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RE: Parameter Estimation in IF Conditioning Statement

From: benjamin.weber
Date: Fri, 20 Sep 2013 07:12:54 +0000

Dear All,

First, I would like to thank you all you quick responses. My main interest =
was to discuss the estimabiltiy of a parameter that only occurs in the IF c=
onditioning statement. The part of the code that I provided was simplified =
and I never meant to claim that both parts were identical. I really appreci=
ate the additional insight that has been given though.

I would like to follow-up on some points.

  
esolve the issue that THRESH=THETA(1) is not estimated. Possibly for the =
reason that Leonid pointed out?

  
continuous random variable can be over a range of approximately 20 units an=
d approximately 500 samples. I agree that in a certain sense all observed v=
ariables are discrete. Which brings me back to my initial questions that ha=
ving a statement like ' Y=THETA(1) IF(X.LT.Y)' and having Y not appear an=
ywhere else in the code causes problems for NONMEN? The reasoning that you =
have been given makes sense to me even though I would not have expected it =
as I assumed that NONMEM also tries larger variable changes.

  
ng a time-varying covariate affects parameters in a disease progression mo=
del. I have gone through your slides several times and I consider them as v=
ery helpful. In this case, CONC=WCMIN is constant within a subject and I =
decided to use $PRED for reducing the run times. In fact, when using ODE wi=
th a time varying CONC2, the same holds true for the estimability of THETA(=
1)=THRESH.

Mit freundlichen Grüßen / Kind regards,
Dr. Benjamin Weber

Boehringer Ingelheim Pharma GmbH & Co. KG
Translational Medicine
Tel.: +49 (7351) 54-143520
Fax: +49 (7351) 83-143520
mailto:benjamin.weber

Boehringer Ingelheim Pharma GmbH & Co. KG, Sitz: Ingelheim am Rhein; Regist=
ergericht Mainz: HR A 22206; Komplementär Boehringer Ingelheim Deutschlan=
d GmbH; Geschäftsführung: Dr. Engelbert Günster (Vorsitzender), Ursul=
a Fuggis-Hahn, Ralf Gorniak, Michael Klein, Dr. Martin Wanning; Vorsitzende=
r des Aufsichtsrates: Dr. Joachim Hasenmaier; Sitz: Ingelheim am Rhein; Reg=
istergericht Mainz: HR B 23260

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-----Original Message-----
From: Mats Karlsson [mailto:mats.karlsson
Sent: Freitag, 20. September 2013 08:12
To: 'Leonid Gibiansky'; Weber,Dr.,Benjamin (TransMed) BIP-DE-B
Cc: nmusers
Subject: RE: [NMusers] Parameter Estimation in IF Conditioning Statement

Dear Benjamin and Leonid,

Although a steep sigmoidal Emax function often works well to approximate a
step function, the rate of change is quite dependent on the value of the X
variable. Another function (below) has some advantages. For details, see
Henin et al., AAPS J. 2012 Jun;14(2):155-63.
A mechanism-based approach for absorption modeling: the Gastro-Intestinal
Transit Time (GITT) model.

STEP = EXP(X*GAM)/(EXP(X*GAM)+EXP(X50*GAM))

Where X50 (inflection point) would be estimated and GAM (steepness)
typically fixed.

Best regards,
Mats
 
Mats Karlsson, PhD
Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala

Phone: +46 18 4714105
Fax + 46 18 4714003
www.farmbio.uu.se/research/researchgroups/pharmacometrics/


-----Original Message-----
From: owner-nmusers
Behalf Of Leonid Gibiansky
Sent: 19 September 2013 21:33
To: benjamin.weber
Cc: nmusers
Subject: Re: [NMusers] Parameter Estimation in IF Conditioning Statement

Hi Benjamin
I think the problem was that when nonmem tested small variations of
THETA(1) in the first version, nothing changed in the OF as these variation
have not resulted in the change in the IF conditions (e.g., if your data
contained WCMIN values 1 and 2 and nothing in between, and
THETA(1) was 1.5, changes of THETA(1) to 1.6 or 1.4 were not resulting in
the changes in OF, gradient was zero, and the gradient method was unable to
move the model. When you put theta(1) in the centering, this resulted in
changes of OF. This is not an unusual behavior. Therefore, it is better to
use continuous functions rather than switches. For example, you can code it
as

