Hi Leonid,
Since coding W = THETA(1) * IPRED + THETA(2) corresponds to implicitly forcing the covariance to be THETA(1)*IPRED*THETA(2) then this essentially assumes that there is perfect correlation between the proportional and additive random effects. That is, CORR(ERR(1), ERR(2)) = 1. I wouldn’t want to go with this expression for W without first at least attempting to estimate the covariance using the $SIGMA BLOCK(2) formulation I suggest below and allow the two residual error random effects to not be perfectly correlated. If the estimate of the correlation is near 1 then reducing the $SIGMA structure using the above expression for W might be reasonable from the standpoint of parsimony. Ken From: kgkowalsk...@gmail.com <kgkowalsk...@gmail.com> Sent: Tuesday, March 5, 2024 5:05 PM To: 'Leonid Gibiansky' <lgibian...@quantpharm.com>; 'T. Preijers' <t.preij...@gmail.com>; nmusers@globomaxnm.com Subject: RE: [NMusers] Warning obtained while running SAEM Oops see correction to the $SIGMA BLOCK(2) labeling below: -----Original Message----- From: kgkowalsk...@gmail.com <mailto:kgkowalsk...@gmail.com> <kgkowalsk...@gmail.com <mailto:kgkowalsk...@gmail.com> > Sent: Tuesday, March 5, 2024 4:56 PM To: 'Leonid Gibiansky' <lgibian...@quantpharm.com <mailto:lgibian...@quantpharm.com> >; 'T. Preijers' <t.preij...@gmail.com <mailto:t.preij...@gmail.com> >; nmusers@globomaxnm.com <mailto:nmusers@globomaxnm.com> Subject: RE: [NMusers] Warning obtained while running SAEM Hi Leonid, I see. Normally we think of the proportional and additive random effects as being independent of each other. For example, we could code the residual error as: THETA(1)*IPRED*ERR(1) + THETA(2)*ERR(2) where $SIGMA DIAGONAL(2) 1 FIXED 1 FIXED which is equivalent to: W = SQRT(THETA(1)**2 * IPRED**2 + THETA(2)**2) with the residual error coded as: W*ERR(1) where $SIGMA DIAGONAL(1) 1 FIXED By coding W = THETA(1) * IPRED + THETA(2) with the residual error coded as W*ERR(1) we are implicitly assuming that the two components are correlated with a covariance corresponding to THETA(1)*IPRED*THETA(2). I did not know that this is what Monolix does. This provides a very specific covariance structure and I wonder how it would compare to a residual error model with IPRED*ERR(1) + ERR(2) where $SIGMA BLOCK(2) xxx ;Var(ERR(1)) xxx xxx ;Cov(ERR(1), ERR(2)) Var(ERR(2)) It seems to me that it would be better to explicitly model this covariance as an additional parameter to directly estimate the covariance rather than assume it corresponds to THETA(1)*IPRED*THETA(2) with no additional parameters. What do you think? Do you have any experience coding the residual error using the W = THETA(1) * IPRED + THETA(2) expression? BTW, I still think Tim should check to see if the gradient for THETA(2) is 0 right from the start with the 0-th iteration as this probably means there is a coding error somewhere. Ken -----Original Message----- From: Leonid Gibiansky < <mailto:lgibian...@quantpharm.com> lgibian...@quantpharm.com> Sent: Tuesday, March 5, 2024 1:42 PM To: <mailto:kgkowalsk...@gmail.com> kgkowalsk...@gmail.com; 'T. Preijers' < <mailto:t.preij...@gmail.com> t.preij...@gmail.com>; <mailto:nmusers@globomaxnm.com> nmusers@globomaxnm.com Subject: Re: [NMusers] Warning obtained while running SAEM Hi Tim and Ken, I do not think this is an error to code W = THETA(1) * IPRED + THETA(2). This does not correspond to the variance of VAR1=(THETA(1)*IPRED)^2+THETA(2)^2 but this is just a different dependence of variance VAR2=(THETA(1)*IPRED+THETA(2))^2 = VAR1+2*THETA(1)*IPRED*THETA(2) on IPRED. I think this is a default way of coding in Monolix (not 100% sure as I do not use it). Also, with regards to the previous post, we need to make sure that variance of EPS1 is fixed to 1 if we use this code. Regards, Leonid On 3/5/2024 11:25 AM, <mailto:kgkowalsk...