Dear NMusers,<?xml:namespace prefix = o ns =
"urn:schemas-microsoft-com:office:office" />
I have run in to an old problem that Vladimir once described here on the users
net. I am trying to implement inter-individual variability in residual variance
and the corresponding OMEGA is not being iterated. Usually, in Dr. Karlsson's
work this error structure is implemented on a proportional or
proportional+additive EPS model. I am wondering if my problem is because I am
trying to implement ETA on EPS using the transform both sides approach as
follows?
$ERROR
CALLFL=0
IPRED = -5
IF (F.GT.0) IPRED = LOG(F)
IRES=DV-IPRED
W=1
IWRES=IRES/W
Y = IPRED + EXP(ETA(.))*EPS(1)
Kindly advice...MNS
--------Cut here
From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
Subject: [NMusers] Implementation of interindividual variability in residual
variance
Date: 2/17/2004 9:37 AM
Dear NONMEM users,
I am trying to implement an interidividual variability in
the residual variance using an additional random effect:
$ERR
Y = F + EXP(ETA(.))*EPS(1)
It turned out the corresponding OMEGA was not iterated, and the final estimate
did not differ from the initial value. Below is an example control stream
and the output illustrating the problem (Note, the actual model I work with is
more complicated).
Thanks in advance.
Best regards,
Vladimir
--------Cut here
Interindividual variability in residual variance
Mahesh,
Did you use the INTERACTION option?
Erik
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] on behalf of Samtani, Mahesh [PRDUS]
Sent: Wed 7/11/2007 2:26 PM
To: [email protected]
Subject: [NMusers] Interindividual variability in residual variance
Dear NMusers,
I have run in to an old problem that Vladimir once described here on the users
net. I am trying to implement inter-individual variability in residual variance
and the corresponding OMEGA is not being iterated. Usually, in Dr. Karlsson's
work this error structure is implemented on a proportional or
proportional+additive EPS model. I am wondering if my problem is because I am
trying to implement ETA on EPS using the transform both sides approach as
follows?
$ERROR
CALLFL=0
IPRED = -5
IF (F.GT.0) IPRED = LOG(F)
IRES=DV-IPRED
W=1
IWRES=IRES/W
Y = IPRED + EXP(ETA(.))*EPS(1)
Kindly advice...MNS
--------Cut here
From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
Subject: [NMusers] Implementation of interindividual variability in residual
variance
Date: 2/17/2004 9:37 AM
Dear NONMEM users,
I am trying to implement an interidividual variability in
the residual variance using an additional random effect:
$ERR
Y = F + EXP(ETA(.))*EPS(1)
It turned out the corresponding OMEGA was not iterated, and the final estimate
did not differ from the initial value. Below is an example control stream
and the output illustrating the problem (Note, the actual model I work with is
more complicated).
Thanks in advance.
Best regards,
Vladimir
--------Cut here
Dear Mahesh,
In order for the IIV in RV to be implemented, it is necessary that you use
the INTERACTION option in $EST, even if you use the additive error.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax +46 18 471 4003
[EMAIL PROTECTED]
_____
Quoted reply history
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Samtani, Mahesh [PRDUS]
Sent: Wednesday, July 11, 2007 14:27
To: [email protected]
Subject: [NMusers] Interindividual variability in residual variance
Dear NMusers,
I have run in to an old problem that Vladimir once described here on the
users net. I am trying to implement inter-individual variability in residual
variance and the corresponding OMEGA is not being iterated. Usually, in Dr.
Karlsson's work this error structure is implemented on a proportional or
proportional+additive EPS model. I am wondering if my problem is because I
am trying to implement ETA on EPS using the transform both sides approach as
follows?
$ERROR
CALLFL=0
IPRED = -5
IF (F.GT.0) IPRED = LOG(F)
IRES=DV-IPRED
W=1
IWRES=IRES/W
Y = IPRED + EXP(ETA(.))*EPS(1)
Kindly advice...MNS
--------Cut here
From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
Subject: [NMusers] Implementation of interindividual variability in residual
variance
Date: 2/17/2004 9:37 AM
Dear NONMEM users,
I am trying to implement an interidividual variability in
the residual variance using an additional random effect:
$ERR
Y = F + EXP(ETA(.))*EPS(1)
It turned out the corresponding OMEGA was not iterated, and the final
estimate
did not differ from the initial value. Below is an example control stream
and the output illustrating the problem (Note, the actual model I work with
is more complicated).
