- On 12 Jun 2002 at 11:28:04, Jeffrey Larson (jlarson.aaa.tanox.com) sent the message

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PK Modelers: A question on covariates in PK modeling. Assume I have an

endogenous molecule called X that is present in the blood of subjects at

concentrations of anywhere from 0.001 to 1 mg/mL, with higher levels

indicative of an atopic state. Drug A is administered to subjects and the

blood concentrations of free drug A are determined at set times after drug

administration. The bioanalytical assay determines only free drug A, not

drug A bound to X. The PK of drug A is dependent on the initial

concentration of X since drug A binds to X. Hence, in a PK model with a

single dose, X will be a covariate in the PK of drug A. My question

relates to modeling multiple dose administrations of drug A. Assume that

endogenous X does not return to atopic baseline levels, but remains in the

range of normal subjects (i.e. 0.001) over the dose interval such that at

the time of the second dose of drug A, the concentration of X is 0.001 and

there is no interaction between free drug A and X. How would one specify

in the model that the kinetics of A are affected by X only at the first

dose, but not at subsequent doses?

Cheers!

Jeffrey L. Larson, Ph.D.

Director of Toxicology and Pharmacokinetics

Tanox, Inc.

4888 Loop Central Drive

Houston, TX 77081-2225

(713) 578-4212 - On 12 Jun 2002 at 13:55:40, "Patrick Smith" (pfsmith.-at-.acsu.buffalo.edu) sent the message

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Jeff,

I am sure there are several means of handling this. One potential method

you might try is with the use of 'mathematical switches'. Since you know

the times of the doses, and the 1st dose is always administered 1st, you can

turn the interaction on and then off at specific time points (using a

program such as ADAPT II, you can fix the time it turns on or off, or fit

that time as a parameter). For example:

Letting S be the switch parameter, you can either multiply by S, or raise to

the power of S based on a 'lag time' type approach. You could call it Toff

for when the interaction is 'turned off'. For a simple 1-compartment model:

if T>Toff then S=0 else S=1

dX/dt = [Dose input] - X/V*(CL*Z^S); where Z is your covariate

therefore, when TToff, s=0 and Z=1

Or, if you know when you want this interaction to exist based on

concentrations of X, you could use a threshold on the concentration of X,

rather than on time.

Others will hopefully have alternative approaches to this?

Good Luck!

Patrick Smith, Pharm.D.

Assistant Professor

University at Buffalo SOPPS

315 Hochstetter Hall

Buffalo, NY 14260

(716) 845-3281

pfsmith.-a-.buffalo.edu - On 12 Jun 2002 at 16:05:27, "fabrice.lagrange" (fabrice.lagrange.aaa.laposte.net) sent the message

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In this model, the concentration of A at t0, only, is a

covariate of X. Test a scatchard equation to describe the t0

concentration in relation to the X, X-A and Free A

concentration. - On 12 Jun 2002 at 16:25:17, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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Jeffrey,

"Jeffrey Larson (by way of David Bourne)" wrote:

> PK Modelers: A question on covariates in PK modeling. Assume I have an

> endogenous molecule called X that is present in the blood of subjects at

> concentrations of anywhere from 0.001 to 1 mg/mL, with higher levels

> indicative of an atopic state. Drug A is administered to subjects and the

> blood concentrations of free drug A are determined at set times after drug

> administration. The bioanalytical assay determines only free drug A, not

> drug A bound to X. The PK of drug A is dependent on the initial

> concentration of X since drug A binds to X. Hence, in a PK model with a

> single dose, X will be a covariate in the PK of drug A.

This is the critical issue. If the PK of A depends on X then

presumably as X goes towards zero the effect of X will decrease until

eventually the X-free value of the PK of A is approached.

> My question

> relates to modeling multiple dose administrations of drug A. Assume that

> endogenous X does not return to atopic baseline levels, but remains in the

> range of normal subjects (i.e. 0.001) over the dose interval such that at

> the time of the second dose of drug A, the concentration of X is 0.001 and

> there is no interaction between free drug A and X. How would one specify

> in the model that the kinetics of A are affected by X only at the first

> dose, but not at subsequent doses?

I cannot see why this causes a problem in your model when you have

multiple doses and X falls to a low value. If you have a sensible

model for the relationship between X and the PK of A then you should

not need any special function to deal with multiple doses.

Nick Holford, Divn Pharmacology & Clinical Pharmacology

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

email:n.holford.at.auckland.ac.nz

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 13 Jun 2002 at 10:03:54, phil.lowe.aaa.pharma.novartis.com sent the message

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Dear Jeffrey,

I know of several cases where a drug with binds to an endogenous ligand

which is present at significant concentrations and therefore generates drug

kinetics which are affected by the concentration of the ligand. The best

way to think about this is not with covariates, but include the ligand as

an integral part of the modelled mechanism of action.

Consider the kinetic scheme A + B <->C. The rate of transfer from A and B

to C is dependent upon the concentrations of both drug (A) and ligand (B)

and can be written as rateon=kon*[A]*[B] which is a second order reaction.

The reverse, off rate, is rateoff=koff*[C]. The ratio kon/koff is the

steady-state affinity. In a system of differentials you can then add normal

PK terms such as for absorption, CL and V. The kinetic parameters need to

cover both the drug, and the turnover of the endogenous ligand (where

instead of absorption there is continuous synthesis). The entire mechanism

is then dependent upon the baseline levels of ligand (as data) without any

need to specify these levels as a covariate. You do not need data for A, B

and C; any 2 from 3 should do although complete data is better of course.

I used this to model the PK and PD of Desferal chelation of iron some years

ago, although I never got round to publishing it due to lack of time. In

other areas, the PK/PD work of WJ Jusko and coworkers has similar schemes

(to start, see Haughey, DB & Jusko WJ (1992) J. Pharmacokin. Biopharm. 4,

333-355).

Best regards, Phil.

Philip Lowe Ph.D.

Preclinical Safety Modelling Group

Novartis Pharma AG

CH-4002 Basel

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