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RE: OMEGA BLOCK with mixture model?

From: Stephen Duffull <stephen.duffull>
Date: Fri, 17 Apr 2009 09:15:11 +1200

Mats

Thanks for your succinct summary.

For point 1. In a more general sense I think a covariance term can be extr=
acted from a BLOCK and estimated as a separate DIAG variance term. The cor=
relation need not be positive, albeit the variance will be positive. This =
is not possible with F in NONMEM due to constraints on its value.

For point 3. I have occasionally compared DIAG(3) with BLOCK(2) and var(F) =
was indeed estimated to be greater than cov(CL/F, V/F) and if var(F) had ha=
ve been the estimate of cov(CL/F, V/F) then the matrix would not have been =
positive definite. (This is only a n=1 experience.)

I like your thoughts on using a mixture on F in NONMEM, I had never conside=
red this possibility.

I agree with your points on parsimony as well (under the assumption of posi=
tive correlation). I think parsimony might be more important with NONMEM u=
sing gradient search algorithms than SAEM algorithms. If a later version o=
f NONMEM includes different search algorithms then perhaps some of difficul=
ties that we have here and that Nele had in her example will be less of an =
issue.

Steve
--



> -----Original Message-----
> From: Mats Karlsson [mailto:mats.karlsson
> Sent: Thursday, 16 April 2009 11:07 p.m.
> To: Stephen Duffull; drmould
> nele.plock
> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
>
> Hi Steve,
>
> For a one-compartment model I think these are differences:
>
> 1) DIAG(3) is more restrictive than BLOCK(2) in the sense
> that only positive correlation between CL/F and V/F can be estimated
> 2) DIAG(3) is less restrictive than BLOCK(2) in the sense
> that different transformations can be used for F
> 3) DIAG(3) provides an EBE that can be used for diagnostic
> purposes (DIAG(3) and BLOCK(2) would give the same estimates
> for the same model so I don't understand your comment of
> var(F) being higher than cov(CL/F,V/F))
> 4) DIAG(3) may facilitate covariate model building (although
> this is minor as you with BLOCK(2) can put the same
> relationship in in two places)
> 5) If there truly is a mixture in F1, then I think DIAG(3)
> has a advantages over BLOCK(2) in number of parameters (two
> fewer) needed to describe the variability model
> 6) If some additional assumptions can be reliably made, such
> as all variability in F1 is truly in bioavailability and
> bioavailability is restricted to be between 0 and 1, some
> additional info may be extracted from the data for example by .
>
> I would not rank any of these as major differences (expect
> possibly the mixture aspect which I've never tried).
>
> For two- or three-compartment models the advantages are that
> if indeed the main covariance structure between CL/F, V1/F,
> Q/F, V2/F is a joint positive correlation due to variability
> in bioavailability, fu etc, then a DIAG(5) is more
> parsimonious than a BLOCK(4).
>
> 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
>
>
> -----Original Message-----
> From: Stephen Duffull [mailto:stephen.duffull
> Sent: Thursday, April 16, 2009 10:13 AM
> To: Mats Karlsson; drmould
> nele.plock
> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
>
> Mats
>
> > 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.
>
> I have often seen these two options considered. I am unclear
> as to the advantages of DIAG(3) over BLOCK(2)? In theory it
> would seem that they should be identical. In practice it
> seems that DIAG(3) is more relaxed since it is not required
> that the variance of relative F if reassigned to the
> covariance of (CL/F, V/F) [under BLOCK(2)] yields a positive
> definite matrix.
>
> I presume an advantage wrt covariate model building would be
> access to the EBEs of F_i. However, given the variance of
> F_i may exceed the covariance of (CL/F, V/F) then I wonder if
> this is a real advantage or an artefact of numerical procedures?
>
> I am keen to learn more about real advantages of application
> of DIAG(3) as an alternative to BLOCK(2).
>
> Steve
> --
> Professor Stephen Duffull
> Chair of Clinical Pharmacy
> School of Pharmacy
> University of Otago
> PO Box 913 Dunedin
> New Zealand
> E: stephen.duffull
> P: +64 3 479 5044
> F: +64 3 479 7034
>
> Design software: www.winpopt.com
>
>
Received on Thu Apr 16 2009 - 17:15:11 EDT

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