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From: Bob Leary <Bob.Leary_at_certara.com>

Date: Wed, 13 Apr 2016 16:08:21 +0000

Rupert, I believe at least in principle you are right (I am not sure of the specifics for NONMEM but I am generally familiar with the implementation challenges that time varying covariates pose for EM methods. ) The basic problem is that mu-modeling works to speed up EM methods because the EM update step can be

reduced to a simple linear regression that is very fast. This cannot be done in the time varying case, so a much more computationally intensive update must be used.

If the regression is done anyway in the time varying case, the results are not necessarily correct.

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Rupert Austin

Sent: Wednesday, April 13, 2016 11:44 AM

To: 'Sadler, Brian'; nmusers_at_globomaxnm.com

Subject: RE: [NMusers] RE: Link different thetas to same omega using mu referencing

I’m not sure that Brian’s suggestion is acceptable due to the following constraint I quote from one of the NONMEM manuals:

“Time dependent covariates cannot be part of the MU_ equation”

If CAT is time-varying (as suggested by Jacob) then “MU_1 = CAT1*THETA(1) + CAT2*THETA(2) + CAT3*THETA(3)” includes time dependent covariates. Rather worryingly, I don’t think NONMEM will trap this problem since I have fallen foul of it with no resulting NONMEM warnings, and I have no idea what the consequences are for the resulting NONMEM run and results.

Rupert

Rupert Austin, PhD

Senior Scientist

BAST Inc Limited

Loughborough University Science and Enterprise Park

Charnwood Wing

Holywell Park

Ashby Road

Loughborough, LE11 3AQ, UK

Tel: +44 (0)1509 222908

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Sadler, Brian

Sent: 13 April 2016 13:26

To: nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] RE: Link different thetas to same omega using mu referencing

Hi Jacob,

I suggest:

CAT1=0

CAT2=0

CAT3=0

IF(CAT.EQ.1) CAT1=1

IF(CAT.EQ.2) CAT2=1

IF(CAT.EQ.3) CAT3=1

MU_1 = CAT1*THETA(1) + CAT2*THETA(2) + CAT3*THETA(3)

CL = EXP(MU_1+ETA(1))

That way you have only one OMEGA. This could be more flexible when expanding OMEGA for additional IIV in block format.

Cheers… Brian

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Michael Fossler

Sent: Wednesday, April 13, 2016 7:56 AM

To: Leander, Jacob; nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] RE: Link different thetas to same omega using mu referencing

This looks like it would work – it seems to obey the rules around mu-referencing. You can simplify the $OMEGA by using SAME(3)

Mike

Michael J. Fossler, Pharm. D., Ph. D., F.C.P.

VP, Quantitative Sciences

Trevena, Inc

mfossler_at_trevenainc.com<mailto:mfossler_at_trevenainc.com>

Office: 610-354-8840, ext. 249

Cell: 610-329-6636

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Leander, Jacob

Sent: Wednesday, April 13, 2016 7:01 AM

To: nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] Link different thetas to same omega using mu referencing

Hi

Consider the case where we have a categorical (potentially time-varying) covariate named CAT that can take several values (e.g. 0,1,2,3).

Let’s say I want to model CL depending on this categorical covariate (where parameters are estimated on log-scale).

A simple solution to this would be

IF(CAT.EQ.1) TVCL = THETA(1)

IF(CAT.EQ.2) TVCL = THETA(2)

IF(CAT.EQ.3) TVCL = THETA(3)

I let CL be described by a log-normal distribution with the same omega element for all CAT values.

CL = EXP(TVCL + ETA(1))

With an omega statement:

$OMEGA 0.1

I now want to switch to the mu referencing framework in NONMEM. Each theta needs to be reference to a MU value, and to force it to be described by the same eta I apply the following approach.

MU_1 = THETA(1)

MU_2 = THETA(2)

MU_3 = THETA(3)

IF(CAT.EQ.1) CL = EXP(MU_1 + ETA(1))

IF(CAT.EQ.2) CL = EXP(MU_2 + ETA(2))

IF(CAT.EQ.3) CL = EXP(MU_3 + ETA(3))

With an omega statement:

$OMEGA BLOCK(1) 0.1

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

where I force the omega element corresponding to ETA1, ETA2 and ETA3 to be the same.

Is this a valid approach to obtain what I need?

Or is there a simpler way in the mu-referencing framework to link different thetas to the same omega element?

All the best,

Jacob

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Received on Wed Apr 13 2016 - 12:08:21 EDT

Date: Wed, 13 Apr 2016 16:08:21 +0000

Rupert, I believe at least in principle you are right (I am not sure of the specifics for NONMEM but I am generally familiar with the implementation challenges that time varying covariates pose for EM methods. ) The basic problem is that mu-modeling works to speed up EM methods because the EM update step can be

reduced to a simple linear regression that is very fast. This cannot be done in the time varying case, so a much more computationally intensive update must be used.

If the regression is done anyway in the time varying case, the results are not necessarily correct.

From: owner-nmusers_at_globomaxnm.com [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Rupert Austin

Sent: Wednesday, April 13, 2016 11:44 AM

To: 'Sadler, Brian'; nmusers_at_globomaxnm.com

Subject: RE: [NMusers] RE: Link different thetas to same omega using mu referencing

I’m not sure that Brian’s suggestion is acceptable due to the following constraint I quote from one of the NONMEM manuals:

“Time dependent covariates cannot be part of the MU_ equation”

If CAT is time-varying (as suggested by Jacob) then “MU_1 = CAT1*THETA(1) + CAT2*THETA(2) + CAT3*THETA(3)” includes time dependent covariates. Rather worryingly, I don’t think NONMEM will trap this problem since I have fallen foul of it with no resulting NONMEM warnings, and I have no idea what the consequences are for the resulting NONMEM run and results.

Rupert

Rupert Austin, PhD

Senior Scientist

BAST Inc Limited

Loughborough University Science and Enterprise Park

Charnwood Wing

Holywell Park

Ashby Road

Loughborough, LE11 3AQ, UK

Tel: +44 (0)1509 222908

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Sadler, Brian

Sent: 13 April 2016 13:26

To: nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] RE: Link different thetas to same omega using mu referencing

Hi Jacob,

I suggest:

CAT1=0

CAT2=0

CAT3=0

IF(CAT.EQ.1) CAT1=1

IF(CAT.EQ.2) CAT2=1

IF(CAT.EQ.3) CAT3=1

MU_1 = CAT1*THETA(1) + CAT2*THETA(2) + CAT3*THETA(3)

CL = EXP(MU_1+ETA(1))

That way you have only one OMEGA. This could be more flexible when expanding OMEGA for additional IIV in block format.

Cheers… Brian

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Michael Fossler

Sent: Wednesday, April 13, 2016 7:56 AM

To: Leander, Jacob; nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] RE: Link different thetas to same omega using mu referencing

This looks like it would work – it seems to obey the rules around mu-referencing. You can simplify the $OMEGA by using SAME(3)

Mike

Michael J. Fossler, Pharm. D., Ph. D., F.C.P.

VP, Quantitative Sciences

Trevena, Inc

mfossler_at_trevenainc.com<mailto:mfossler_at_trevenainc.com>

Office: 610-354-8840, ext. 249

Cell: 610-329-6636

From: owner-nmusers_at_globomaxnm.com<mailto:owner-nmusers_at_globomaxnm.com> [mailto:owner-nmusers_at_globomaxnm.com] On Behalf Of Leander, Jacob

Sent: Wednesday, April 13, 2016 7:01 AM

To: nmusers_at_globomaxnm.com<mailto:nmusers_at_globomaxnm.com>

Subject: [NMusers] Link different thetas to same omega using mu referencing

Hi

Consider the case where we have a categorical (potentially time-varying) covariate named CAT that can take several values (e.g. 0,1,2,3).

Let’s say I want to model CL depending on this categorical covariate (where parameters are estimated on log-scale).

A simple solution to this would be

IF(CAT.EQ.1) TVCL = THETA(1)

IF(CAT.EQ.2) TVCL = THETA(2)

IF(CAT.EQ.3) TVCL = THETA(3)

I let CL be described by a log-normal distribution with the same omega element for all CAT values.

CL = EXP(TVCL + ETA(1))

With an omega statement:

$OMEGA 0.1

I now want to switch to the mu referencing framework in NONMEM. Each theta needs to be reference to a MU value, and to force it to be described by the same eta I apply the following approach.

MU_1 = THETA(1)

MU_2 = THETA(2)

MU_3 = THETA(3)

IF(CAT.EQ.1) CL = EXP(MU_1 + ETA(1))

IF(CAT.EQ.2) CL = EXP(MU_2 + ETA(2))

IF(CAT.EQ.3) CL = EXP(MU_3 + ETA(3))

With an omega statement:

$OMEGA BLOCK(1) 0.1

$OMEGA BLOCK(1) SAME

$OMEGA BLOCK(1) SAME

where I force the omega element corresponding to ETA1, ETA2 and ETA3 to be the same.

Is this a valid approach to obtain what I need?

Or is there a simpler way in the mu-referencing framework to link different thetas to the same omega element?

All the best,

Jacob

________________________________

Confidentiality Notice: This message is private and may contain confidential and proprietary information. If you have received this message in error, please notify us and remove it from your system and note that you must not copy, distribute or take any action in reliance on it. Any unauthorized use or disclosure of the contents of this message is not permitted and may be unlawful.

________________________________

Notice: This e-mail message, together with any attachments, contains information of Trevena, Inc., 1018 West 8th Avenue, King of Prussia, PA 19406, USA. This information may be confidential, proprietary, copyrighted and/or legally privileged.

It is intended solely for use by 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 and delete it and any attachments from your system.

ICON plc made the following annotations.

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

This e-mail transmission may contain confidential or legally privileged information that is intended only for the individual or entity named in the e-mail address. If you are not the intended recipient, you are hereby notified that any disclosure, copying, distribution, or reliance upon the contents of this e-mail is strictly prohibited. If you have received this e-mail transmission in error, please reply to the sender, so that ICON plc can arrange for proper delivery, and then please delete the message.

Thank You,

ICON plc

South County Business Park

Leopardstown

Dublin 18

Ireland

Registered number: 145835

NOTICE: The information contained in this electronic mail message is intended only for the personal and confidential

use of the designated recipient(s) named above. This message may be an attorney-client communication, may be protected

by the work product doctrine, and may be subject to a protective order. As such, this message is privileged and

confidential. If the reader of this message is not 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 possession (whether hard copies or electronically stored copies). Thank you.

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Received on Wed Apr 13 2016 - 12:08:21 EDT