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RE: Lapacian estimation without second derivatives?

From: Ludden, Thomas <Thomas.Ludden>
Date: Fri, 5 Dec 2008 08:51:46 -0500

Dear Martin and all.
The Laplacian method with the INTERACTION option was added to NONMEM VI
but the documentation was not revised. Thank you for bringing this to
our attention. This will be corrected in documentation for the next
release of NONMEM.
The numerical calculation of second derivatives does not require the
analytical calculations provided in FSUBS when only LAPLACIAN is
specified. The numerical derivatives are calculated by multiple calls
to the subroutines that provide predicted values, including the
routines in FSUBS.


From: owner-nmusers
On Behalf Of Martin Bergstrand
Sent: Friday, December 05, 2008 5:02 AM
To: 'Matt Hutmacher'; nmusers
Subject: RE: [NMusers] Lapacian estimation without second derivatives?

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 well.





From: owner-nmusers
On 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
On 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 =
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





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Received on Fri Dec 05 2008 - 08:51:46 EST

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