- On 4 Jul 2003 at 10:23:49, "Poli Gianluigi" (G.Poli.at.chiesigroup.com) sent the message

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Does anyone have any suggestion how to perform a PK/PD modeling using

urinary excretion data (rate of excretion or total urinary excretion)

for a drug that is not detectable in plasma but measurable in urine ?

Best regards

Gianluigi Poli

Chiesi Farmaceutici (Italy) - On 5 Jul 2003 at 10:23:45, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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Poli,

> Does anyone have any suggestion how to perform a PK/PD modeling using

> urinary excretion data (rate of excretion or total urinary excretion)

> for a drug that is not detectable in plasma but measurable in urine ?

>

First of all you need to find a method for modelling that would let you

describe both plasma concentrations and urine excretion rate

observations. Then set up the method for a one compartment disposition

model and bolus and make the renal clearance be the same as the plasma

clearance of your drug.

In the simplest case (bolus input) there are 2 parameters you might

want to estimate: volume of distribution/Ff and clearance/Ffu where Ffu

is the product of the unknown extent of bioavailability and unknown

fraction excreted in the urine. To do the modelling you will have to

assume Ffu=1.

Because you don't have any plasma concentrations you can only estimate

clearance from the time course of urine excretion rate by fitting the

model to the urine excretion rate observations. You will therefore have

to assume a reasonable value for volume. If you have no idea what it is

then fix it to 1 but remember that the estimate of clearance will be

dependent on the value you assume. Because the ratio of

clearance/volume is directly identifiable the relationship between the

true and estimated values is CLtrue = Vtrue*CLest/Vfix.

It is not essential to have plasma concentration data to fit the urine

data with this model.

If your urine excretion rate time course gives some clue about the

absorption rate (i.e. excretion rates rise to a peak and then fall) you

can describe the drug absorption process e.g. if you assume first order

input then you can estimate the absorption rate constant (ka).

You indicate that you want to do PKPD modelling. If you have got drug

effect observations then you can learn more about the time course of

plasma concentrations by simultaneously fitting the time course of

urine excretion rates and effects. The success of this will depend on

how much effect data you have and the complexity of the model needed to

describe any delay between plasma concentration and effect.

Examples of fitting urine excretion rate data with both bolus

[bo1renal] and first order [ka1renal] input can be found here:

http://www.health.auckland.ac.nz/courses/Pharmcol716/

Error%20Models%20and%20Objective%20Functions/olsels.xls

[Sorry about the long URL which you will have to manually re-create if

word-wrap splits it across 2 lines]

The examples use Excel to simulate urine excretion rate data (including

residual error). The parameters of the PK model and the residual error

model can be estimated using the Excel Solver. You may enter your own

real urine excretion data (in the Yobs column) if you want to try it

out on your own data.

An extended least squares (ELS) objective function is minimized by the

Solver. You can change this to ordinary least squares (OLS) or

iteratively re-weighted least squares (IRLS) by changing the Solver

target to minimize.

The residual error model assumes a proportional error for IRLS and ELS.

You can change this by modifying the Virlsi or Velsi formulae which

define the predicted variance of the residual error.

Some background on objective functions and error models can be found

here:

http://www.health.auckland.ac.nz/courses/Pharmcol716/

Commments and suggestions for improvements in this material are very

welcome.

[You can find the Solver under Tools menu. If it's not there then go to

Tools Add-Ins... and check Solver Add-In. If you can't see the Solver

Add-In then you will need to the Office Installation program and ask

for the Solver Add-In to be installed. It comes free with all versions

of Office but unfortunately it is not installed by default. While you

are doing this you may want to install the Analysis ToolPak for simple

statistics.]

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 7 Jul 2003 at 08:03:32, "Cotler, Stanley {NCDS~Nutley}" (STANLEY.COTLER.aaa.ROCHE.COM) sent the message

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Look At the Loo-Reigelman Equations (Gibaldi's book on PK

Stanley Cotler

Non-Clinical Drug Safety

Nutley, NJ 07110

Phone 973-235-2857

Fax 973-235-7010 - On 8 Jul 2003 at 15:25:54, "Poli Gianluigi" (G.Poli.-at-.chiesigroup.com) sent the message

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The following message was posted to: PharmPK

Many thanks for the answer.

Unfortunately I have some problem in using the Excel file you

suggested. Please where may I find some explanations how to use the

model ?

In addition when I perform a fitting of the urinary data, I obtain an

estimate of plasma concentrations; I am asking if these estimated

plasma concentrations (lower than the limit of quantification of the

method) should be used together with dynamic response for PK/PD

modeling ?

Thanking you in advance, best regards

Gianluigi Poli

[It might be better if you keep the drug in the body as amount (in your

model) and not try to use concentrations (even with a volume of 1). You

could then model the PD part in terms of amount. You would still have a

EC(50%) type parameter but as effective amount 50%. Same number of

parameters, except no made-up V term. - db] - On 9 Jul 2003 at 08:07:49, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

Poli,

Poli Gianluigi wrote:

> Unfortunately I have some problem in using the Excel file you

> suggested.

Please describe the problems e.g. cannot open Excel file, don't know

how to enter data, etc.

> Please where may I find some explanations how to use the

> model ?

Look at the Excel formulae. Read the Excel help on the Solver Add-in.

If you put some effort into trying to describe exactly what you think

you need explaining you may find the answer becomes clear to you.

> In addition when I perform a fitting of the urinary data, I obtain an

> estimate of plasma concentrations; I am asking if these estimated

> plasma concentrations (lower than the limit of quantification of the

> method) should be used together with dynamic response for PK/PD

> modeling ?

It makes no difference if the PREDICTED plasma concs are lower than the

quantification limit of the method. The PREDICTED plasma concs are fine

to predict MEASURED urine and MEASURED effect observations. This is one

of the great advantages of using models insted of relying only on

observed data.

Nick

Nick Holford, Dept Pharmacology & Clinical Pharmacology

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

Zealand

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

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

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