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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
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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/
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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.
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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).
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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
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The following message was posted to: PharmPK
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.
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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
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The following message was posted to: PharmPK
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/
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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
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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]
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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]
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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
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The following message was posted to: PharmPK
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]
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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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