- On 4 Mar 2003 at 15:49:26, "Isabelle Ragueneau-Majlessi" (imaj.aaa.u.washington.edu) sent the message

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Hello-- I am currently analyzing PK data from patients who received

stable doses of phenytoin, in whom we studied the effect of the

addition of a drug X. The patients did not receive the same dose

ofphenytoin but had their individual dose stabilized before and

throughout the study. Becausephenytoin PK is known to be nonlinear, I

was wondering which would be the best way to compare phenytoin PK

parameters (before and after drug X) in that case. Can I still

normalized to a common dose before performing the log transformation of

AUC and Cmax?

Thanks for your input.

Isabelle

Isabelle Ragueneau-Majlessi, MD

University of Washington

Dept. of Pharmaceutics, Box 357610

Health Sciences Building -H272

imaj.aaa.u.washington.edu

Phone- (206) 543 4669

Fax-: (206) 543 3204 - On 5 Mar 2003 at 18:21:27, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

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If you dose normalize for each patient (say the dose when not taking

drug X) then did a pairwise comparison e.g. paired t-test, of the AUC

and Cmax before and after drug X then you could test the null

hypothesis that drug X has no effect on phenytoin PK. This should not

be very sensitive to the assumption of concentration independence if

you were reasonably successful in titrating the dose before and after

drug X to similar phenytoin concentrations.

If you want to do some pharmacokinetic science (as opposed to simply

being satisified with a P less than perspective) then you could

consider estimating the parameters of a pharmacokinetic model that

recognized the concentration dependent elimination of phenytoin. You

could then learn something about the interaction (if it exists) beyond

simply answering the question "Is there an interaction?".

Nick

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 5 Mar 2003 at 09:20:51, "Ana Ruiz" (anar.aaa.sonuspharma.com) sent the message

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Dear Isabelle,

If you know the reason for the no linearity, you should fit the

phenytoin data (all the different doses ) to a model accounting for this

lack of linearity. Normalization of dose is an easy and naive way to

hide the problem, but it is not a real PK solution when there is a known

non-linear behavior.

The other aspect to consider is non-compartmental versus compartmental

data, in this case, I am almost sure that a compartmental analysis will

give you a better estimation.

Normalize a curve of plasmatic concentrations versus time when you have

a no linearity going on does not help at all because you don't know the

correction factor to apply for each dose and how this correction factor

is affected. Think about this: why dose should be the correction

factor???, that applies for linear behavior and the superposition

principle is the rationale behind it but , non linearity is another

business, not all the non-linearities behaves equally. Only a PK model

analyzing the non-linear problem can give you the pk rate constants ,

those should be the same for all the doses. Probably a Michaelis-Menten

kinetics in the elimination process should be the easy option,

Therefore you will define two new pk parameters Vm and Km those will be

relevant at lower concentrations. the knowledge of these two parameters

will allow you to compare data at different doses, but be careful maybe

AUC and Cmax are not the best things to compare!!!

I hope that helps you

Ana Ruiz Pharm.D, PhD.

Sonus Pharmaceuticals

Bothell, WA. - On 5 Mar 2003 at 10:55:05, "Vuong Trieu" (vtrieu.at.AmericanBioScience.com) sent the message

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Nonlinearity is frequently observed when either volume of distribution

is being overwhelmed or when clearance is overwhelmed. The common mean

of analyzing nonlinearity is a plot of AUC versus dose (or Cmax versus

dose). If you cannot fit a linear line through, you have nonlinearity.

Having said that. Is there a commercial package analyzing nonlinearity?

In WinNonLin you would need to simulataneously fit the data for all

doses to give the core Vmax and Km (doable for 2 compartment analysis

but become increasingly complex for 3 compartment analysis). - On 5 Mar 2003 at 18:42:55, "Takimoto, Chris" (ctakimot.-a-.idd.org) sent the message

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With all due respect, I would like to correct your statement. Linearity

in

the AUC vs dose (or Cmax versus dose) plot is not the same as linear

pharmacokinetics. Linear pharmacokinetics refers to a system that can be

described by linear differential equations, such as a multicompartmental

model with first order rate constants and elimination from the central

compartment. A regression line that fits the AUC vs dose plot but does

not

pass through the origin is not strictly linear (doubling the dose does

not

exactly double the AUC). For this reason, it may be preferable to use

the

term "dose proportional" instead of linearity. Also, unweighted

regression

is a poor test for dose proportionality. Potentially better approaches

include application of the power model, ANOVA testing of the log

transformed

AUC/dose or log transformed CL vs dose, or non-parametric tests of the

untransformed AUC or CL vs dose relationship.

For a nice discussion of the power model see the reference by Gough K,

Hutchison M, Keene O, et al: Assessment of dose proportionality: Report

from

the statisticians in the pharmaceutical industry/pharmacokinetics UK

joint

working party. Drug Information Journal 29:1039-1048, 1995

Chris H. Takimoto, MD, PhD, FACP

Associate Professor

Division of Medical Oncology, Department of Medicine

University of Texas Health Science Center at San Antonio - On 5 Mar 2003 at 17:46:57, "Vuong Trieu" (vtrieu.at.AmericanBioScience.com) sent the message

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Thank you for the response!! If the plot of AUC/dose versus dose

deviate from a straight horizontal line, you are having nonlinear PK or

failure of the proportionality test. If Vmax deviates significantly more

than AUC, then is it reasonable to assume saturation of volume of

distribution? In this case Km/Vmax need to be included in the equation

describing Cld to obtain the values which are dose independent. Which

program works better for this? Simultaneously solving equations for 4-5

doses is kind of tough. - On 5 Mar 2003 at 19:21:54, Walt Woltosz (walt.-at-.simulations-plus.com) sent the message

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GastroPlus(tm) handles this easily for up to 3-compartment

pharmacokinetics.

