Re: omega matrix - friendly suggestion
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
Quoted reply history
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
> >
> > [email protected] <mailto:[email protected]>
> >
> > www.a2pg.com http://www.a2pg.com
> >
> > *From:* [email protected] [ mailto: [email protected] ] *On Behalf Of * [email protected]
> >
> > *Sent:* Tuesday, June 12, 2012 10:24 AM
> > *To:* [email protected]
> > *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:[email protected]
> ------------------------------------------------
--
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: [email protected]
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford