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Re: OMEGA BLOCK with mixture model?

From: Nick Holford <n.holford>
Date: Thu, 16 Apr 2009 10:07:19 +0200

Nele,
I dont agree that with this assertion "I know that in a one-compartment
model, NONMEM would not be able to differentiate between IIV on volume
or IIV on F1"

If you use this approach (similar to that suggested by Mats)

$OMEGA 0.5 ; BSV_F1
$OMEGA BLOCK(2)
.5 ; BSV_CL
0 .5 ; BSV_V ; Note zero covariance between CL and V
$PK
F1=EXP(BSV_F1) ; relative 'bioavailability, protein binding, etc.'
CL=POP_CL*EXP(BSV_CL)
V=POP_CL*EXP(BSV_V)

then you can in theory identy the 3 BSV components. This is because
anything that causes between subject variability in F1 (which can be
differences in bioavailability, protein binding, dose error) will affect
CL and V identically. If there is an additonal uncorrelated source of
BSV for CL e.g. renal function, and BSV for V e.g. partition into fat,
then this can be identified. The $PK code above is equivalent to this:

CL=POP_CL*EXP(BSV_F1 + BSV_CL)
V=POP_CL*EXP(BSV_F1 + BSV_V)

Nick

nele.plock
>
> Dear Mats,
>
> thank you, that is exactly what I am trying now (as I have IIV on
> central volume). I will now only include the diagonal elements of the
> omega matrix, and have included the correlation in the thetas as CL/F.
> Let's see how this works.
> One question out of curiosity: I know that in a one-compartment model,
> NONMEM would not be able to differentiate between IIV on volume or IIV
> on F1. But with more compartments, this should work, shouldn't it,
> even if I only have oral data?
>
> Best wishes
> Nele
> ______________________________________________________________
>
> Dr. Nele Plock
> Pharmacometrics -- Modeling and Simulation
>
> Nycomed GmbH
> Byk-Gulden-Str. 2
> D-78467 Konstanz, Germany
>
> Fon: (+49) 7531 / 84 - 4759
> Fax: (+49) 7531 / 84 - 94759
>
> mailto: nele.plock
> http://www.nycomed.com
>
> County Court: Freiburg, Commercial Register HRB 701257
> Chairman Supervisory Board: Charles Depasse
> Management Board: Dr. Barthold Piening, Gilbert Rademacher, Dr. Anders
> Ullman
>
>
>
> *mats.karlsson
>
> 16.04.2009 09:05
>
>
> To
> drmould
> nmusers
> cc
>
> Subject
> RE: [NMusers] OMEGA BLOCK with mixture model?
>
>
>
>
>
>
>
>
>
> Hi Diane,
>
> With oral data only I would normally model with BLOCK(2) on CL/F and
> V/F or a DIAG(3) on CL/F, V/F and relative F. The latter may have some
> advantages for diagnostics, covariate model building etc. Also, if the
> underlying model truly is a mixture model on F, it could be
> parsimonious, needing mixture only one parameter only. You can’t have
> IIV on CL, V and relF + off-diagonal elements without
> overparameterizing the model. However, although I have never tried it,
> I guess that a BLOCK(2) on CL and relative F could work, provided you
> have no ETA on V. If you also have an ETA on V all the problems you
> mention would be realized. I don’t know if Nele has IIV on V, but if
> so, she should definitely reduce IIV model size. With respect to the
> mixture model, maybe it is possible to reparameterize such that the
> mixture component only concerns one ETA.
>
> Best regards,
> Mats
>
> 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:* Diane R Mould [mailto:drmould
> Sent:* Wednesday, April 15, 2009 6:16 PM*
> To:* 'Mats Karlsson'; nele.plock
> Subject:* RE: [NMusers] OMEGA BLOCK with mixture model?
>
> 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 structure.
>
> 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,
> Diane
>
>
> ------------------------------------------------------------------------
>
> *From:* owner-nmusers
> [mailto:owner-nmusers
> 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
>
>
> 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
> [mailto:owner-nmusers
> *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:
> $OMEGA BLOCK(3)
> 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
> Nele
> ______________________________________________________________
>
> Dr. Nele Plock
> Pharmacometrics -- Modeling and Simulation
>
> Nycomed GmbH
> Byk-Gulden-Str. 2
> D-78467 Konstanz, Germany
>
> Fon: (+49) 7531 / 84 - 4759
> Fax: (+49) 7531 / 84 - 94759
>
> mailto: nele.plock
> http://www.nycomed.com
>
> County Court: Freiburg, Commercial Register HRB 701257
> Chairman Supervisory Board: Charles Depasse
> Management Board: Dr. Barthold Piening, Gilbert Rademacher, Dr. Anders
> Ullman
>
>
>
>
>
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>
> ----------------------------------------------------------------------
> Proprietary or confidential information belonging to Nycomed Group may
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> In such case, please destroy this message and notify the sender by
> reply e-mail. Please advise the sender immediately if you or your
> employer do not consent to Internet e-mail for messages of this kind.
> Opinions, conclusions and other information in this message that
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> represent the opinion of the sender and do not necessarily represent
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>

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holford
mobile: +33 64 271-6369 (Apr 6-Jul 17 2009)
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Received on Thu Apr 16 2009 - 04:07:19 EDT

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