- On 15 Mar 2002 at 14:44:59, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

"anand iyer (by way of David Bourne)" wrote:

>I am fresher who is just learning population PK. And this is something

which has been bothering me a for some time. When we use population Pk

approach we consider the issue of inter as well as intra subject

variability. And it is often said that using population Pk approach we

can calculate intra as well as inter subject variability. My question is

when we use destructive sampling or even in clinical scenario if we able

to get just one sample for each time point from each subject how are we

able to calculate intra-subject variability? The basic logic being that

you need at least 2 samples from the same subject/animal for the same

time point to calculate intra subject variability. I understand the fact

by putting in various co-variaties like body weight, age etc we can

determine inter-subject variability. But can we estimate intra subject

variability using these?

This an excellent question. First of all let me caution you about the

use of the term "intra-individual variability". I think

"intra-individual" is quite misleading. What is estimated is better

called residual unidentified variability (RUV). It is residual because

it is what is left over after all the other sources have been accounted

for. It is unidentified because it is attributable to a variety of

confounded sources including 1) model misspecification -- in many cases

I suspect this is the biggest component. 2) measurement error -- this

includes both the dependent variable e.g. concentration, and independent

variables such at time,dose, weight etc. 3) some true within subject

parameter variability (WSV) (although this is really model

misspecification).

You are quite correct in pointing out that that there are

identifiability problems with the destructive sampling (one sample per

subject) design. Imagine the simplest PK experiment of a constant rate

input that is know to have reached steady state. With one concentration

measurement it is impossible to distinguish between variability arising

from differences in clearance from subject to subject (population

parameter variability; PPV) and RUV. One approach to solving this

problem is to assume a value for RUV -- say 20% of the predicted

concentration. With this assumption the variability in concs can then be

assigned to PPV.

The use of covariates to identify predictable differences between

subjects e.g. by using weight to assign higher clearances in heavier

people, can help in reducing the size of PPV. Indeed, if you consider

the PPV without weight in the model this can be thought of as being the

sum of predictable (PPVP) varibility and apparently random (PPVR)

variability. As each covariate is added to the model its influence is to

move variability from PPVR to PPVP but the total PPV does not change and

there should be no effect on RUV (except via model misspecification

which may be decreased with an appropriate covariate model). Note that

PPVR includes variability from true between subject variability in

parameters (BSV) and true within subject variability in parameters

(WSV). These components can be identified by the use of another

covariate (occasion) if it is possible to estimate the parameter on more

than one occasion within the same subject.

In summary, covariates cannot help to estimate RUV except via decreasing

model misspecification and if you misspecify the covariate model you can

increase RUV.

Destructive sampling designs are a priori unidentifiable with respect to

distinguishing PPV from RUV.

The following reference illustrates some of the approaches to this

problem: Is Mixed Effects Modeling or Na•ve Pooled Data Analysis

Preferred for the Interpretation of Single Sample per Subject

Toxicokinetic Data? Hing J.P.; Woolfrey S.G.; Greenslade D.; Wright

P.M.C. Journal of Pharmacokinetics and Pharmacodynamics, April 2001,

28(2):193-210

Nick

--

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/

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