Hello Jeroen,
Thank you for your response. It was a practical question. I understand
the theory. What is the reason different packages show such different
results and present eigenvalues differently? What is the best way?
NONMEM demonstrated much larger max/min values but did not give warning
messages about non-positive defined matrix. The runs were stable. Runs
became unstable only when simulated annealing was used; instability
kicked in at the moment when NONMEM stopped simulated annealing; so I
had to remove simulated annealing. Monolix sometimes gave non-positive
defined matrix stopping optimization in the middle; sometime it became
unstable in the middle with or without simulated annealing.
I do not take sides. I just try to understand it. As max/min is
frequently reported in BLAs, it is nice to understand what we report and
why it can be so different across different packages.
Thanks,
Pavel
On Thu, Nov 05, 2015 at 05:14 PM, Jeroen Elassaiss-Schaap (PD-value
B.V.) wrote:
Hi Pavel,
Principal component analysis can be validly performed on any
matrix,
and it is just a matter of convention that the eigenvalue ratios of
min/max of the total covariance matrix of estimation are reported
as
the condition number for a given model. This as a metric of how
easily the dimensionality of estimators could be reduced.
The idea behind the separation of eigenvalues, as you show here for
your model in Monolix, is actually attractive, because the
off-diagonal elements do reduce the freedom of the described
variance rather than increasing it. Furthermore they are the
byproduct of sampling methods like SAEM, not so much the result of
separate estimation. Two reasons to separate them.
The separation of diagonal variance components and PK parameters as
you note is less obvious to me, although I am pretty sure there
will
be a good rationale for that in the realm of sampling approaches
(tighter linkage?).
Even though the off-diagonal elements are associated with a decent
condition number, it is still larger than the "PK" block, assuming
the blocks are of comparable size. In other to better compare the
results my suggestion would be to break up the nonmem covariance
matrix (as was done for Monolix) in blocks of structural, diagonal
and off-diagonal elements (throwing away a large remainder), and
calculate the condition number on each matrix. Than you are
comparing apples to apples, enabling a more straightforward
discussion of the differences.
Hope this helps,
Jeroen
http://pd-value.com <http://pd-value.com>
jer...@pd-value.com <mailto:jer...@pd-value.com>
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-- More value out of your data!
On 11/04/2015 05:55 PM, Pavel Belo
wrote:
Hello NONMEM Users,
I try to make sense of the results and one of the ways to do
it is to compare the same or similar models across software
packages. 5x5 full omega matrix is used because it was
prohibitive to remove some insignificant correlations from the
matrix without removing significant correlations (All
recommended ways to do it were tested. Diagonal omega was also
tested, of course). Adding correlations has little effect on
PK
parameters, but it has some effect on simulations.
NONMEM provides all eigenvalues in one pocket. Here is an
example.
************************************************************************************************************************
********************
********************
******************** STOCHASTIC APPROXIMATION
EXPECTATION-MAXIMIZATION ********************
******************** EIGENVALUES OF COR
MATRIX OF ESTIMATE (S) ********************
********************
********************
************************************************************************************************************************
1 2 3 4
5 6 7 8 9 10
11 12
13 14 15 16 17
18 19 20 21 22 23
3.36E-05 5.69E-03 3.40E-02 6.32E-02 9.19E-02
1.24E-01 1.53E-01 2.79E-01 3.20E-01 4.32E-01 5.74E-01
6.45E-01
7.25E-01 7.67E-01 9.73E-01 1.08E+00 1.42E+00
1.63E+00 1.86E+00 2.14E+00 2.31E+00 3.12E+00 4.26E+00
Monolix provides them in 3 pockets:
PK parameters: Eigenvalues (min, max, max/min): 0.22 2 9.2
OMEGA (diagonal) and SIGMA: Eigenvalues (min, max, max/min):
0.66 1.5 2.2
OMEGA (correlations): Eigenvalues (min, max, max/min):
0.097 2.5 25
Even though the results look similar, eigenvalues look
different. Taking into account that max/min ratio is
frequently
reported, it is important to understand the difference. It
almost look like different sets of parameters are estimated
separately in the Monolix example, which most likely is not the
case. Even if we combine all eigenvalues in one pocket,
max/min
looks good. It is impressive that max/min ratio for OMEGA
correlations may look OK even though there are small
correlations such as -0.0921, SE=0.064, RSE=70%.
What is the best way to report estimate and report max/min
ratios?
Take care,
Pavel
