From: Bob Leary <*Bob.Leary*>

Date: Tue, 8 Oct 2013 08:40:28 -0400

Paolo -

That is correct - if a symmetric matrix has a zero on the diagonal, it cann=

ot be positive definite. At best it is positive semidefinite (all eigenvalu=

es non-negative, but one or more are zero).

If there is a negative on the diagonal, then it cannot even be positive sem=

idefinite - there must be at least one negative eigenvalue.

Note that the idea of a 'real part' does not apply - all eigenvalues of a r=

eal symmetric matrix are real.

From: owner-nmusers

Behalf Of Paolo Denti

Sent: Tuesday, October 08, 2013 8:11 AM

To: Lindauer, A (Andreas); nmusers

Subject: Re: [NMusers] RE: Simulations with OMEGA BLOCK

Hi Andreas,

I believe your OMEGA matrix is positive SEMI-definite, because one of the e=

igeinvalues is 0.

I think the definition is that the real part of all eigenvalues must be STR=

ICTLY larger than 0.

I am no "matrix talker", but I think that if there is a zero on the diagona=

l, the matrix can't be positive definite (strictly).

I hope this helps, or that some gurus will shed some light.

Ciao,

Paolo

On 2013/10/08 12:40, Lindauer, A (Andreas) wrote:

Hi Douglas,

Please note that this is all about simulations - I'm not trying to estimate=

36 elements of random effects.

The BLOCK(7) suggestion works, just as did the first example that I provide=

d. My apologies for not being very clear in my previous e-mail, I'm not loo=

king for a work around for that particular example, but rather was seeking =

for ways to rewrite a 'cluttered' OMEGA statement in a more general, machin=

e-readable format as a triangular matrix.

Hi Paolo,

Thanks for your response. You said:

Also, the block matrix is either all zeros and FIXED, or it must be positiv=

e definite. If you fix one of the elements of the diagonal to 0, it goes ag=

ainst these rules.

Well, the matrix that I showed as an example is in fact positive definite. =

Or is it that NONMEM just checks if there is any zero diagonal element in B=

LOCK and returns an error without actually checking if the matrix is truly =

non-positive definite? This is how I would interpret the explanations that =

are given in the NONMEM help.

Thanks again, Andreas.

From: Eleveld, DJ [mailto:d.j.eleveld

Sent: Tuesday, October 08, 2013 11:33 AM

To: Lindauer, A (Andreas); nmusers

.com>

Subject: RE: Simulations with OMEGA BLOCK

Hi Andreas,

You cant fix part of a block in NONMEM, you have to fix the whole block. So=

the trick is to construct the covaiance matrix structure you want out of s=

maller blocks.

And when you fix an ETA on the diagonal to zero the corresponding covarianc=

es have to be zero as well. (i.e. the left-most variables in you BLOCK(8) m=

atrix)

So what I think you want for your full-matrix is something like:

$OMEGA

0 FIX ; IIV_CL2

$OMEGA BLOCK(7)

0.1 ; IIV_V2

0 0.1 ; IIV_F1

0 0 0.01 ; IIV_KA

0 0 0 0.01 ; IOV_KA

0 0 0 0 0.01

0 0 0 0 0 0.01

0 0 0 0 0 0 0.01

I hope you have LOTS of data since a BLOCK(7) marix has LOTS of paramaters =

to estimate.

You are also combining IIV and IOV variances in a single matrix.

Does it make sense to expect the IIV_KA and IOV_KA to be correlated?

I cant imagine how this is supposed to work, but admittedly I havent given =

it all that much thought.

It just looks fishy to me. I cant seem to understand what behavior you are =

trying to capture in this kind of covariance structure.

warm regards,

Douglas Eleveld

________________________________

Van: owner-nmusers

lto:owner-nmusers

Verzonden: October 8, 2013 10:22 AM

Aan: nmusers

Onderwerp: [NMusers] Simulations with OMEGA BLOCK

Hi NMUSERS,

I have a question regarding the use of OMEGA BLOCK statements in simulation=

s when one (or more) elements of the matrix are 0.

