RE: Interindividual variability in residual variance

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]