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RE: Lapacian estimation without second derivatives?

From: Martin Bergstrand <martin.bergstrand>
Date: Fri, 5 Dec 2008 11:02:19 +0100

Dear Matt,


Thanks for your help with this matter; you are right about the numerical
computation of the second derivatives. All models that I used for comparison
included the "INTERACTION" option. Laplacian estimation with the INTERACTION
option can only be performed given numerical calculation of the second
derivatives. NONMEM therefore used numerical calculation in both cases and
that was why I saw no differences.


I however find it interesting that the NONMEM users guide statement and
error messages stating that the DERIV2=NO can't be used together with
Laplacian only is true given non-numerical calculation of the second
derivatives. The option can still be useful to reduce internal table sizes
in case of numerical calculation of the second derivatives. It is further
more a bit puzzeling that the code in the FSUBS file does not reflect the
numerical computation.


Best regards,




From: Matt Hutmacher [mailto:matt.hutmacher
Sent: den 4 december 2008 22:28
To: 'Matt Hutmacher'; 'Martin Bergstrand'; nmusers
Cc: 'Joakim Nyberg'
Subject: RE: [NMusers] Lapacian estimation without second derivatives?




I was just talking to Ken. And we thought that perhaps the report file
would state that NUMERICAL was used in this case. You might look there as





From: owner-nmusers
Behalf Of Matt Hutmacher
Sent: Thursday, December 04, 2008 4:17 PM
To: 'Martin Bergstrand'; nmusers
Cc: 'Joakim Nyberg'
Subject: RE: [NMusers] Lapacian estimation without second derivatives?




It has been a while, but my recollection is that NONMEM is computing the
second derivatives numerically when you supply LAPLACE and $ABBREVIATED
DERIV2=NO. I think NONMEM supplies this option automatically in just this
case. You might test this by using the above with NONUMERICAL on the $EST
record and see if NONMEM complains. Again, it has been a while so if anyone
can corroborate this I would appreciate it.




From: owner-nmusers
Behalf Of Martin Bergstrand
Sent: Thursday, December 04, 2008 3:48 PM
To: nmusers
Cc: 'Joakim Nyberg'
Subject: [NMusers] Lapacian estimation without second derivatives?


Dear NONMEM community,

Due to a mistake on my part I recently executed a NONMEM job with the
Laplacian estimation method and calculation of the second derivatives turned
off ($ABBREVIATED DERIV2=NO). This is according to the NONMEM users guide
and common sense about the estimation method an impossible combination. When
the estimation started and also converged I was sure that what had happened
was that NONMEM had corrected my mistake by ignoring the statement regarding
turning of the second derivatives. To my surprise I found that that couldn't
be it, because if I tried to restart the model without the $ABBREVIATED
statement I got an error message where NONMEM complains about "to large
internal table sizes".

My second guess was that the Laplacian estimation method was turned into a
more FOCE like estimation without the second derivatives. To test this
hypothesis I have tested a number of different methods with three different
estimation alternatives, FOCE, Laplacian and Laplacian without the second
derivatives. With a hundred percent consistency I have in these examples
seen identical results for the two Laplacian methods and different results
for the FOCE method. Furthermore I have compared the FSUBS files for the two
Laplacian models (with and without DERIV2=NO) and can there see substantial
differences. Together with my colleague Joakim Nyberg I have briefly
analysed these differences and we find that there are no calculation of
second derivatives of ETAs in the FSUBS file when the DERIV2=NO function is
used. It puzzles us how these differences are compatible with the observed
identical estimations. We would be happy if anyone could shine some light
upon these findings.

The models that I have used for comparison ranges over both models with
analytical solutions ($PRED), differential equations ($DES), the LIKE option
and the F_FLAG option. No truly reliable benchmarking have been done in
terms of runtimes for the models with and without calculation of the second
derivatives, however our impression is that omitting the second derivatives
yield similar or faster runtimes.

Kind regards,

Martin Bergstrand & Joakim Nyberg, PhD students


Division of Pharmacokinetics and Drug Therapy,
Department of Pharmaceutical Biosciences,
Uppsala University


P.O. Box 591

SE-751 24 Uppsala





Work: +46 18 471 4639

Mobile: +46 709 994 396

Fax: +46 18 471 4003

Received on Fri Dec 05 2008 - 05:02:19 EST

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