When I use the following lines to describe the OMEGA structure and run the =

simulation everything works well:

$OMEGA

0 FIX ; IIV_CL2

0.1 ; IIV_V2

0.1 ; IIV_F1

0.01 ; IIV_KA

$OMEGA BLOCK(1) 0.01 ; IOV_KA

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

However, rewriting the above as a full matrix gives me an error message:

$OMEGA BLOCK(8)

0 FIX

0 0.1

0 0 0.1

0 0 0 0.01

0 0 0 0 0.01

0 0 0 0 0 0.01

0 0 0 0 0 0 0.01

0 0 0 0 0 0 0 0.01

NM-TRAN MESSAGES

AN ERROR WAS FOUND IN THE CONTROL STATEMENTS.

AN ERROR WAS FOUND ON LINE 75 AT THE APPROXIMATE POSITION NOTED:

0 0 0 0 0 0 0 0.01

224 A VARIANCE IS ZERO, BUT THE BLOCK IS NOT FIXED TO ZERO.

I tried numerous different ways of placing the term FIX in the block, or no=

t mentioning it at all - nothing worked, except replacing the 0 diagonal el=

ement by a very small number. I know that there are certain constrains of u=

sing 0 values in an OMEGA BLOCK (band symmetric form), but I always thought=

this was only relevant for estimation.

Has anyone come across a similar issue when simulating?

Best regards, Andreas.

Andreas Lindauer, Ph.D.

Associate Principal Scientist, Clinical PKPD

Pharmacokinetics, Pharmacodynamics, and Drug Metabolism

Merck & Co. / MSD

Notice: This e-mail message, together with any attachments, contains

information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates Direct contact information

for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

proprietary copyrighted and/or legally privileged. It is intended solely

for the use of the individual or entity named on this message. If you are

not the intended recipient, and have received this message in error,

please notify us immediately by reply e-mail and then delete it from

your system.

________________________________

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadre=

sseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik maken van di=

t bericht, het niet openbaar maken of op enige wijze verspreiden of vermeni=

gvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomple=

te aankomst of vertraging van dit verzonden bericht.

The contents of this message are confidential and only intended for the eye=

s 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 i=

n any way. The UMCG cannot be held responsible for incomplete reception or =

delay of this transferred message.

Notice: This e-mail message, together with any attachments, contains

information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates Direct contact information

for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

proprietary copyrighted and/or legally privileged. It is intended solely

for the use of the individual or entity named on this message. If you are

not the intended recipient, and have received this message in error,

please notify us immediately by reply e-mail and then delete it from

your system.

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

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

------------------------------------------------

________________________________

UNIVERSITY OF CAPE TOWN

This e-mail is subject to the UCT ICT policies and e-mail disclaimer publis=

hed on our website at http://www.uct.ac.za/about/policies/emaildisclaimer/ =

or obtainable from +27 21 650 9111. This e-mail is intended only for the pe=

rson(s) to whom it is addressed. If the e-mail has reached you in error, pl=

ease notify the author. If you are not the intended recipient of the e-mail=

you may not use, disclose, copy, redirect or print the content. If this e-=

mail is not related to the business of UCT it is sent by the sender in the =

sender's individual capacity. NOTICE: The information contained in =

this electronic mail message is intended only for the personal and confiden=

tial use of the designated recipient(s) named above. This message may =

be an attorney-client communication, may be protected by the work prod=

uct doctrine, and may be subject to a protective order. As such, this messa=

ge is privileged and confidential. If the reader of this message is no=

t the intended recipient or an agent responsible for delivering it to =

the intended recipient, you are hereby notified that you have received this=

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copying of this message is strictly prohibited. If you have received this=

communication in error, please notify us immediately by telephone and=

e-mail and destroy any and all copies of this message in your possess=

ion (whether hard copies or electronically stored copies). Thank you. =

buSp9xeMeKEbrUze

Received on Tue Oct 08 2013 - 08:40:28 EDT

Date: Tue, 8 Oct 2013 08:40:28 -0400

Paolo -

That is correct - if a symmetric matrix has a zero on the diagonal, it cann=

ot be positive definite. At best it is positive semidefinite (all eigenvalu=

es non-negative, but one or more are zero).

