# RE: RE: Link different thetas to same omega using mu referencing

From: Bob Leary <Bob.Leary>
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 mailto:owner-nmusers
Sent: Wednesday, April 13, 2016 11:44 AM
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
Loughborough, LE11 3AQ, UK
Tel: +44 (0)1509 222908

From: owner-nmusers
Sent: 13 April 2016 13:26
To: nmusers
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 er-nmusers
Sent: Wednesday, April 13, 2016 7:56 AM
To: Leander, Jacob; nmusers xnm.com<mailto:nmusers
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 nc.com>
Office: 610-354-8840, ext. 249
Cell: 610-329-6636

From: owner-nmusers sers
Sent: Wednesday, April 13, 2016 7:01 AM
To: nmusers 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

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