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
eigenvalues
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
[email protected]
@PD_value
+31 6 23118438
-- More value out of your data!
Quoted reply history
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
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
Quoted reply history
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
[email protected] <mailto:[email protected]>
@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
Dear Pavel,
Are you using MATRIX=R when using NONMEM or the default sandwich estimator for
the covariance matrix? Most nonlinear regression packages use the equivalent
of MATRIX=R in NONMEM. You might try MATRIX=R on the $COV step and then
compare to Monolix.
Ken
Sent from my iPhone
Quoted reply history
> On Nov 6, 2015, at 8:42 AM, Pavel Belo <[email protected]> wrote:
>
> 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
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
[email protected]
@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
Quoted reply history
> 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
> [email protected]
> @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
Hello Pavel,
Could you share the COV matrices from Monolix and NONMEM? I have an idea of
what could be going on, but it would be good to see the matrices to check if
the hypothesis makes sense.
Best,
Matt
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Jeroen Elassaiss-Schaap
Sent: Friday, November 06, 2015 11:34
To: Pavel Belo
Cc: “[email protected]”
Subject: Re: [NMusers] eigenvalues
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
[email protected]
@PD_value
+31 6 23118438
-- More value out of your data!
Pavel:
In NONMEM, the best variance-covariance is obtained during evaluation of the
objective function by the importance sampling step (expectation only, EONLY=1,
so the final parameters do not change from what was assessed by SAEM).
The SAEM step only evaluates the S matrix version of the variance-covariance.
To obtain the R matrix version, set $COV MATRIX=R, and evaluate the importance
sampling step, from which you get the proper marginal density objective
function, as well as a full Monte-Carlo assessed variance-covariance matrix.
For example:
$EST METHOD=SAEM ….
$EST METHOD=IMP NITER=10 EONLY=1 MAPITER=0 ISAMPLE=1000
…
$COV MATRIX=R PRINT=E UNCONDITIONAL
You should assess the eigenvalues from the variance-covariance evaluated at the
IMP step.
Robert J. Bauer, Ph.D.
Vice President, Pharmacometrics R&D
ICON Early Phase
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com
Hello Jeroen,
Thank you for the advice
for starters. It advances some of us to an intermediate or even higher level.
The question can be
deeper. Here we mostly do not refer to population PK models as
hierarchical models. In Monolix books statements like "we
take advantage of the hierarchical structure of the model" are
everywhere. It makes little sense to estimate theta, diagonal of omega
and sigma, and omega correlations all together as correlated parameters and then ignore correlations between some groups of parameters when eigenvalues are calculated (for example, correlations of theta and omega). It makes more
sense to do it when there is a theory, which suggests that under certain
conditions the groups of parameters are not correlated.
It is interesting to
understand a rationale for a potential assumption (or a result of another
assumption) that estimates of certain groups of parameters are not
correlated.
Take care,
Pavel
Quoted reply history
On Fri, Nov 06, 2015 at 11:34 AM, Jeroen Elassaiss-Schaap wrote:
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 http://pd-value.com
[email protected] <mailto:[email protected]>
@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 http://pd-value.com
[email protected] <mailto:[email protected]>
@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