If there is a negative on the diagonal, then it cannot even be positive sem=

idefinite - there must be at least one negative eigenvalue.

Note that the idea of a 'real part' does not apply - all eigenvalues of a r=

eal symmetric matrix are real.

From: owner-nmusers

Behalf Of Paolo Denti

Sent: Tuesday, October 08, 2013 8:11 AM

To: Lindauer, A (Andreas); nmusers

Subject: Re: [NMusers] RE: Simulations with OMEGA BLOCK

Hi Andreas,

I believe your OMEGA matrix is positive SEMI-definite, because one of the e=

igeinvalues is 0.

I think the definition is that the real part of all eigenvalues must be STR=

ICTLY larger than 0.

I am no "matrix talker", but I think that if there is a zero on the diagona=

l, the matrix can't be positive definite (strictly).

I hope this helps, or that some gurus will shed some light.

Ciao,

Paolo

On 2013/10/08 12:40, Lindauer, A (Andreas) wrote:

Hi Douglas,

Please note that this is all about simulations - I'm not trying to estimate=

36 elements of random effects.

The BLOCK(7) suggestion works, just as did the first example that I provide=

d. My apologies for not being very clear in my previous e-mail, I'm not loo=

king for a work around for that particular example, but rather was seeking =

for ways to rewrite a 'cluttered' OMEGA statement in a more general, machin=

e-readable format as a triangular matrix.

Hi Paolo,

Thanks for your response. You said:

Also, the block matrix is either all zeros and FIXED, or it must be positiv=

e definite. If you fix one of the elements of the diagonal to 0, it goes ag=

ainst these rules.

Well, the matrix that I showed as an example is in fact positive definite. =

Or is it that NONMEM just checks if there is any zero diagonal element in B=

LOCK and returns an error without actually checking if the matrix is truly =

non-positive definite? This is how I would interpret the explanations that =

are given in the NONMEM help.

Thanks again, Andreas.

From: Eleveld, DJ [mailto:d.j.eleveld

Sent: Tuesday, October 08, 2013 11:33 AM

To: Lindauer, A (Andreas); nmusers

.com>

Subject: RE: Simulations with OMEGA BLOCK

Hi Andreas,

You cant fix part of a block in NONMEM, you have to fix the whole block. So=

the trick is to construct the covaiance matrix structure you want out of s=

maller blocks.

And when you fix an ETA on the diagonal to zero the corresponding covarianc=

es have to be zero as well. (i.e. the left-most variables in you BLOCK(8) m=

atrix)

So what I think you want for your full-matrix is something like:

$OMEGA

0 FIX ; IIV_CL2

$OMEGA BLOCK(7)

0.1 ; IIV_V2

0 0.1 ; IIV_F1

0 0 0.01 ; IIV_KA

0 0 0 0.01 ; IOV_KA

0 0 0 0 0.01

0 0 0 0 0 0.01

0 0 0 0 0 0 0.01

I hope you have LOTS of data since a BLOCK(7) marix has LOTS of paramaters =

to estimate.

You are also combining IIV and IOV variances in a single matrix.

Does it make sense to expect the IIV_KA and IOV_KA to be correlated?

I cant imagine how this is supposed to work, but admittedly I havent given =

it all that much thought.

It just looks fishy to me. I cant seem to understand what behavior you are =

trying to capture in this kind of covariance structure.

warm regards,

Douglas Eleveld

________________________________

Van: owner-nmusers

lto:owner-nmusers

Verzonden: October 8, 2013 10:22 AM

Aan: nmusers

Onderwerp: [NMusers] Simulations with OMEGA BLOCK

Hi NMUSERS,

I have a question regarding the use of OMEGA BLOCK statements in simulation=

s when one (or more) elements of the matrix are 0.

