RE: [EXTERNAL] Re: MU referencing and time-varying covariates
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
Quoted reply history
From: [email protected] <[email protected]> On Behalf Of
Nick Holford
Sent: Monday, January 13, 2025 5:49 PM
To: Bauer, Robert <[email protected]>; 'Leonid Gibiansky'
<[email protected]>; Sébastien Bihorel
<[email protected]>; [email protected]
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: <mailto:[email protected]> [email protected]
web: http://holford.fmhs.auckland.ac.nz/ http://holford.fmhs.auckland.ac.nz/
From: Bauer, Robert <[email protected] <mailto:[email protected]>
>
Sent: Tuesday, 14 January 2025 5:34 am
To: Nick Holford <[email protected] <mailto:[email protected]> >;
'Leonid Gibiansky' <[email protected]
<mailto:[email protected]> >; Sébastien Bihorel
<[email protected] <mailto:[email protected]> >;
[email protected] <mailto:[email protected]>
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
<mailto:[email protected]> [email protected]
http://www.iconplc.com/ www.iconplc.com
From: Nick Holford <[email protected] <mailto:[email protected]>
>
Sent: Saturday, January 11, 2025 9:29 PM
To: Bauer, Robert <[email protected] <mailto:[email protected]>
>; 'Leonid Gibiansky' <[email protected]
<mailto:[email protected]> >; Sébastien Bihorel
<[email protected] <mailto:[email protected]> >;
[email protected] <mailto:[email protected]>
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: <mailto:[email protected]> [email protected]
web: http://holford.fmhs.auckland.ac.nz/ http://holford.fmhs.auckland.ac.nz/
From: [email protected] <mailto:[email protected]>
<[email protected] <mailto:[email protected]> > On Behalf
Of Bauer, Robert
Sent: Saturday, 11 January 2025 8:32 pm
To: 'Leonid Gibiansky' <[email protected]
<mailto:[email protected]> >; Sébastien Bihorel
<[email protected] <mailto:[email protected]> >;
[email protected] <mailto:[email protected]>
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
[email protected] <mailto:[email protected]>
www.iconplc.com http://www.iconplc.com
-----Original Message-----
From: [email protected] <mailto:[email protected]>
<[email protected] <mailto:[email protected]> > On Behalf
Of Leonid Gibiansky
Sent: Friday, January 10, 2025 5:21 PM
To: Sébastien Bihorel <[email protected]
<mailto:[email protected]> >; [email protected]
<mailto:[email protected]>
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
> [email protected] <mailto:[email protected]>
>
>
> Regeneron - Internal
>
> ********************************************************************