@gmail.com> kgkowalsk...@gmail.com wrote: > Hi Tim, > > Are you getting a zero gradient for TH2 on the 0-th iteration? If so, > this may be indicative of a coding error. You might check to make > sure that THETA(2) is not being assigned to another parameter (say a > fixed effect parameter) in addition to the standard deviation for the > additive residual error. Note that it is the variances of the > proportional and additive residual errors that can be summed for two > independent random effects and not the standard deviations. So, > adding the proportional and additive standard deviations in the specification > of W: > > W = THETA(1) * IPRED + THETA(2) > > is not correct. > > If the gradient for TH2 is not zero on the 0-th iteration and you > don’t find any coding errors involving say multiple assignments for > TH2, but the gradient goes to zero after several iterations, this > might mean you don’t have rich enough information to estimate the > additive error component. If so, try fixing TH2 to 0 and just > estimate the proportional error component. Make sure that you are not > including any DVs (e.g., the predose sample at TIME=0) where IPRED=0 > in the estimation since the proportional error is 0 and hence IWRES is > undefined. > > Regards, > > Ken > > Kenneth G. Kowalski > > President > > Kowalski PMetrics Consulting, LLC > > Email: <mailto:kgkowalsk...@gmail.com> kgkowalsk...@gmail.com < > <mailto:kgkowalsk...@gmail.com> mailto:kgkowalsk...@gmail.com> > > Cell: 248-207-5082 > > *From:*owner-nmus...@globomaxnm.com < <mailto:owner-nmus...@globomaxnm.com> > owner-nmus...@globomaxnm.com> *On > Behalf Of *T. Preijers > *Sent:* Tuesday, March 5, 2024 8:09 AM > *To:* <mailto:nmusers@globomaxnm.com> nmusers@globomaxnm.com > *Subject:* [NMusers] Warning obtained while running SAEM > > Dear NMusers, > > While running a simple 1-comp model in NONMEM using SAEM, we > discovered a warning resulting from $ERROR. Using a SQRT( **2) > describing a mixed error model resulted in zero gradients for the > additive error (see Example error model 1 below). > > */Example error model 1/* > > $ERROR > > IPRED = F > > IRES = DV-IPRED > > W = SQRT(THETA(1)**2 * IPRED**2 + THETA(2)**2) > > IF (W.EQ.0) W = 1 > > IWRES = IRES/W > > Y = IPRED+W*ERR(1) > > However, when simplifying the $ERROR code omitting the use of SQRT() > and > THETA(x)**2 (see Example error model 2 below), a successful SAEM run > was obtained. > > */Example error model 2/* > > $ERROR > > IPRED = F > > IRES = DV-IPRED > > W = THETA(1) * IPRED + THETA(2) > > IF (W.EQ.0) W = 1 > > IWRES = IRES/W > > Y = IPRED + W*ERR(1) > > Initial values for both THETAs were positive (TH1: 0.417, TH2: 0.545) > and constrained with a lower boundary of 0. Moreover, the expected > values for IPRED were ranged from 1-700 mg/L. > > Our interest lies in what has driven this error. Perhaps someone else > has encountered this before? > > Looking forward to receiving any answers/comments! > > Kind regards, > > *Dr. T. Preijers, PharmD, PhD* > > /Hospital Pharmacist and Clinical Pharmacologist/ > > Hospital Pharmacy Erasmus MC Rotterdam The Netherlands > > Rotterdam Clinical Pharmacometrics Group >