Thanks in advance.
Best regards,
Vladimir
--------Cut here
1) The original email and responses can be found at
http://www.cognigencorp.com/nonmem/nm/99feb172004.html
2) Your model does not make sense. In effect
Y = LOG(F) + EXP(ETA(.))*EPS(1)
This is equivalent to
EXP(Y)=EXP(LOG(F))*EXP(EXP(ETA(.))*EPS(1))
EXP(Y)=F*EXP(EXP(ETA(.))*EPS(1))
Note the exp of exp.
When working with logs,an additive error term makes more sense
Y = LOG(F) + ETA(.)*EPS(1)
LOG(Y)=EXP(LOG(F) + ETA(.)*EPS(1))=EXP(LOG(F))*EXP(ETA(.)*EPS(1))
LOG(Y)=F*EXP(ETA(.)*EPS(1))
This is now a proportional error model.
On Wed, 11 Jul 2007 08:26:54 -0400, "Samtani, Mahesh [PRDUS]"
<[EMAIL PROTECTED]> said:
> Dear NMusers,<?xml:namespace prefix = o ns =
> "urn:schemas-microsoft-com:office:office" />
>
> I have run in to an old problem that Vladimir once described here on the
> users net. I am trying to implement inter-individual variability in
> residual variance and the corresponding OMEGA is not being iterated.
> Usually, in Dr. Karlsson's work this error structure is implemented on a
> proportional or proportional+additive EPS model. I am wondering if my
> problem is because I am trying to implement ETA on EPS using the
> transform both sides approach as follows?
>
>
>
> $ERROR
>
> CALLFL=0
>
> IPRED = -5
>
> IF (F.GT.0) IPRED = LOG(F)
>
> IRES=DV-IPRED
>
> W=1
>
> IWRES=IRES/W
>
> Y = IPRED + EXP(ETA(.))*EPS(1)
>
>
>
> Kindly advice...MNS
>
>
>
> --------Cut here
>
> From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
>
> Subject: [NMusers] Implementation of interindividual variability in
> residual variance
>
> Date: 2/17/2004 9:37 AM
>
>
>
> Dear NONMEM users,
>
>
>
> I am trying to implement an interidividual variability in
>
> the residual variance using an additional random effect:
>
>
>
> $ERR
>
> Y = F + EXP(ETA(.))*EPS(1)
>
>
>
> It turned out the corresponding OMEGA was not iterated, and the final
> estimate
>
> did not differ from the initial value. Below is an example control stream
>
> and the output illustrating the problem (Note, the actual model I work
> with is more complicated).
>
>
>
> Thanks in advance.
>
>
>
> Best regards,
>
> Vladimir
>
> --------Cut here
>
>
--
Alison Boeckmann
[EMAIL PROTECTED]
Dear Alison,
The addition of EXP(ETA(.)) is to provide a scaling for the residual error
magnitude. This scaling factor is 1 for the typical individual (ETA=0) and
the sigma estimate is thus the residual error magnitude for the typical
subject. Other subjects will have scaling factors larger or smaller than 1,
but all will be >0. I see no problem in the "exp of exp" - it does exactly
what is desired.
With the alternative model
Y = LOG(F) + ETA(.)*EPS(1)
the typical individual (with ETA=0) is having a zero residual error
magnitude. Clearly that model does not work.
Best regards,
Mats
Mats Karlsson, PhD
Professor of Pharmacometrics
Div. of Pharmacokinetics and Drug Therapy
Dept. of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
SE-751 24 Uppsala
Sweden
phone +46 18 471 4105
fax +46 18 471 4003
[EMAIL PROTECTED]
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Alison Boeckmann
Sent: Thursday, July 12, 2007 02:04
To: Samtani, Mahesh [PRDUS]; [email protected]
Subject: Re: [NMusers] Interindividual variability in residual variance
1) The original email and responses can be found at
http://www.cognigencorp.com/nonmem/nm/99feb172004.html
2) Your model does not make sense. In effect
Y = LOG(F) + EXP(ETA(.))*EPS(1)
This is equivalent to
EXP(Y)=EXP(LOG(F))*EXP(EXP(ETA(.))*EPS(1))
EXP(Y)=F*EXP(EXP(ETA(.))*EPS(1))
Note the exp of exp.
