA Welch, JT

Callaghan, ST Forgue. Confidence Interval Criteria for Assessment of

Dose Proportionality. Pharmaceutical Research, Vol. 17, No. 10, 2000.

Dan Combs

Combs Consulting Service - On 4 Jan 2006 at 17:26:34, Angusmdmclean.-at-.aol.com sent the message

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Shilpi

You regession model is as you indicate and I reproduce it below:

P = a * Dose^b where P is a Pk exposure parameter e.g. Cmax.

My comment is as follows:

Can you tell me what your null hypothesis (Ho) is and how are you

evaluating the p value for this test.

Angus McLean Ph.D,

8125 Langport Terrace,

Suite 100,

Gaithersburg,

MD 20877

Tel 301-869-1009

fax 301-869-5737 - On 5 Jan 2006 at 09:22:05, "Vikesh Kumar Shrivastav" (vikeshk.shrivastav.-a-.ranbaxy.com) sent the message

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The following message was posted to: PharmPK

Hi Shilpi

Yes the equation of power model for testing Dose Linearity is

P = a * Dose^b

where P represents the dependent variable (Cmax, AUClast, AUCinf)

But i think apart from log-transformation data also needs to be dose-

normalized either to Higher Dose or Lower Dose.

On log transformation our equation becomes: Log(p) = a + b*log(dose)

Our null hypothesis is H0: b = 1.

We can use Proc Reg in SAS on the log-transformed data.

You can add following statement in Proc reg inorder to test for b=1:

SLOPE : test Log_DOSE = 1;

Hope this helps.....

Vikesh S - On 5 Jan 2006 at 09:12:12, "Henri Merdjan" (henri.-at-.novexel.com) sent the message

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Dear Shilpi,

The suggested model makes perfect sense. However, I would like to

challenge the use of log-transformation. In my humble opinion, you

may do a better job by running non-linear regression on untransformed

data. In that case, linear regression on log-transformed data would

still be useful in providing initial parameter estimates.

Hope this helps.

Henri

Henri MERDJAN, Pharm, AIHP

Head of Drug Metabolism and Pharmacokinetics

NOVEXEL S.A.

Parc Biocitech

102 Route de Noisy

F-93230 Romainville

France

Tel +33 (0)1 57 14 07 45

Fax +33 (0)1 48 46 39 26

Web www.novexel.com - On 5 Jan 2006 at 18:57:26, =?ISO-8859-1?Q?J=FCrgen_Bulitta?= (bulitta.-at-.ibmp.osn.de) sent the message

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Dear Dr Merdjan, Dear All,

I agree that the power model (AUC = a * Dose^b) is a reasonable way

to statistically test dose linearity. There might be some drawbacks

for Cmax, because the rate of absorption is sometimes slower at

higher doses (e.g. if the drug has low solubility). In this case

fitting the full population PK model will be superior to NCA in order

to better understand the PK data.

It is important to adequately account for the between subject

variability (BSV) in Cmax and AUC, irrespective if one uses linear or

log-scale to fit the data. I would assume a log-normal distribution

for Cmax and AUC. If one fits the power model on linear scale, one

would have to account for a proportional error structure (BSV)

explicitly. Therefore, I would prefer ANCOVA on log-scale as a quick

way to analyze dose linearity data, because an additive error

structure on log-scale turns into a proportional error structure on

linear scale.

Besides a criterion for statistical significance of dose linearity,

an equivalence based criterion should also be considered. Even if a

drug shows a nonlinear curve of AUC vs. dose, this may have only a

limited effect on the pharmacodynamics at therapeutic doses. One way

to do so is to use equivalence statistics with dose-normalized AUC

(and Cmax) in addition to fitting the power model.

Hope this helps

Best regards

Juergen

--

Juergen Bulitta, M.Sc.

Research Scientist

IBMP - Institute for Biomedical and Pharmaceutical Research

Paul-Ehrlich-Strasse 19

90562 Nurnberg - Heroldsberg

Germany - On 5 Jan 2006 at 13:13:11, Angusmdmclean.-at-.aol.com sent the message

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Henri:

What you suggest to evaluate nonlinear regression on untransformed

data makes sense but exactly how would you introduce the null

hypotheses and obtain a p factor. Exactly what computer program do

you have in mind.

can you comment?

Angus McLean Ph.D,

8125 Langport Terrace,

Suite 100,

Gaithersburg,

MD 20877

tel 301-869-1009

fax 301-869-5737 - On 11 Jan 2006 at 10:25:23, "Henri Merdjan" (henri.-at-.novexel.com) sent the message

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The following message was posted to: PharmPK

Dear Angus,

I guess a sensible way of approaching the problem would be to state

the null hypothesis as: " exponent=1 ". I would expect a nonlinear

regression piece of software to provide confidence intervals around

parameters' estimates (by the way, I am not recommending any specific

soft). Accepting/rejecting H0 is then straightforward. Just answer

the question: does the CI include 1? So far, this is theory.

Real life may be a bit different. In my experience, the major

drawback of the hypothesis testing approach is that an exponent may

be statistically different from, however "close" to unity. Let me go

through a numerical example. Let's imagine the exponent is 1.08 with

a 95%CI of 1.03 to 1.13. In strict statistical terms, this is a

significant deviation from linearity. However, what is its practical

relevance? Such a power model would suggest that each time you double

the dose, the PK parameter of interest (eg Cmax or AUC) will increase

by a 2.1-fold factor instead of 2. Not a big deal!

In summary, you may find some interest in setting acceptance limits

for the exponent rather than, or in addition to, testing some

hypothesis.

Hope this helps,

Henri

Henri MERDJAN, Pharm, AIHP

Head of Drug Metabolism and Pharmacokinetics

NOVEXEL S.A.

France

Tel +33 (0)1 57 14 07 45

Fax +33 (0)1 48 46 39 26

Web www.novexel.com - On 12 Jan 2006 at 11:21:55, "J.H.Proost" (J.H.Proost.at.med.umcg.nl) sent the message

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The following message was posted to: PharmPK

Dear Henri,

I fully agree with your statement about the relevance of confidence

intervals.

But is real life, there may be also a different problem. What should

one conclude if the exponent differs from 1 to a clinically relevant

extent, but with a confidence interval including 1? E.g. exponent 1.3

and confidence interval 0.9 to 1.7. What is the conclusion now?

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.rug.nl - On 12 Jan 2006 at 14:04:20, Angusmdmclean.-at-.aol.com sent the message

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Johannes: what a physician want to know is if you double the dose

would you get double the maximum concentration (Cmax)? Given the

adverse event profile of the drug on a case by case basis there may

be concern about the probability of the drug (on dose doubling)

producing disproportionately higher adverse events on account of

higher Cmax values (than anticipated from linearity). Perhaps in

cases, where there is uncertainty about proportionality

considerations, then dose would be more carefully titrated with

clinical response in mind to a patient over a period of time with

intermediate dose strengths.

Best Regards,

Angus McLean Ph.D,

8125 Langport Terrace,

Suite 100,

Gaithersburg,

MD 20877

tel 301-869-1009

fax 301-869-5737 - On 13 Jan 2006 at 14:04:19, "Henri Merdjan" (henri.aaa.novexel.com) sent the message

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The following message was posted to: PharmPK

Dear Johannes,

This is a fair point. The question you are asking illustrates the

level of uncertainty possibly associated with a parameter estimate.

In this particular example, the CI is so "wide" that you cannot

really decide whether the exponent value is actually closer to unity,

or to the central estimate of 1.3, or to some even higher value. In

such a scenario, I would simply recommend a careful dose escalation.

Best regards,

Henri

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