Dear NMusers, Documentation relevant to this discussion (Intro to NONMEM 7.5.1. p 185-186): Time dependent covariates, or covariates changing with each record within an individual, cannot be part of the MU_ equation. For example MU_3=THETA(1)*TIME+THETA(2) should not be done. Or, consider MU_3=THETA(2)*WT Where WT is not constant within an individual, but varies with observation record (time). This would also not be suitable. However, we could phrase as MU_3=THETA(2) CL=WT*(MU_3+ETA(3)) where MU_3 represents a population mean clearance per unit weight, which is constant with time (observation record), and is more universal among subjects. The MU variables may vary with inter-occasion, but not with time.
Suppose we have a situation where WT has an unknown power term associated with it modeled as THETA(3) in this example: CL=THETA(2)*WT**THETA(3)*EXP(ETA(1)) Normally, we could efficiently linear model this as follows: MU_1=THETA(2)+THETA(3)*LOG(WT) CL=EXP(MU_1+ETA(1)) with THETA(2) transformed into the log of clearance domain. However, if WT changes record by record within the individual, then LOG(WT) may not be in the Mu modeling. We would then remove the THETA(3)*LOG(WT) term from MU_1: MU_1=LOG(THETA(2)) CL=WT**THETA(3)*EXP(MU_1+ETA(1)) And THETA(3) itself would not be MU modeled. Best wishes Pyry On Tue, 14 Jan 2025 at 23:00, <kgkowalsk...@gmail.com> wrote: > I got an email indicating my message below may not have gone through so, > I’m sending it again. Apologies if you receive this message twice. -Ken > > > > > > Hi Bob, > > > > I agree with the sentiments of Nick’s email below that if EM and Bayes’ > methods are simply averaging the time-varying covariates and essentially > treating them as time-invariant values set to the average covariate values, > then this would be a MAJOR deficiency in how EM and Bayes methods in NONMEM > handle time-varying covariates. Afterall, the main reason we investigate > time-varying covariates is to evaluate whether certain parameters can > change over time within a subject where the time-varying covariates may > help explain some of the within-subject variation (e.g., IOV). If the EM > and Bayes’ methods as implemented in NONMEM treat the time-varying > covariates as time-invariant at the arithmetic mean value, then the > predictions will not be properly considering these time-varying > covariates. However, I suspect that this is not the case, and the EM and > Bayes’ methods as implemented in NONMEM are actually considering the > time-varying nature of these covariates and the confusion comes from an > ambiguous explanation of what NONMEM is doing. Let me see if I can explain > what NONMEM is doing, and you can correct me if I’m wrong or further > elaborate on Nick’s and my concerns. > > > > I assume that EM and Bayes methods are actually using the time-varying > covariates, however, the EM and Bayes’ methods perform centering and/or > scaling based on the subject-specific arithmetic mean values of the > covariates when mu-referencing is implemented. This is to enhance > numerical stability when estimating the fixed effects associated with > time-varying covariates. Thus, the EM and Bayes’ methods are actually > using the time-varying values of the covariates in the prediction of the > responses and the averaging of the covariates within a subject is only > implemented for MU referencing. Is my understanding correct? > > > > Thanks, > > > > Ken > > > > > > > > *From:* owner-nmus...@globomaxnm.com <owner-nmus...@globomaxnm.com> *On > Behalf Of *Nick Holford > *Sent:* Monday, January 13, 2025 5:49 PM > *To:* Bauer, Robert <robert.ba...@iconplc.com>; 'Leonid Gibiansky' < > lgibian...@quantpharm.com>; Sébastien Bihorel < > sebastien.biho...@regeneron.com>; nmusers@globomaxnm.com > *Subject:* RE: [EXTERNAL] Re: [NMusers] MU referencing and time-varying > covariates > > > > Hi Bob, > > > > Thanks for explaining that EM and BAYES methods are a form of naïve pooled > data analysis for the individual. > > > > I will make sure I stick to the classic methods when dealing with clinical > data with time varying covariates such as body mass, post-menstrual age and > serum creatinine. > > > > Best wishes, > > Nick > > > > -- > > Nick Holford, Professor Emeritus Clinical Pharmacology, MBChB, FRACP > > mobile: NZ+64(21) 46 23 53 ; FR+33(6) 62 32 46 72 > > email: n.holf...@auckland.ac.nz > > web: http://holford.fmhs.auckland.ac.nz/ > > > > *From:* Bauer, Robert <robert.ba...@iconplc.com> > *Sent:* Tuesday, 14 January 2025 5:34 am > *To:* Nick Holford <n.holf...@auckland.ac.nz>; 'Leonid Gibiansky' < > lgibian...@quantpharm.com>; Sébastien Bihorel < > sebastien.biho...@regeneron.com>; nmusers@globomaxnm.com > *Subject:* RE: [EXTERNAL] Re: [NMusers] MU referencing and time-varying > covariates > > > > Hello Nick: > > The statement I made pertains only to EM algorithms (ITS, SAEM, IMP), and > BAYES. The classic methods (FOCEI, Laplace), do not engage in averaging > the covariates across records even when thetas are MU referenced, as the > classic algorithms do not use EM update methods to advance the theta > estimates. > > > > Robert J. Bauer, Ph.D. > > Senior Director > > Pharmacometrics R&D > > ICON Early Phase > > 731 Arbor way, suite 100 > > Blue Bell, PA 19422 > > Office: (215) 616-6428 > > Mobile: (925) 286-0769 > > robert.ba...@iconplc.com > > www.iconplc.com > > > > *From:* Nick Holford <n.holf...