When working with logs,an additive error term makes more sense
Y = LOG(F) + ETA(.)*EPS(1)
LOG(Y)=EXP(LOG(F) + ETA(.)*EPS(1))=EXP(LOG(F))*EXP(ETA(.)*EPS(1))
LOG(Y)=F*EXP(ETA(.)*EPS(1))
This is now a proportional error model.
On Wed, 11 Jul 2007 08:26:54 -0400, "Samtani, Mahesh [PRDUS]"
<[EMAIL PROTECTED]> said:
> Dear NMusers,<?xml:namespace prefix = o ns =
> "urn:schemas-microsoft-com:office:office" />
>
> I have run in to an old problem that Vladimir once described here on the
> users net. I am trying to implement inter-individual variability in
> residual variance and the corresponding OMEGA is not being iterated.
> Usually, in Dr. Karlsson's work this error structure is implemented on a
> proportional or proportional+additive EPS model. I am wondering if my
> problem is because I am trying to implement ETA on EPS using the
> transform both sides approach as follows?
>
>
>
> $ERROR
>
> CALLFL=0
>
> IPRED = -5
>
> IF (F.GT.0) IPRED = LOG(F)
>
> IRES=DV-IPRED
>
> W=1
>
> IWRES=IRES/W
>
> Y = IPRED + EXP(ETA(.))*EPS(1)
>
>
>
> Kindly advice...MNS
>
>
>
> --------Cut here
>
> From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
>
> Subject: [NMusers] Implementation of interindividual variability in
> residual variance
>
> Date: 2/17/2004 9:37 AM
>
>
>
> Dear NONMEM users,
>
>
>
> I am trying to implement an interidividual variability in
>
> the residual variance using an additional random effect:
>
>
>
> $ERR
>
> Y = F + EXP(ETA(.))*EPS(1)
>
>
>
> It turned out the corresponding OMEGA was not iterated, and the final
> estimate
>
> did not differ from the initial value. Below is an example control stream
>
> and the output illustrating the problem (Note, the actual model I work
> with is more complicated).
>
>
>
> Thanks in advance.
>
>
>
> Best regards,
>
> Vladimir
>
> --------Cut here
>
>
--
Alison Boeckmann
[EMAIL PROTECTED]
OOPS, here is a correction to earlier email.
With Y = LOG(F) + EXP(ETA(.))*EPS(1),
the cross partial (2nd. derivative) of Y wrt ETA and EPS is EXP(ETA),
which depends on ETA.
With Y = LOG(F) + ETA*EPS, the cross partial is 1, which does not depend
on ETA.
Another good reason for using EXP(ETA) in the model for eta on eps.
On Thu, 12 Jul 2007 13:24:00 -0700, "Alison Boeckmann"
<[EMAIL PROTECTED]> said:
> Dear Mats, thanks for the explanation. Very helpful.
>
> You and others have said that INTERACTION is needed when there is an eta
> on EPS. Some people may wonder why. Perhaps I can help explain this a
> little -
>
> Consider any model that uses eta on eps, eg,
> Y = LOG(F) + EXP(ETA(.))*EPS(1)
>
> During estimation , values of EPS are always 0, even with conditional
> estimation. Hence, even if NONMEM changes the ETA, this has no
> direct effect on the prediction Y, because any value of the ETA is
> multiplied by 0.
>
>
> With INTERACTION, the partial derivatives of "Y" with respect to eps and
> etas are used in the objective function. In the above model, the partial
> of Y wrt EPS is ETA, and the "cross partial" wrt ETA,EPS is 1.
>
> This allows estimation of the eta on eps.
>
> There is some discussion of this in GUide VI (PREDPP), chapter IV
> (ERROR routine) and in Guide VII (Conditional Estimation methods.)
>
>
>
> On Thu, 12 Jul 2007 10:02:03 +0200, "Mats Karlsson"
> <[EMAIL PROTECTED]> said:
> > Dear Alison,
> >
> > The addition of EXP(ETA(.)) is to provide a scaling for the residual
> > error magnitude. This scaling factor is 1 for the typical individual
> > (ETA=0) and the sigma estimate is thus the residual error magnitude
> > for the typical subject. Other subjects will have scaling factors
> > larger or smaller than 1, but all will be >0. I see no problem in the
> > "exp of exp" - it does exactly what is desired.
