# PharmPK Discussion - Dose Linearity

PharmPK Discussion List Archive Index page
• On 25 Sep 2007 at 15:20:58, "Jay Parikh" (Jay.Parikh.aaa.veedacr.com) sent the message

Dear all,

We are doing a Double-blind, Placebo-controlled, Randomized, Single-
dose, Dose-ascending Study to Evaluate the Safety, Tolerability and
Pharmacokinetics of study in Healthy Male Subjects. I have a
concentration profile but I have no idea about how to calculate the
dose linearity, so guide me how to calculate the dose linearity? Is
it calculated through WinNonLin? If yes, then guide me for this.

Jay Parikh
Biostatistician
Veeda Clinical Research Pvt. Ltd.
Web: www.veedacr.com

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• On 25 Sep 2007 at 12:08:18, "Adane, Eyob D" (edadan2.aaa.email.uky.edu) sent the message

The following message was posted to: PharmPK

One simple way is to calculate the AUCs(areas under the concentration
curve) and plot them as a fuction of dose. The relationship should be
linear.

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• On 25 Sep 2007 at 09:50:45, "Toufigh Gordi" (tgordi.aaa.Depomedinc.com) sent the message

The following message was posted to: PharmPK

Dear Jay,

Assuming a drug has linear PK, one would expect Cmax and AUC to increase
proportional to dose, i.e., if you for example give a 3 times higher
dose you should observe 3 times higher Cmax and AUC values. There are
several ways to take a look at this:

- Estimate the AUC after each dose and then plot them vs. dose. You
should see a straight line with proportional increase in the AUC with
increasing dose. The same goes for Cmax.

- Estimate the AUC/dose values and plot them against dose. You should
see a flat line, i.e. a slope of zero. Again, you can do the same for
Cmax.

- Take the concentrations at each time-point and divide them by dose.
Then make a concentration vs. time plot, including all these values. If
you have a linear PK, the dose normalized concentrations should
superimpose.

To be honest with you, I am not really sure why you would be interested
in just knowing whether your compound has linear PK or not. What I would
do with the data you have is to build a compartmental PK model and use
that for future studies. Looking at your plasma concentration data and
non-compartmental analysis (AUC, Cmax, etc.) you get a good picture of
what model would best fit the data and can include non-linearity terms,
if necessary. Once you have the PK model in place, you have a good tool
to simulate what-if scenarios with regard to dosing (as long as you stay
within the known data realm). In my opinion, this would be far more
useful than just finding out whether your compound is linear or
nonlinear.

Toufigh Gordi

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• On 25 Sep 2007 at 17:44:32, "Charlie Brindley" (charlie.brindley.-at-.kinetassist.com) sent the message

The following message was posted to: PharmPK

Dear Jay,

I would suggest using the power model to assess dose proportionality as
described by:
Gough K, Hutchison M, Keene O, Byrom B, Ellis S, Lacey L and McKellar J.
Assessment of dose proportionality: report from the statisticians in the
pharmaceutical industry / pharmaceutics UK joint working party. Drug
Information Journal 1995; 29: 1039 1048.

and further developed by:
Smith B. Assessment of dose proportionality. In Bonate P, Howard D
editors,
Pharmacokinetics in drug development: Clinical study design and
analysis.
AAPS Press, USA, 2004. p 363-382.

Regards,

Charlie

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• On 25 Sep 2007 at 23:22:44, "Akshanth Polepally" (akshanth.-at-.gmail.com) sent the message

Dear Jay Parikh,

With the concentration profile, you just calculate the AUCs for the
respective doses and plot a curve AUC vs dose. This will explain you
the dose linearity. (check the regression coefficient).

If you want to check the dose proportionality then calculate the dose
normalized AUCs (AUC/Dose) and plot AUC/Dose vs dose. If the plot is
a staight line parallel to X-axis then the data generated is dose
proportional.

regards
Akshanth
Jr. Scientist
DMPK, Discovery Research,
Dr, Reddy's Laboratories Ltd, India

--
Akshanth Reddy Polepally
Junior Scientist, Drug Metabolism & Pharmacokinetics (DMPK),
Discovery Research (DR),
Dr. Reddys Laboratories, Hyderabad,
A.P., India - 500 049

Email: akshanthrp.aaa.drreddys.com
akshanth484.-at-.yahoo.com

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• On 25 Sep 2007 at 17:44:16, Anila Desai (desai_anila.aaa.yahoo.com) sent the message

This is a very important topic. Listed below please find reference
papers that describes hypothesis testing and CI methods for
assessing dose proportionality based on linear regression and WLS
linear regression and others.

