Hi Pavel,
For starters, it is simple to calculate using R:
mymat<-abs(matrix(rnorm(25^2),ncol=25))
mymat <- mymat /max(mymat)
#replace mymat with your nonmem $cov matrix
eigenval<-eigen(mymat,symm=T)$values# should be similar to nonmem
reported
cn<-max(eigenval)/min(eigenval)
eigenval<-eigen(mymat[1:10,1:10],symm=T)$values
cn1<-max(eigenval)/min(eigenval) # could be compared to the "PK"
parameters ratio from monolix
Assuming a 25x25 covariance matrix, and theta in 1:10. You will need to
do some rearrangement of the cells to isolate the off-diagonal elements
of $OMEGA, but with this approach you can compare apples by apples.
Until you have done that you will not know whether the platforms provide
different results or similar wrt the condition number.
The difference in behavior with respect to objective function impact is
puzzling, assuming you refer to SAEM estimation in Nonmem. My advice
here would be to focus on (visual) predictive checks, and compare how
well the two platforms perform on that aspect.
Hope this helps,
Jeroen
--
http://pd-value.com
jer...@pd-value.com
@PD_value
+31 6 23118438
-- More value out of your data!
Op 06-11-15 om 17:05 schreef Pavel Belo:
NONMEM demonstrated very large differences in objective function when
variability or correlations were added or removed. Monolix
demonstrated close-to-insignificant differences. When differences in
software start to affect important conclusions it becomes
interesting. It feels like we need to make sure we report the most
meaningful results.
NONMEM runs as if the covariance matrix is more a byproduct than an
essential part of the optimization. Monolix runs as if the covariance
matrix an essential part of the optimization. NONMEM teachers
recommend to try a full covariance matrix. Monolix teachers recommend
to be careful and try a diagonal matrix first.
Thanks,
Pavel
On Fri, Nov 06, 2015 at 08:42 AM, Pavel Belo wrote:
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
jer...@pd-value.com
@PD_value
+31 6 23118438
-- 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