When I use the following lines to describe the OMEGA structure and run the =

simulation everything works well:

$OMEGA

0 FIX ; IIV_CL2

0.1 ; IIV_V2

0.1 ; IIV_F1

0.01 ; IIV_KA

$OMEGA BLOCK(1) 0.01 ; IOV_KA

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

However, rewriting the above as a full matrix gives me an error message:

$OMEGA BLOCK(8)

0 FIX

0 0.1

0 0 0.1

0 0 0 0.01

0 0 0 0 0.01

0 0 0 0 0 0.01

0 0 0 0 0 0 0.01

0 0 0 0 0 0 0 0.01

NM-TRAN MESSAGES

AN ERROR WAS FOUND IN THE CONTROL STATEMENTS.

AN ERROR WAS FOUND ON LINE 75 AT THE APPROXIMATE POSITION NOTED:

0 0 0 0 0 0 0 0.01

224 A VARIANCE IS ZERO, BUT THE BLOCK IS NOT FIXED TO ZERO.

I tried numerous different ways of placing the term FIX in the block, or no=

t mentioning it at all - nothing worked, except replacing the 0 diagonal el=

ement by a very small number. I know that there are certain constrains of u=

sing 0 values in an OMEGA BLOCK (band symmetric form), but I always thought=

this was only relevant for estimation.

Has anyone come across a similar issue when simulating?

Best regards, Andreas.

Andreas Lindauer, Ph.D.

Associate Principal Scientist, Clinical PKPD

Pharmacokinetics, Pharmacodynamics, and Drug Metabolism

Merck & Co. / MSD

Notice: This e-mail message, together with any attachments, contains

information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates Direct contact information

for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

proprietary copyrighted and/or legally privileged. It is intended solely

for the use of the individual or entity named on this message. If you are

not the intended recipient, and have received this message in error,

please notify us immediately by reply e-mail and then delete it from

your system.

________________________________

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadre=

sseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik maken van di=

t bericht, het niet openbaar maken of op enige wijze verspreiden of vermeni=

gvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomple=

te aankomst of vertraging van dit verzonden bericht.

The contents of this message are confidential and only intended for the eye=

s 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 i=

n any way. The UMCG cannot be held responsible for incomplete reception or =

delay of this transferred message.

Notice: This e-mail message, together with any attachments, contains

information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station,

New Jersey, USA 08889), and/or its affiliates Direct contact information

for affiliates is available at

http://www.merck.com/contact/contacts.html) that may be confidential,

proprietary copyrighted and/or legally privileged. It is intended solely

for the use of the individual or entity named on this message. If you are

not the intended recipient, and have received this message in error,

please notify us immediately by reply e-mail and then delete it from

your system.

--

------------------------------------------------

Paolo Denti, PhD

Pharmacometrics Group

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

------------------------------------------------

________________________________

UNIVERSITY OF CAPE TOWN

This e-mail is subject to the UCT ICT policies and e-mail disclaimer publis=

hed on our website at http://www.uct.ac.za/about/policies/emaildisclaimer/ =

or obtainable from +27 21 650 9111. This e-mail is intended only for the pe=

rson(s) to whom it is addressed. If the e-mail has reached you in error, pl=

ease notify the author. If you are not the intended recipient of the e-mail=

you may not use, disclose, copy, redirect or print the content. If this e-=

mail is not related to the business of UCT it is sent by the sender in the =

sender's individual capacity. NOTICE: The information contained in =

this electronic mail message is intended only for the personal and confiden=

tial use of the designated recipient(s) named above. This message may =

be an attorney-client communication, may be protected by the work prod=

uct doctrine, and may be subject to a protective order. As such, this messa=

ge is privileged and confidential. If the reader of this message is no=

t the intended recipient or an agent responsible for delivering it to =

the intended recipient, you are hereby notified that you have received this=

message in error and that any review, dissemination, distribution, or=

copying of this message is strictly prohibited. If you have received this=

communication in error, please notify us immediately by telephone and=

e-mail and destroy any and all copies of this message in your possess=

ion (whether hard copies or electronically stored copies). Thank you. =

buSp9xeMeKEbrUze

Received on Tue Oct 08 2013 - 08:40:28 EDT