INT = THETA(4)+(THETA(5)-THETA(4))/(1+(THETA(1)/WCMIN)**GAM)

SLOPE = THETA(3)+INT*CONC+ETA(2)

When GAM is infinity, this is equivalent to your model. You may use large
GAM (or even estimated GAM)

Leonid



--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566



On 9/19/2013 2:31 PM, benjamin.weber
> Dear NONMEM users,
>
> My goal was to add a drug effect to a disease progression model in a
> way that the drug effect is different when a certain threshold
> concentration is exceeded (similarly to modeling a 'hockey-stick' when
> performing covariate analysis). First, I did it in the following way
> (partial simplified code)
>
> $PRED
>
> THRESH = THETA(1) ;threshold concentration
>
> INT = THETA(2)+ ETA(1)
>
> IF(WCMIN.LE.THRESH) SLOPE = THETA(3)+THETA(4)*CONC+ETA(2)
>
> IF(WCMIN.GT.THRESH) SLOPE = THETA(3)+THETA(5)*CONC+ETA(2)
>
> IPRED=INT+SLOPE*TIME
>
> and NONMEM did not manage to estimate THRESH=THETA(1) (i.e., the
> initial estimate did not change during minimization and the gradient
> was zero throughout). I tried this for several different initial
estimates.
>
> I then centered the observed CONC on THRESH and run the following
> model because colleagues mentioned that they have successfully run a
> 'hockey-stick' estimating the threshold parameter (partial simplified
> code)
>
> IF(WCMIN.LE.THRESH) SLOPE = THETA(3)+THETA(4)*(CONC-THRESH)+ETA(2)
>
> IF(WCMIN.GT.THRESH) SLOPE = THETA(3)+THETA(5)*(CONC- THRESH)+ETA(2)
>
> This time, NONMEM provided very reasonable estimates for all model
> parameters and the covariance step was successful.
>
> I wonder now if the centering of the variable (and hence something
> particular to the data set) caused the difference in estimability of
> the threshold parameter or whether NONMEN cannot estimate parameters
> that only occur in the conditioning part of the IF statement (Note
> that after centering THRESH also appears in another part of the code).
>
> Could somebody please provide some insight on this? I have searched in
> the NONMEM user group but could not find anything.
>
> Mit freundlichen Grüßen / Kind regards, Dr. Benjamin Weber
>
> Boehringer Ingelheim Pharma GmbH & Co. KG Translational Medicine
> Tel.: +49 (7351) 54-143520
> Fax: +49 (7351) 83-143520
> mailto:benjamin.weber
>
> Boehringer Ingelheim Pharma GmbH & Co. KG, Sitz: Ingelheim am Rhein;
> Registergericht Mainz: HR A 22206; Komplementär Boehringer Ingelheim
> Deutschland GmbH; Geschäftsführung: Dr. Engelbert Günster
> (Vorsitzender), Ursula Fuggis-Hahn, Ralf Gorniak, Michael Klein, Dr.
> Martin Wanning; Vorsitzender des Aufsichtsrates: Dr. Joachim
> Hasenmaier;
> Sitz: Ingelheim am Rhein; Registergericht Mainz: HR B 23260
>
> Diese E-Mail ist vertraulich zu behandeln. Sie kann besonderem
> rechtlichem Schutz unterliegen. Wenn Sie nicht der richtige Adressat
> sind, senden Sie bitte diese E-Mail an den Absender zurück, löschen
> die eingegangene E-Mail und geben den Inhalt der E-Mail nicht weiter.
> Jegliche unbefugte Bearbeitung, Nutzung, Vervielfältigung oder
> Verbreitung ist verboten. / This e-mail is confidential and may also
> be legally privileged. If you are not the intended recipient please
> reply to sender, delete the e-mail and do not disclose its contents to
> any person. Any unauthorized review, use, disclosure, copying or
> distribution is strictly prohibited.
>
Received on Fri Sep 20 2013 - 03:12:54 EDT

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