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
[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
