NONMEM Users Network Archive

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Re: omega matrix - friendly suggestion

From: Nick Holford <n.holford>
Date: Wed, 13 Jun 2012 19:20:10 +0200

Paolo,

You may remember this discussion about the history of the correlation
feature for OMEGA (and SIGMA) blocks.
http://www.cognigencorp.com/nonmem/current/2009-July/1804.html

IMHO the only sensible way for a human to write a covariance matrix is
using the SD and correlation style introduced in NONMEM 7. If I
understand things correctly (this kind of math is not my strong point)
it should be impossible to write non-positive definitive matrices
provided the correlations are -1<=0<=+1 (although NONMEM might complain
at -1 or +1).

Can anyone provide any good reason to prefer the variance-covariance
parameterization over the SD-correlation parametization?

The other issue brought up by Pavel is a different one -- how to specify
more simply a zero correlation|covariance between random effects.

Monolix has a 0|1 matrix that allows a user to fix any covariance matrix
element to zero so presumably the math exists somewhere to allow NONMEM
how to understand a matrix to be recognized in this format.

  Bob (Bauer) -- do you know how to do this? Perhaps you could talk to
Marc Lavielle and consider adding something similar to NM-TRAN. I'd
prefer the style shown by Pavel to having to write a separate matrix of
0|1 elements as used in the Monolix GUI.

Best wishes,

Nick



On 13/06/2012 5:16 p.m., Paolo Denti wrote:
> Dear Pavel and Ken,
> I also share the same pain, especially when coding correlations for
> between-occasion variability ETAs. This implies reorganizing them in
> blocks and renumbering everything. A real chore, and a very
> error-prone process.
>
> Maybe one can think of using the OMEGA in the correlation format,
> which should make it easier to write "legitimate" OMEGA matrices. Or
> NONMEM can check the positive definiteness of the initial estimate and
> complain if necessary (I believe it already does so).
>
> So, dear NONMEM developers, please count a +1 in the survey for this
> feature. :)
>
> Thank you and ciao,
> Paolo
>
> On 2012/06/12 17:08, Ken Kowalski wrote:
>>
>> Dear Pavel,
>>
>> I certainly feel your pain but you have to be careful how you fix
>> certain elements in Omega to ensure that you have a valid positive
>> definite covariance matrix. The starting values in your $OMEGA block
>> do not give rise to a valid covariance matrix. Note in particular
>> that the covariance between ETA3 and ETA4 is too large relative to
>> the variances for ETA3 and ETA4 such that the correlation is greater
>> than 1.0, i.e.,
>>
>> Corr(ETA3,ETA4) = 0.03/[SQRT(0.0166)*SQRT(0.0166)]=1.807 > 1
>>
>> You also have the same problem for Corr(ETA1,ETA3) > 1.
>>
>> Ken
>>
>> Kenneth G. Kowalski
>>
>> President & CEO
>>
>> A2PG - Ann Arbor Pharmacometrics Group, Inc.
>>
>> 110 Miller Ave., Garden Suite
>>
>> Ann Arbor, MI 48104
>>
>> Work: 734-274-8255
>>
>> Cell: 248-207-5082
>>
>> Fax: 734-913-0230
>>
>> ken.kowalski
>>
>> www.a2pg.com <http://www.a2pg.com>
>>
>> *From:*owner-nmusers
>> [mailto:owner-nmusers
>> *Sent:* Tuesday, June 12, 2012 10:24 AM
>> *To:* nmusers
>> *Subject:* [NMusers] omega matrix - friendly suggestion
>>
>> Hello NONMEM Community,
>>
>> Sometimes it takes more time to choose the best omega matrix than to
>> develop a PD model. Selecting the omega matric is a tedious, time
>> consuming and less creative part of the model development. I hope
>> you feel my pain. Will it be helpful to rewrite the NONMEM software
>> so that any element of the omega matrix can be fixed to any value?
>> It may look like this:
>>
>> $OMEGA BLOCK (4) 3.60E-02 FIX
>>
>> 0.01 3.23E-02
>> 0.03 0 FIX 1.66E-02
>> 0.01 0 FIX 0.03 FIX 1.66E-02
>>
>> This change can make many NONMEM users happy.
>>
>> Thanks!
>>
>> Pavel
>>
>
> --
> ------------------------------------------------
> Paolo Denti, PhD
> Junior Lecturer
> Division of Clinical Pharmacology
> Department of Medicine
> University of Cape Town
>
> K45 Old Main Building
> Groote Schuur Hospital
> Observatory, Cape Town
> 7925 South Africa
> phone: +27 21 404 7719
> fax: +27 21 448 1989
> email:paolo.denti
> ------------------------------------------------

--
Nick Holford, Professor Clinical Pharmacology

First World Conference on Pharmacometrics, 5-7 September 2012
Seoul, Korea http://www.go-wcop.org

Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53
email: n.holford
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford


Received on Wed Jun 13 2012 - 13:20:10 EDT

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