@auckland.ac.nz> > *Sent:* Saturday, January 11, 2025 9:29 PM > *To:* Bauer, Robert <robert.ba...@iconplc.com>; 'Leonid Gibiansky' < > lgibian...@quantpharm.com>; Sébastien Bihorel < > sebastien.biho...@regeneron.com>; nmusers@globomaxnm.com > *Subject:* RE: [EXTERNAL] Re: [NMusers] MU referencing and time-varying > covariates > > > > Hi Bob, > > > > I am really puzzled by this statement. I would expect NONMEM to recognize > time varying covariates provide information about the fixed effects and > used the time specific value of the covariate to make a prediction. > > Averaging the covariate across all the records for a subject seems like a > poor use of information. > > Is your statement saying something special associated with the > mu-referenced transformation? If so would you please clarify your statement > about averaging? > > > > Best wishes, > > Nick > > > > -- > > Nick Holford, Professor Emeritus Clinical Pharmacology, MBChB, FRACP > > mobile: NZ+64(21) 46 23 53 ; FR+33(6) 62 32 46 72 > > email: n.holf...@auckland.ac.nz > > web: http://holford.fmhs.auckland.ac.nz/ > > > > *From:* owner-nmus...@globomaxnm.com <owner-nmus...@globomaxnm.com> *On > Behalf Of *Bauer, Robert > *Sent:* Saturday, 11 January 2025 8:32 pm > *To:* 'Leonid Gibiansky' <lgibian...@quantpharm.com>; Sébastien Bihorel < > sebastien.biho...@regeneron.com>; nmusers@globomaxnm.com > *Subject:* RE: [EXTERNAL] Re: [NMusers] MU referencing and time-varying > covariates > > > > If a covariate varies across records within a subject, NONMEM obtains a > simple average among the records and uses this as the covariate value for > that subject. > > Robert J. Bauer, Ph.D. > Senior Director > Pharmacometrics R&D > ICON Early Phase > 731 Arbor way, suite 100 > Blue Bell, PA 19422 > Office: (215) 616-6428 > Mobile: (925) 286-0769 > robert.ba...@iconplc.com > www.iconplc.com > > -----Original Message----- > From: owner-nmus...@globomaxnm.com <owner-nmus...@globomaxnm.com> On > Behalf Of Leonid Gibiansky > Sent: Friday, January 10, 2025 5:21 PM > To: Sébastien Bihorel <sebastien.biho...@regeneron.com>; > nmusers@globomaxnm.com > Subject: [EXTERNAL] Re: [NMusers] MU referencing and time-varying > covariates > > Hi Sébastien, > > As you did these experiments, can you share the results: have you seen any > differences in the fit, parameter estimates, precision, convergence speed > (number of iteration), and evaluation time for SAEM/IMP (I think, FOCEI > does not have this restriction of time-independence even if you use Mu > referencing, so results should be identical or very close). > > As code is encrypted, only Bob can answer the question but my > understanding is that some kind of averaging is used to get time > independent value of WT that is then used by the SAEM/IMP algorithm for > parameter update procedure. > > As WT changes slowly and not very significantly, it could be hard to see > the differences. A more stringent test would be to use time-dependent and > strongly influential ADA (0/1): how bad is the incorrect version 1 in this > case? > > Thank you > Leonid > > On 1/10/2025 2:56 PM, Sébastien Bihorel wrote: > > > > Happy New Year, > > > > I hope everybody is ready for a great 2025 ! > > > > I'll start my message/question by defining 2 different ways of coding > > a simple power relationship between body weigh on clearance. > > > > * > > Coding 1 > > > > MU_1 = THETA(1) + THETA(2) * LOG(WGT/70) CL = EXP( MU_1 + ETA(1) ) > > > > * > > Coding 2 > > > > MU_1 = THETA(1) > > CL = EXP( MU_1 + ETA(1) ) * ( WGT/70 )**THETA(2) > > > > The reference and training materials for NONMEM clearly indicate that > > MU variables should be time invariant within occasions and recommend > > using coding 2 when body weight is time varying. Nevertheless, it is > > possible for an analyst to use coding 1. As far as I can tell from > > some limited testing, this is not a "fatal" error. Either with FOCE(I) > > or SAEM/IMP, NONMEM reports a warning but performs the model > > optimization. The table outputs also report CL as a time varying > > variable changing as body weight changes. > > > > So my questions are the following: when coding 1 is used and body > > weight is time varying, what is NONMEM actually doing during model > > optimization? Does NONMEM internally create occasions to break the > > records by interval of constant body weight and constant MU1? > > Alternatively, does NONMEM internally calculate an average of MU1? > > Something entirely different? What's the risk taken by an analyst when > > using coding 1 versus coding 2? > > > > Thank you in advance for you input > > > > > > __ > > Sébastien Bihorel > > Director, Quantitative Pharmacology > > +1 914-648-9581 > > sebastien.biho...@regeneron.com > > > > > > Regeneron - Internal > > > > ******************************************************************** > > > > ICON plc made the following annotations. > ------------------------------------------------------------------------------ > > This e-mail transmission may contain confidential or legally privileged > information that is intended only for the individual or entity named in the > e-mail address. If you are not the intended recipient, you are hereby > notified that any disclosure, copying, distribution, or reliance upon the > contents of this e-mail is strictly prohibited. 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