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RE: OMEGA BLOCK with mixture model?

From: Diane R Mould <drmould>
Date: Wed, 15 Apr 2009 12:16:00 -0400

Dear All


I am not sure if this topic has been covered before or not, but as its
related to the question below, I thought I would bring it up again.


I have to wonder at the appropriateness of including the IIV term for F in
an omega BLOCK structure in the first place? I can certainly understand
estimating relative bioavailability and even estimating the associated
variability for F, although there are often estimatability issues for an IIV
term for F, even with IV data to help estimate F (or at least using a
reference value for F like one formulation or one occasion).


However because with orally administered drugs, CL is really CL/F then there
is an inherent correlation between CL and F. With F and CL, this
correlation is really in the THETA values so that if the model captures the
correlation at the THETA level, ie allow for larger clearance with larger F
(or vice versa), then the random effects for F and CL may be uncorrelated.
However, if the population model does not capture that correlation at the
THETA level, then correlation will be captured via the random effects,
possibly resulting in an over-parameterized OMEGA matrix. As this latter
situation seems to be very common (e.g. that the correlation between F and
CL etc is picked up in the etas) then one might expect to see high condition
numbers, zero gradients etc when IIV on F is added to the omega BLOCK


I would guess that as a rule, its probably more appropriate to keep the IIV
term for F out of a BLOCK structure. Can anybody comment on this?


Best regards,




From: owner-nmusers
Behalf Of Mats Karlsson
Sent: Tuesday, April 14, 2009 2:08 PM
To: nele.plock
Subject: RE: [NMusers] OMEGA BLOCK with mixture model?


Dear Nele,


I think you may want to reconsider your model. If you have a negative
correlation between CL and F1, it is likely to be related to high
presystemic metabolism (first-pass) effect. If so, it seems strange to
assume that the F1 distribution would not change between the two
subpopulations. I think you need to have separate CL as well as F1 for the
two subpopulations. Thus I would have CL and F1 described by ETA(1) and
ETA(2) for subpopulation 1 and CL and F1 described by ETA(3) and ETA(4) for
the second subpopulation. If hepatic elimination is responsible for the
correlation, it is probably more parsimonious to use a semi-mechanistic
model with a hepatic compartment (with a single ETA for variation in
metabolic activity). Two examples of implementations of a separate hepatic
compartment are :

Piotrovskij et al. Pharm Res. 1997 Feb;14(2):230-7.

Gordi et al., Br J Clin Pharmacol. 2005 Feb;59(2):189-98


Best regards,




Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003


From: owner-nmusers
Behalf Of nele.plock
Sent: Tuesday, April 14, 2009 5:09 PM
To: nmusers
Subject: [NMusers] OMEGA BLOCK with mixture model?


Dear all,

I am trying to fit a PK model to oral data. In the data, we observed two
things: First, CL seems to be negatively correlated with F1. Secondly, there
seem to be two subpopulations in the exposure, let's say a large group with
'normal' and a second group with high exposure. I would like to identify the
subpopulations using a mixture model, but keep the correlation between CL
and F1. Now I ran into problems when coding the $OMEGA BLOCK.

I figured the block to be something like:
0.1 ;CL1
0 FIX 0.1 ;CL2
0.01 0.01 0.1 ;F1

The error message that appears is:
a covariance is zero, but the block is not a band matrix

I assume that this means that I am not allowed to fix the correlation
between the two clearance-omegas to zero. However, it would be unreasonable
to allow a correlation, because the omegas belong to different
subpopulations, so there can't be a correlation. On the other hand, I did
not include subpopulations for F1, so how can I keep this correlation to
both CL-subgroups?

Any thoughts on this would be highly appreciated!
Best wishes

Dr. Nele Plock
Pharmacometrics -- Modeling and Simulation

Nycomed GmbH
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Received on Wed Apr 15 2009 - 12:16:00 EDT

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