Sorry, there was a typos in the code, here is the version with
continuous SLOPE function
IF(CONC.LE.THRESH) SLOPE = THETA(3)+THETA(4)*CONC+ETA(2)
IF(CONC.GT.THRESH) SLOPE =
THETA(3)+THETA(4)*THRESH+THETA(5)*(CONC-THRESH)+ETA(2)
Then, if you rename
NEWTHETA3 = THETA(3)+THETA(4)*THRESH
you will have
IF(CONC.LE.THRESH) SLOPE = NEWTHETA3+THETA(4)*(CONC-THRESH)+ETA(2)
IF(CONC.GT.THRESH) SLOPE = NEWTHETA3+THETA(5)*(CONC-THRESH)+ETA(2)
exactly as your second version (up to the parametrization).
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 6:42 PM, Leonid Gibiansky wrote:
Benjamin.
Even as WCMIN is continuous by nature, it is not continuous in the
dataset (at observation points). You may look at your WCMIN values in
the data file (I assume this values are in the data file?) and see where
the initial conditions for THETA(1) placed in that range. Step for
gradient computations can be quite small, so it will not see continuous
nature of the variable, and will treat it as discrete.
One the same model but separate topic, I am not sure that you can code
the model as you coded it if you indeed assume that WCMIN=CONC.
It is better to write as (set aside problems with the gradient):
IF(WCMIN.LE.THRESH) SLOPE = THETA(3)+THETA(4)*CONC+ETA(2)
IF(WCMIN.GT.THRESH) SLOPE = THETA(3)*WCMIN+THETA(5)*(CONC-WCMIN)+ETA(2)
Otherwise, you SLOP function will be discontinuous at WCMIN as a
function of CONC.
Note also that your two models are not exactly equivalent. If you use
IF(WCMIN.LE.THRESH) SLOPE = THETA(3)+THETA(4)*CONC+ETA(2)
IF(WCMIN.GT.THRESH) SLOPE = THETA(3)+THETA(5)*CONC+ETA(2)
your values at WCMIN=THRESH are equal to
SLOPE = THETA(3)+THETA(4)*THRESH+ETA(2)
SLOPE = THETA(3)+THETA(5)*THRESH+ETA(2)
immediately before and after WCMIN=THRESH (different)
while for the second model they are equal to
SLOPE = THETA(3)+ETA(2)
SLOPE = THETA(3)+ETA(2)
and equal to each other
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 4:29 PM, [email protected] wrote:
Hi Leonid. Thanks for your quick response. WCMIN is continuous. In
fact, it is actually identical to CONC (forgot to change it while
simplifying). Any thoughts on this?Ben
----- Originalnachricht -----
Von: Leonid Gibiansky [mailto:[email protected]]
Gesendet: Thursday, September 19, 2013 09:32 PM
An: Weber,Dr.,Benjamin (TransMed) BIP-DE-B
Cc: [email protected] <[email protected]>
Betreff: 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, [email protected] wrote:
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:[email protected]
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
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