RE: [NMusers] Interindividual variability in residual variance

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"
<mats.karlsson_at_farmbio.uu.se> 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
> mats.karlsson_at_farmbio.uu.se
>
>
>
>
>
>
>
>
>
> -----Original Message----- From: owner-nmusers_at_globomaxnm.com [mailto:owner-
> nmusers_at_globomaxnm.com] On Behalf Of Alison Boeckmann Sent: Thursday,
> July 12, 2007 02:04 To: Samtani, Mahesh [PRDUS];
> nmusers_at_globomaxnm.com 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]"
> <MSamtani_at_prdus.jnj.com> 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]" - VPIOTROV_at_PRDBE.jnj.com
> >
> > 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 alisonboeckmann_at_fastmail.fm
>
>
--
  Alison Boeckmann
  alisonboeckmann_at_fastmail.fm

Received on Thu Jul 12 2007 - 16:24:00 EDT