References

1. Using SAS to assess dose proportionality in dose escalation
studies. Aurhor: Keith Dunnigan, Mallinckrodt/ TycoHealthcare, St.
Louis, MO

2. Confidence interval criteria for assessment of dose
proportionality. Smith BP et al, Pharm Res 2000: 17:1278-1283

3. Linear stastical models: An applied approach, Second edition, PWS-
Kent Publishing Company, Boston, 1990. 644-661.

Regards,
Anila

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• On 25 Sep 2007 at 22:39:28, "Toufigh Gordi" (tgordi.-at-.Depomedinc.com) sent the message

Hi Anila,

You wrote:

"This is a very important topic."

Could you elaborate a little more on why it is so important to find
out if a compound has linear or nonlinear kinetics, using the methods
described in the references you have mentioned? Imagine that you have
characterized the pharmacokinetics of your drug and have a PK model
in place that describes it well, including nonlinearity terms, if
evident. Why would you then be concerned whether your compound
exhibits a linear or nonlinear PK?

Toufigh Gordi

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• On 26 Sep 2007 at 18:17:30, Anila Desai (desai_anila.-at-.yahoo.com) sent the message

The linearity of dose is important because if it is a non-linear
kinetic one has to investigate the reasons for non-linearity.

-Is the metabolism an issue or transporter?
-Are there any particular metabolites that not seen in other species?
-If the major metabolic pathway is glucuronidation that can be a
substrate for certain transporters?
-Which isoforms are responsible for metabolism? Is the saturation
due to first pass effect?
-Unusual toxicity observed in larger animal model that was not
observed in small animal models? Is the metabolite toxic?

another example:
A remarkable non-linearity was found between dose and transfection
activities of non-viral gene delivery systems, such as a
Lipofectamine/DNA complex and an octaarginine-modified
multifunctional envelope-type nano device (R8-MEND). We measured the
nuclear delivery of pDNA to distinguish the non-linearity in
intracellular pharmacokinetics or pharmacodynamics after transfection
with R8-MEND at different doses. A remarkable positive non-linearity
was found in the pharmacodynamics when the dose was increased. Even
dummy pDNA enhanced the efficiency of transcription and/or
translation per pDNA in the nucleus, but empty liposomes did not.
These results suggest the importance of controlled pharmacodynamics
as well as the importance of intracellular pharmacokinetics for the
rational design of non-viral gene delivery systems.

As far as using method described in the papers - Pharmaceutical
companies use various methods to assess dose proportionality. You
have to decide which method fits your situation and giving you the
confidence. Methods like WLS allows us to order dose ordering
information, assess dose linearity on dose by dose basis and overcome
the homogeneity of variance objection commonly raised against the
linear regression model. I hope this helps.

Best regards,
Anila

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• On 27 Sep 2007 at 11:19:04, =?WINDOWS-1252?Q?M=E1ria_Duri=9Aov=E1?= (exfamadu.-a-.savba.sk) sent the message

The following message was posted to: PharmPK

Hi,
Drug dose is neither linear nor nonlinear. If the drug behavior, i.e.
the series of the dynamic processes involved in absorption,
distribution, elimination, and metabolism (if it is the case) of the
drug, fulfils the linearity axioms [1,2] in a drug-dose range, the drug
behavior can be appropriately approximated by a linear mathematical
model in the given range.
1.

http://202.41.85.103/manuals/planetmath/entries/15/LinearAlgebra/
LinearAlgebra.html
[Note: No domain name - db]
2. P. Muller, Computational Intelligence, 18, (3), pp. 420-450, Aug
2002.
With best regards,
Maria Durisova DSc (Math/Phys)

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• On 27 Sep 2007 at 10:48:50, "Toufigh Gordi" (tgordi.at.Depomedinc.com) sent the message

The following message was posted to: PharmPK

Hi Anila,

I guess I did not formulate my question well. I'll try to do a better
job this time.

As I wrote in my original post, I'd rather come up with a PK model that
describes the data well, compared to just a look at whether AUC or Cmax
values vs. Dose show a straight line. I totally agree with you on the
need to find out the reasons for observed peculiarities of the PK of a
compound. My bias is that I strongly believe that a compartmental model
is a better approach in analyzing the data compared to a simpler
regression analysis. In fact, if there are any nonlinearities involved,
modeling can offer more understanding of the data and provide some
estimates of the parameters associated with the observed nonlinearity. I
understand that building a PK model is normally more elaborate compared
to the linearity tests but in my opinion it is a time well spent.

So, the question is what the knowledge gained by a regression analysis
provides that is superior to a PK model. I can certainly think of
several reasons why a PK model would be superior to the regression
analysis results. But, aside from the simplicity of the regression
analysis, I am not sure if I can think of any other advantages.

Maybe I should also make it clear that I am not dismissing
non-compartmental analysis or regression analysis of the parameters
obtained through it. Rather, I think these are good intermediary steps
toward the build-up of the correct compartmental model.

Toufigh

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