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RE: OMEGA BLOCK with mixture model?

From: Alison Boeckmann <alisonboeckmann>
Date: Wed, 15 Apr 2009 10:53:31 -0700

I think Christian is referring to this feature of NONMEM 5 (from the
NONMEM 5 Supplement guide):

"Changes to NONMEM Inputs
Band Symmetric Matrices
An initial estimate of a diagonal block of ether the OMEGA or
SIGMA matrices may have a band symmetric form, in which case
the final estimate has the same form."

With these structures for (e.g.) OMEGA BLOCK(3), the
0's are preserved:

x
0x
00x

x
xx
0xx

No need to FIX the off-diag (off-band) 0's.
So it is not actually undocumented.
Unfortunately, the OMEGA entry in on-line help was not updated with this
feature. It will be included in the NONMEM 7 help.

On Wed, 15 Apr 2009 15:47:35 +0200, "Christian Laveille"
<christian.laveille
> Dear all,
>
>
>
> There is an undocumented option in NONMEM called Band, allowing to fix at
> least one correlation to zero in a block(n).
>
> In the specific case you just have to put zero as initial estimate for
> Omega
> (CL1,CL2).
>
> It should work I used it in the past with NONMEM V!
>
>
>
> Hope this helps.
>
>
>
> Christian
>
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> From: owner-nmusers
> On
> Behalf Of Bob Leary
> Sent: mercredi 15 avril 2009 15:16
> To: andreas.krause
> nmusers
> Subject: RE: [NMusers] OMEGA BLOCK with mixture model?
>
>
>
> If you want both CL1 and CL2 to be correlated with F (i.e. allow
> Omega(CL1,F) and Omega(CL2,F) to be free in
>
> the objective function optimization),
>
> then I don't think there is any simple reordering of the random effects
> that will allow the correlation
>
> between CL1 and CL2 to be fixed to zero - i.e. the element Omega(CL1,CL2)
> must also be free.
>
>
>
> The reason for the Nonmem manual entry
>
> part VIII, p 94 ($OMEGA), "If FIXED appears anywhere among the list of
> values, the entire block is fixed."
> that Andreas pointed out is that internally Nonmem parameterizes the
> Omega
> matrix by its
>
> Cholesky factor elements, not the elements of the Omega matrix itself.
> The
> Cholesky factor has the
>
> same block diagonal structure as the Omega matrix, but due to the
> 'fill-in'
> phenomenon during
>
> a factorization, an internal zero element inside an Omega block will not
> necessarily be preserved
>
> as a zero in the Cholesky factor. So there is no way to force an internal
> element in an Omega block to be zero.
>
>
>
> Robert H. Leary, PhD
> Fellow
>
> Pharsight - A CertaraT Company
>
> 5625 Dillard Dr., Suite 205
> Cary, NC 27511
>
> Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871
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> -----Original Message-----
> From: owner-nmusers
> [mailto:owner-nmusers
> Behalf Of andreas.krause
> Sent: Wednesday, April 15, 2009 6:6 AM
> To: nele.plock
> Cc: nmusers
> Subject: Re: [NMusers] OMEGA BLOCK with mixture model?
>
>
> Nele,
>
> going by the nonmem user manual, part VIII, p 94 ($OMEGA), "If FIXED
> appears
> anywhere among the list of values, the entire block is fixed."
> I did not see anyone pointing that out yet.
>
> This does in fact imply that you need to reorder the sequence of random
> effects (which can be quite a nuisance if you have a sequence of models
> and
> the parameters do not correspond any more across models).
>
> Andreas
>
>
> -----
>
> Andreas Krause, PhD
> Lead Scientist Modeling and Simulation
>
> Actelion Pharmaceuticals Ltd / Gewerbestrasse 16 / CH-4123 Allschwil /
> Switzerland
> phone +41 61 565 6891 / fax +41 61 565 66 96
> andreas.krause
>
>
>
>
>
> nele.plock
> Sent by: owner-nmusers
>
> 04/14/2009 05:08 PM
>
>
> To
>
> nmusers
>
>
> cc
>
>
>
>
> 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
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> D-78467 Konstanz, Germany
>
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--
  Alison Boeckmann
  alisonboeckmann
Received on Wed Apr 15 2009 - 13:53:31 EDT

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