> >
> > With the alternative model
> >
> > Y = LOG(F) + ETA(.)*EPS(1)
> >
> > the typical individual (with ETA=0) is having a zero residual error
> > magnitude. Clearly that model does not work.
> >
> > Best regards, Mats
> >
> >
> > Mats Karlsson, PhD Professor of Pharmacometrics
> > Div. of Pharmacokinetics and Drug Therapy Dept. of Pharmaceutical
> > Biosciences Faculty of Pharmacy Uppsala University Box 591 SE-751
> > 24 Uppsala Sweden phone +46 18 471 4105 fax +46 18 471 4003
> > [EMAIL PROTECTED]
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > -----Original Message----- From: [EMAIL PROTECTED] [mailto:owner-
> > [EMAIL PROTECTED] On Behalf Of Alison Boeckmann Sent: Thursday,
> > July 12, 2007 02:04 To: Samtani, Mahesh [PRDUS];
> > [email protected] Subject: Re: [NMusers] Interindividual
> > variability in residual variance
> >
> > 1) The original email and responses can be found at
> > http://www.cognigencorp.com/nonmem/nm/99feb172004.html
> >
> > 2) Your model does not make sense. In effect Y = LOG(F) +
> > EXP(ETA(.))*EPS(1) This is equivalent to
> > EXP(Y)=EXP(LOG(F))*EXP(EXP(ETA(.))*EPS(1))
> > EXP(Y)=F*EXP(EXP(ETA(.))*EPS(1)) Note the exp of exp.
> >
> > When working with logs,an additive error term makes more sense Y =
> > LOG(F) + ETA(.)*EPS(1) LOG(Y)=EXP(LOG(F) +
> > ETA(.)*EPS(1))=EXP(LOG(F))*EXP(ETA(.)*EPS(1))
> > LOG(Y)=F*EXP(ETA(.)*EPS(1)) This is now a proportional error
> > model.
> >
> >
> > On Wed, 11 Jul 2007 08:26:54 -0400, "Samtani, Mahesh [PRDUS]"
> > <[EMAIL PROTECTED]> said:
> > > Dear NMusers,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-
> > > com:office:office" />
> > >
> > > I have run in to an old problem that Vladimir once described here on
> > > the users net. I am trying to implement inter-individual variability
> > > in residual variance and the corresponding OMEGA is not being
> > > iterated. Usually, in Dr. Karlsson's work this error structure is
> > > implemented on a proportional or proportional+additive EPS model. I
> > > am wondering if my problem is because I am trying to implement ETA
> > > on EPS using the transform both sides approach as follows?
> > >
> > >
> > >
> > > $ERROR
> > >
> > > CALLFL=0
> > >
> > > IPRED = -5
> > >
> > > IF (F.GT.0) IPRED = LOG(F)
> > >
> > > IRES=DV-IPRED
> > >
> > > W=1
> > >
> > > IWRES=IRES/W
> > >
> > > Y = IPRED + EXP(ETA(.))*EPS(1)
> > >
> > >
> > >
> > > Kindly advice...MNS
> > >
> > >
> > >
> > > --------Cut here
> > >
> > > From: "Piotrovskij, Vladimir [PRDBE]" - [EMAIL PROTECTED]
> > >
> > > Subject: [NMusers] Implementation of interindividual variability in
> > > residual variance
> > >
> > > Date: 2/17/2004 9:37 AM
> > >
> > >
> > >
> > > Dear NONMEM users,
> > >
> > >
> > >
> > > I am trying to implement an interidividual variability in
> > >
> > > the residual variance using an additional random effect:
> > >
> > >
> > >
> > > $ERR
> > >
> > > Y = F + EXP(ETA(.))*EPS(1)
> > >
> > >
> > >
> > > It turned out the corresponding OMEGA was not iterated, and the
> > > final estimate
> > >
> > > did not differ from the initial value. Below is an example control
> > > stream
> > >
> > > and the output illustrating the problem (Note, the actual model I
> > > work with is more complicated).
> > >
> > >
> > >
> > > Thanks in advance.
> > >
> > >
> > >
> > > Best regards,
> > >
> > > Vladimir
> > >
> > > --------Cut here
> > >
> > >
> > --
> > Alison Boeckmann [EMAIL PROTECTED]
> >
> >
> --
> Alison Boeckmann
> [EMAIL PROTECTED]
>
--
Alison Boeckmann
[EMAIL PROTECTED]