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

E-mail: walt.aaa.simulations-plus.com - On 6 Mar 2003 at 16:41:58, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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Vuong Trieu wrote:

> If Vmax deviates significantly more

> than AUC, then is it reasonable to assume saturation of volume of

> distribution?

I doubt if this is a reasonable explanation. To distinguish parameters

and explore if they are a function of dose/concentration then you need

to stop wasting time with AUC methods and bite the bullet and apply a

differential equation defined compartmental model.

> In this case Km/Vmax need to be included in the equation

> describing Cld to obtain the values which are dose independent. Which

> program works better for this? Simultaneously solving equations for

> 4-5

> doses is kind of tough.

Why make life tough by using methods that are intrinsically wrong for

the problem you are trying to investigate? Compartmental model based

approaches don't care how many doses you want to try.

Nick

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 6 Mar 2003 at 08:56:16, Toufigh Gordi (tgordi.at.buffalo.edu) sent the message

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Dear Vuong,

I guess I agree with people promoting a "real" modeling of your data.

It seems that you have information from several doses, which is an

ideal situation. The process of constructing a model will result in

better understanding of the data as well as what the underlying reasons

for any non-linearity might be. A good starting point would be to find

out more about the compound, its disposition and elimination and put up

a system of "compartments" that describes the observed trend. A good

model will not only fit all your doses resonably well, but also give

you the power to predict un-tried dosings not far off the model limits.

Most software packages will allow you to do a compartmental analysis.

It is fun!

Toufigh Gordi - On 6 Mar 2003 at 08:01:25, "Vuong Trieu" (vtrieu.-at-.AmericanBioScience.com) sent the message

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I was talking about compartmental analysis. However, if there is

nonproportionality between dose and AUC then what?

[The AUC versus dose plot can give an indication of nonlinearity then

.... include nonlinear elimination (MM) in your model and compare fit

with linear versus nonlinear models - db] - On 6 Mar 2003 at 08:12:51, "Vuong Trieu" (vtrieu.aaa.AmericanBioScience.com) sent the message

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Ok. Let clarify this. The kinetic of my compound is nonlinear (meaning

doubling dose does not result in doubling AUC). A three compartmental

model was built and fit into one dose giving correlation of 0.99. Data

from another dose was studied and fitted giving again correlation of

0.98. However, due to the nonlinearity, the parameters for the two

models were completedly different (for instance Vd of one was 8000 and

the other was 80). It is obvious that Vd is limiting and Vmax/Km

function need to be introduced to take into account of this effect and

at least 5 different doses need to be fitted simulataneously to obtain

the correct Vmax and Km. However, this increased the number of

parameters and processing time beyond a regular computer-- you are

talking about 15 differential equations and 7-9 parameters. Anyway of

reducing it down.

[Sounds like you have a nice set of data - 15 de's after 5 does isn't

really a problem - most nonlinear regression programs would handle it

OK. Boomer for example handle 25 de's ;-) - db] - On 6 Mar 2003 at 14:42:29, Toufigh Gordi (tgordi.-at-.buffalo.edu) sent the message

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Dear Vuong,

I am not sure if I follow you when you state that trying to fit the all

the data simultaneously with a model that takes into account a

non-linear process will result in extra parameters. If you analyse the

data by dose group, each group will require a new set of parameters and

the total number of parameters will be quite large. Moreover, those

models will not be of much use for any predictions, since the parameter

estimates you obtain are good for that dose group only. I wouldn't

worry about the number of parameters, initially. If you have enough

data from a broad dosing range you have a good chance to be able to

estimate the necessary parameters.

What do you mean by "processing time" beyond a regular computer"? Most

software packages will be fairly fast to give you estimates. I think a

couple of hours extra is a well-spent time for what you will get out of

a finel model, where non-linearities are integrated and

concentration-time profiles can be described for all dose groups

simultaneously.

Toufigh Gordi - On 7 Mar 2003 at 08:49:51, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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Vuong,

> However, this increased the number of

> parameters and processing time beyond a regular computer-- you are

> talking about 15 differential equations and 7-9 parameters. Anyway of

> reducing it down.

>

Thank you for revealing that you have been attempting to use a DE

defined model and not simply fussing about with AUC :-)

3 compartment disposition = 7 parameters (mixed order elimination) + 3

differential equations

input model = 1 (or 2; lag time?) parameters + 1 DE

I can understand why you say 7-9 parameters but not 15 DEs. I think you

only need 4.

Nick

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

[Busy day for PharmPK - Nick, I think the number of de's depends on the

program. with Boomer or SAAM II fitting simultaneously I would set up

five models with 3 or 4 de's per model for five doses, thus 15 (or 20

de's total), its a fudge of sorts. NONMEM would probably only require

the 3 or 4 de's and treat each dose as different treatment/period(?) -

db] - On 6 Mar 2003 at 13:57:21, Walt Woltosz (walt.-at-.simulations-plus.com) sent the message

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Dear Vuong Trieu,

Agn, GastroPlus handles such problems quickly and easily. The

simulation consists of nearly 90 differential equations to account for

regional permeability, pH-dependent solubility and dissolution,

saturable gut metabolism, saturable liver metabolism, saturable

transport (influx and efflux), up to 3-compartment pharmacokinetics,

and, if desired, pharmacodynamics.

Your problem is not unusual, and it is not difficult with GastroPlus. A

typical solution for Vmax and Km can be fitted in a matter of minutes

once you have the inputs specified. This type of analysis is not to be

feared! Please feel free to contact us if we can be of help.

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

E-mail: walt.at.simulations-plus.com

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