NONMEM Users Network Archive

Hosted by Cognigen

Re: OMEGA matrix

From: Pavel Belo <nonmem>
Date: Tue, 30 Sep 2014 12:23:30 -0400 (EDT)

Dear Joren and the NONMEM Team,


Your email is definitely informative. 


    1. "Off-diagonal elements (as explained by Bob Bauer) are available
as sample correlations and do not have to be separately computed in
contrast to linearization approaches such as FOCE."  It may explain th=
stability of the results when very large block matrix is used.  On the=
other hand, it is not clear why Monolix SAEM may not work the same way.=

Is Monolix estimating correlations? Also, when we deal with "sample
correlations", we may be talking about correlations between observed=
minus individual predicted values.  Shrinkage can possibly affect such=


    1. "I would advise to explore its properties further using matrix
decomposition approaches (PCA etc)".  Do you suggest to decompose the=
omega matrix and explore derived variables instead of original
off-diagonal elements?  It seems straightforward, but I recall error=


If you can point at some publications for both items 1 and 2 above, it
will be greatly appreciated. 


The importance of improving the OMEGA matrix may come from PD modeling.=

PD models are frequently more empirical than PK models and strong
correlations come from nowhere.  They are difficult to interpret, but=
important to account for when simulations are requested by the
agencies.  There are correlations, which change from 0 to 0.6 when
models are slightly different indicating that they may be
insignificant.  Monolix allows us to set a single correlation to zero.=
NONMEM may require a different approach. I am searching for the
different approaches because after many years I am emotionally attached
to NONMEM and because NONMEM is very flexible. 



Kind regards,



On Mon, Sep 29, 2014 at 07:00 PM, Jeroen Elassaiss-Schaap wrote:




Dear Pavel, others,

The underlying technical difference is that SAEM is in its core a
sampling methodology. Off-diagonal elements (as explained by Bob Bauer)
are available as sample correlations and do not have to be separately
computed in contrast to linearization approaches such as FOCE.

The more interesting question to me, as also eluted to by Ken, is what
criteria to set up for inclusion of an off-diagonal element. I
completely support his argument for simulation performance of the model,
as e.g. judged using a VPC. Whether to score it as an additional degree
of freedom may be up to debate. An off-diagonal element in essence
limits the freedom of the model as the random space in which samples can
be generated will be smaller. In that perspective one could argue to
retain any off-diagonal element that is sufficiently deviating from zero
regardless of ofv changes, and to not apply the concept of
over-parametrization (or at least not in comparison to other types of
parameters). In practice inclusion of an important off-diagonal is
mostly accompanied by a sound improvement in ofv anyway.

More can be found in earlier discussions we had on this list, see e.g.
quite an extensive one from 2010. Here also an r-script to visualize the
parameter space impact can be found ;-).

In cases where a larger full or banded omega block is found, I would
advice to explore its properties further using matrix decomposition
approaches (PCA etc) to evaluate propagated correlations across the
matrix.  But also on the basis of physiology/pharmacology as a data
sample may not be informative enough to support robust interpretation of
correlations. A discussion along those lines in reporting seems the more
fruitful to me.

Best regards,
Jeroen <>

-- More value out of your data!

-----Original Message-----
From: owner-nmusers
Sent: Friday, September 26, 2014 09:15
To: Kowalski, Ken; 'Eleveld, DJ'; 'Pavel Belo'; nmusers
Subject: RE: [NMusers] OMEGA matrix
Dear Pavel,
To answer your question I suggest you go on Bob Bauer's NONMEM 7 course.
The understanding I gleaned from that course (which I think was enhanced
by the excellent wine we had at lunch in Alicante) was that with
appropriate MU parameterisation there is virtually no computational
disadvantage to estimating the full block with the newer algorithms. So
you might as well do it, at least in early runs where you want an idea
of which parameter correlations might be useful/reasonably estimated.

