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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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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)