Joseph F Standing
MRC Fellow, UCL Institute of Child Health
Antimicrobial Pharmacist, Great Ormond Street Hospital
Tel: +44(0)207 905 2370
Mobile: +44(0)7970 572435

From: owner-nmusers
Behalf Of Ken Kowalski [ken.kowalski
Sent: 25 September 2014 22:43
To: 'Eleveld, DJ'; 'Pavel Belo'; nmusers
Subject: RE: [NMusers] OMEGA matrix
Warning: This message contains unverified links which may not be safe.
You should only click links if you are sure they are from a trusted
Hi Douglas,
My own thinking is that you should fit the largest omega structure that
be supported by the data rather than just always assuming a diagonal
structure. This does not necessarily mean always fitting a full block
structure, as it can often lead to an ill-conditioned model, however,
may be a reduced block omega structure that is more parsimonious than
diagonal omega structure. Getting the omega structure right is
important for simulation of individual responses. For example, if you
always simulate from a diagonal omega structure for CL and V when there
evidence that the random effects are highly positively correlated then
may end up simulating individual PK profiles for combinations of
CLs and Vs that are not represented in your data (i.e., high correlation
would suggest that individuals with high CL will tend to also have high
and vice versa whereas a simulation assuming that they are independent
result in simulating for some individuals with high CL and low V and
individuals with low CL and high V that might not be represented in your
data). This could lead to simulations that over-predict the variation in
the concentration-time profiles even though the diagonal omega may be
sufficient for purposes of predicting central tendency in the PK
You can confirm this by VPC looking at your ability to predict say the
and 90th percentiles in comparison to the observed 10th and 90th
in your data. That is, if you simulate from the diagonal omega when
is correlation in the random effects you may find that your prediction
the 10th and 90th percentiles are more extreme than that in your
data. I see this all the time in VPC plots where the majority of the
observed data are well within the predictions of the 10th and 90th
percentiles when we should expect about 10% of our data above the 90th
percentile prediction and 10% below the 10th percentile prediction.
Best regards,
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 <>

-----Original Message-----
From: owner-nmusers
Behalf Of Eleveld, DJ
Sent: Thursday, September 25, 2014 4:36 PM
To: Pavel Belo; nmusers
Subject: RE: [NMusers] OMEGA matrix
Hi Pavel,
My question is: Why is it desirable to fit a complete omega matrix if
physical interpretation is unclear? Etas are variation of unknown origin
i.e. not explained by the structural model. A full omega matrix allows
unknown variation of one paramater to have a (linear?) relationship with
some other thing that is also unknown. If unknown A is found to have a
linear relationship with unknown B, then what knowlegde is gained? I do
think it can be instructive to to look at correlations and use this
information to make a better structural model. But I think diagonal
matrix is more desirable if it works ok.
warm regards,
Douglas Eleveld

From: owner-nmusers
of Pavel Belo [nonmem
Sent: Thursday, September 25, 2014 4:24 PM
To: nmusers
Subject: [NMusers] OMEGA matrix
Hello Nonmem Community,
It seems like NONMEM developers may advise to start with full OMEGA
at the beginning of model development. Monolix developers may advise to
start with a diagonal matrix. Is there something different in NONMEM
algorithms that makes model stable when a lot of statistically
correlations/covariances are estimated in the model?
It seems like NONMEM SAEM can be very stable in very "hard cases" (a lot
outliers, partially misspecified model, overparameterized model, etc.).
omega matrix is a part of the puzzle.
When it is impossible to test every correlation coefficient for
due to some limitations, it becomes a regulatory issue. We may need to
able to make a statement that the model is safe and sound even when
matrix can be overparameterized (tries to estimate too many
parameters within the OMEGA matrix).
Kind regards,

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de
geadresseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik
van dit bericht, het niet openbaar maken of op enige wijze verspreiden
vermenigvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor
incomplete aankomst of vertraging van dit verzonden bericht.
The contents of this message are confidential and only intended for the
of the addressee(s). Others than the addressee(s) are not allowed to use
this message, to make it public or to distribute or multiply this
message in
any way. The UMCG cannot be held responsible for incomplete reception or
delay of this transferred message.

This message may contain confidential information. If you are not the
intended recipient please inform the
sender that you have received the message in error before deleting it.
Please do not disclose, copy or distribute information in this e-mail or
take any action in reliance on its contents:
to do so is strictly prohibited and may be unlawful.
Thank you for your co-operation.
NHSmail is the secure email and directory service available for all NHS
staff in England and Scotland
NHSmail is approved for exchanging patient data and other sensitive
information with NHSmail and GSi recipients
NHSmail provides an email address for your career in the NHS and can be
accessed anywhere

Received on Tue Sep 30 2014 - 12:23:30 EDT

The NONMEM Users Network is maintained by ICON plc. Requests to subscribe to the network should be sent to:

Once subscribed, you may contribute to the discussion by emailing: