Dear NM Users,
I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an error message saying the parameter estimate is near its boundary (See also the discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS BOUNDARY ). After digging through the documentation I am still unsure where the problem is originating from. What I figured out is that the problem lies in the OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is only introduced since NM7.2. The estimate in this matrix that is giving problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a boundary).
Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs, is related to the OMEGA - CORR MATRIX value. What does this value actually mean, and what does it mean for my error message, as the correlation estimate itself seems to be fine? In the print below you can see the model and resulting estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2) and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an proportional error model,
Thanks in advance for any insights and help,
Best, Jules Heuberger
$SUB ADVAN=6 TOL=5 $MODEL COMP=(CENTRAL) COMP=(PERI)
$PK
; structural model K10=IK10 V1 =IV1 K12=EXP(-1.29) K21=EXP(-0.63) V2=K12*V1/K21 BSL=IBSL E0=THETA(1)*EXP(ETA(1)) EMAX=THETA(2)*EXP(ETA(2)) EC50=THETA(3)
; $DES DADT(1) = -K10*A(1)-K12*A(1)+K21*A(2) DADT(2) = K12*A(1)-K21*A(2) $ERROR CP=F EFF=E0-EMAX*F/(EC50+F) Y= EFF*(1+ERR(1))+ERR(2) IPRE=EFF
$THETA 55 20.9 364
; $OMEGA BLOCK(2) 0.2 0.01 0.2
$SIGMA 0.01 0 FIX
$EST PRINT=5 MAX=9999 METHOD=1 INTERACTION POSTHOC NOABORT MSFO=mfi
__________________________________________________________
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
ETA1 ETA2 ETA1 + 2.44E-02 ETA2 + 5.26E-02 1.13E-01
SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
EPS1 EPS2 EPS1 + 1.11E-02 EPS2 + 0.00E+00 0.00E+00 1
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
ETA1 ETA2 ETA1 + 1.56E-01 ETA2 + 1.00E+00 3.37E-01
SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
EPS1 EPS2 EPS1 + 1.05E-01 EPS2
+ 0.00E+00 0.00E+00
Jules Heuberger
Clinical Scientist Centre for Human Drug Research Zernikedreef 8 2333 CL Leiden The Netherlands
'
+31 (0)71 5246400
(
+31 (0)6 43937461
7
+31 (0)71 5246499
+
[email protected]
http://www.chdr.nl
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Hi Jules,
it seems that your two ETAs are heavily correlated (1.00) and this causes
problems for NONMEM. Next to evaluating if you really need two destinct
ETAs or should use just one as in e.g.
E0= THETA(1)*EXP(ETA(1))
EMAX = E0+THETA(2)
I would suggest to re-code your Emax and E0 in logit space if you are
trying to model a DV that is between 0 and 1.
E0 = EXP(THETA(1) + ETA(1))/(1+EXP(THETA(1)+ETA(1))
EMAX =
EXP(THETA(1)+THETA(2)+ETA(1)+ETA(2))/(1+EXP(THETA(1)+THETA(2)+ETA(1)+ETA(2)))
again check if ETA(2) (or ETA(1)) is really necessary. THETA(2) should be
positive in all examples.
Kind Regards
Sven Mensing
Quoted reply history
2013/9/17 Jules Heuberger <[email protected]>
> Dear NM Users,
>
> I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving
> an error message saying the parameter estimate is near its boundary (See
> also the discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE
> IS NEAR ITS BOUNDARY ). After digging through the documentation I am still
> unsure where the problem is originating from. What I figured out is that
> the problem lies in the OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
> *******, a matrix I believe is only introduced since NM7.2. The estimate in
> this matrix that is giving problems is the one for the OMEGA BLOCK, which
> is estimated to be 1 (a boundary).
>
> Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA -
> COV MATRIX as the sqrt of its estimate. However, it is unclear to me how
> the OMEGA BLOCK estimate (COV MATRIX), which gives the correlation between
> the two ETAs, is related to the OMEGA - CORR MATRIX value. What does this
> value actually mean, and what does it mean for my error message, as the
> correlation estimate itself seems to be fine? In the print below you can
> see the model and resulting estimates, the important ones being 5.26E-02
> (OMEGA - COV MATRIX of ETA1-ETA2) and 1.00E+00 (OMEGA - CORR MATRIX of
> ETA1-ETA2). The model has two ETAs and an proportional error model,
>
> Thanks in advance for any insights and help,
>
> Best,
>
> Jules Heuberger
>
>
>
> $SUB ADVAN=6 TOL=5
> $MODEL
> COMP=(CENTRAL)
> COMP=(PERI)
>
> $PK
> ; structural model
> K10=IK10
> V1 =IV1
> K12=EXP(-1.29)
> K21=EXP(-0.63)
> V2=K12*V1/K21
> BSL=IBSL
> E0=THETA(1)*EXP(ETA(1))
> EMAX=THETA(2)*EXP(ETA(2))
> EC50=THETA(3)
> ;
> $DES
>
> DADT(1) = -K10*A(1)-K12*A(1)+K21*A(2)
> DADT(2) = K12*A(1)-K21*A(2)
> $ERROR
> CP=F
> EFF=E0-EMAX*F/(EC50+F)
> Y= EFF*(1+ERR(1))+ERR(2)
> IPRE=EFF
>
> $THETA
> 55
> 20.9
> 364
>
> ;
> $OMEGA BLOCK(2)
> 0.2
> 0.01 0.2
>
> $SIGMA
> 0.01
> 0 FIX
>
> $EST PRINT=5 MAX=9999 METHOD=1 INTERACTION POSTHOC NOABORT MSFO=mfi
>
>
> __________________________________________________________
>
> OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
>
> ETA1 ETA2
>
> ETA1
> + 2.44E-02
>
> ETA2
> + 5.26E-02 1.13E-01
>
>
> SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
>
> EPS1 EPS2
>
> EPS1
> + 1.11E-02
>
> EPS2
> + 0.00E+00 0.00E+00
>
> 1
>
> OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
>
> ETA1 ETA2
>
> ETA1
> + 1.56E-01
>
> ETA2
> + 1.00E+00 3.37E-01
>
>
> SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
>
> EPS1 EPS2
>
> EPS1
> + 1.05E-01
>
> EPS2
> + 0.00E+00 0.00E+00
>
>
>
> *Jules Heuberger **
> *Clinical Scientist
> Centre for Human Drug Research
> Zernikedreef 8
> 2333 CL Leiden
> The Netherlands
> '+31 (0)71 5246400******
>
> (+31 (0)6 43937461
> 7+31 (0)71 5246499
> +*[email protected]*
> http://www.chdr.nl**
>
> *[image: CHDR_logo_verticaal_onderregel_fc_positief.jpg]***
>
Hi Jules, it seems like the problem is due to the fact that you are coding your OMEGA matrix as a 2x2 block, and the estimate for the correlation is 1, which is a boundary, since the correlation needs to sit between -1 and 1. This boundary cannot be defined easily for the covariance matrix, since the correlation is calculated by rescaling by the sqrt of the two variances. Have a look at
http://en.wikipedia.org/wiki/Covariance_matrix
and particularly at the section correlation matrix. Unless explicitly specified, the OMEGA block is coded as covariance, not correlation. So the boundary is not easy to spot unless you convert into correlations matrix or, as you did, you look at the output that NONMEM gives you also as correlation matrix. When you have two ETAs that are 100% correlated (corr=1) it means that your model cannot separate one from the other. What you can do in this case is either simplifying your model, or using the same ETA for both, and apply a scaling factor between the two. See the code for this second option below. BSVCL=ETA(x) ; BSV for the first parameter BSVV=THETA(y)*BSVCL ; BSV for the second parameter, 100% correlated to the first. THETA(y) is a scaling factor between the two BSV (a ratio of their SDs) I hope this helps. Greetings from Cape Town, Paolo
Quoted reply history
On 2013/09/17 12:41, Jules Heuberger wrote:
> Dear NM Users,
>
> I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an error message saying the parameter estimate is near its boundary (See also the discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS BOUNDARY ). After digging through the documentation I am still unsure where the problem is originating from. What I figured out is that the problem lies in the OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is only introduced since NM7.2. The estimate in this matrix that is giving problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a boundary).
>
> Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs, is related to the OMEGA - CORR MATRIX value. What does this value actually mean, and what does it mean for my error message, as the correlation estimate itself seems to be fine? In the print below you can see the model and resulting estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2) and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an proportional error model,
>
> Thanks in advance for any insights and help,
>
> Best, Jules Heuberger
>
> $SUB ADVAN=6 TOL=5 $MODEL COMP=(CENTRAL) COMP=(PERI)
>
> $PK
>
> ; structural model K10=IK10 V1 =IV1 K12=EXP(-1.29) K21=EXP(-0.63) V2=K12*V1/K21 BSL=IBSL E0=THETA(1)*EXP(ETA(1)) EMAX=THETA(2)*EXP(ETA(2)) EC50=THETA(3)
>
> ; $DES DADT(1) = -K10*A(1)-K12*A(1)+K21*A(2) DADT(2) = K12*A(1)-K21*A(2) $ERROR CP=F EFF=E0-EMAX*F/(EC50+F) Y= EFF*(1+ERR(1))+ERR(2) IPRE=EFF
>
> $THETA 55 20.9 364
>
> ; $OMEGA BLOCK(2) 0.2 0.01 0.2
>
> $SIGMA 0.01 0 FIX
>
> $EST PRINT=5 MAX=9999 METHOD=1 INTERACTION POSTHOC NOABORT MSFO=mfi
>
> __________________________________________________________
>
> OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
>
> ETA1 ETA2 ETA1 + 2.44E-02 ETA2 + 5.26E-02 1.13E-01
>
> SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
>
> EPS1 EPS2 EPS1 + 1.11E-02 EPS2 + 0.00E+00 0.00E+00 1
>
> OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
>
> ETA1 ETA2 ETA1 + 1.56E-01 ETA2 + 1.00E+00 3.37E-01
>
> SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
>
> EPS1 EPS2 EPS1 + 1.05E-01 EPS2
>
> + 0.00E+00 0.00E+00
>
> Jules Heuberger
>
> Clinical Scientist
>
> Centre for Human Drug Research
> Zernikedreef 8
> 2333 CL Leiden
> The Netherlands
>
> '
>
> +31 (0)71 5246400
>
> (
>
> +31 (0)6 43937461
>
> 7
>
> +31 (0)71 5246499
>
> +
>
> [email protected]
>
> http://www.chdr.nl
--
------------------------------------------------
Paolo Denti, PhD
Pharmacometrics Group
Division of Clinical Pharmacology
Department of Medicine
University of Cape Town
K45 Old Main Building
Groote Schuur Hospital
Observatory, Cape Town
7925 South Africa
phone: +27 21 404 7719
fax: +27 21 448 1989
email: [email protected]
------------------------------------------------
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Hi Jules,
If the correlation between two ETAs is 0 then you should be able to remove one
ETA and replace it by a scaled version of the other ETA and get the same
objective function value.
This model would not have a correlation problem (since only one ETA) so your
problem would be "solved" in a superficial way.
Of course you might not be satisfied with the idea that one of your ETAs is
(except for scale) wholly determined by the ETA for a different paramater with
a different physical interpretation.
What reason might be that these paramaters are so strongly related in your data?
I think that usually this suggests that the model is too complex for the
information available in the dataset. Or maybe some other model structure would
be better.
Douglas Eleveld
________________________________
Quoted reply history
Van: [email protected] [mailto:[email protected]] Namens
Jules Heuberger
Verzonden: September 17, 2013 12:42 PM
Aan: [email protected]
Onderwerp: [NMusers] OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Dear NM Users,
I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an
error message saying the parameter estimate is near its boundary (See also the
discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS
BOUNDARY ). After digging through the documentation I am still unsure where the
problem is originating from. What I figured out is that the problem lies in the
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is
only introduced since NM7.2. The estimate in this matrix that is giving
problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a
boundary).
Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV
MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA
BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs,
is related to the OMEGA - CORR MATRIX value. What does this value actually
mean, and what does it mean for my error message, as the correlation estimate
itself seems to be fine? In the print below you can see the model and resulting
estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2)
and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an
proportional error model,
Thanks in advance for any insights and help,
Best,
Jules Heuberger
$SUB ADVAN=6 TOL=5
$MODEL
COMP=(CENTRAL)
COMP=(PERI)
$PK
; structural model
K10=IK10
V1 =IV1
K12=EXP(-1.29)
K21=EXP(-0.63)
V2=K12*V1/K21
BSL=IBSL
E0=THETA(1)*EXP(ETA(1))
EMAX=THETA(2)*EXP(ETA(2))
EC50=THETA(3)
;
$DES
DADT(1) = -K10*A(1)-K12*A(1)+K21*A(2)
DADT(2) = K12*A(1)-K21*A(2)
$ERROR
CP=F
EFF=E0-EMAX*F/(EC50+F)
Y= EFF*(1+ERR(1))+ERR(2)
IPRE=EFF
$THETA
55
20.9
364
;
$OMEGA BLOCK(2)
0.2
0.01 0.2
$SIGMA
0.01
0 FIX
$EST PRINT=5 MAX=9999 METHOD=1 INTERACTION POSTHOC NOABORT MSFO=mfi
__________________________________________________________
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
ETA1 ETA2
ETA1
+ 2.44E-02
ETA2
+ 5.26E-02 1.13E-01
SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
EPS1 EPS2
EPS1
+ 1.11E-02
EPS2
+ 0.00E+00 0.00E+00
1
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
ETA1 ETA2
ETA1
+ 1.56E-01
ETA2
+ 1.00E+00 3.37E-01
SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
EPS1 EPS2
EPS1
+ 1.05E-01
EPS2
+ 0.00E+00 0.00E+00
Jules Heuberger
Clinical Scientist
Centre for Human Drug Research
Zernikedreef 8
2333 CL Leiden
The Netherlands
'+31 (0)71 5246400
(+31 (0)6 43937461
7+31 (0)71 5246499
[email protected]<mailto:[email protected]>
http://www.chdr.nl/
[CHDR_logo_verticaal_onderregel_fc_positief.jpg]
________________________________
Dear Jules,
You are correct in pointing out where the problem lies.
However, the covariance matrix is not fine since it is at the boundary just as
much as the translation into correlation.
Correlation is calculated by this equation:
Cor(eta1,eta2)=OM1,2 /(sqrt(OM1,1)*sqrt(OM2,2))
Where:
OM1,1 and OM2,2, represents eta variance (as reported by nonmem output in the
OMEGA cov matrix, i.e. on var scale and not the sd scale that is reported in
the OMEGA corr matrix) and
OM1,2 represents Cov(eta1,eta2), i.e. as reported for the off diagonal on the
OMEGA cov matrix
I did not check your control stream thoroughly, but apparently, with the
current data and model baseline (E0) and Emax are completely correlated on the
individual level, maybe because of lack of information, maybe because of
physiology – you currently have an additive effect, but maybe Emax would be
bringing the PD endpoint all the way to zero or reducing the endpoint by a
certain fraction (i.e. a multiplicative model), or maybe healthy can not be
reduced at all, wheras elevated values can be reduced (almost) down to healthy
values? If you get that “structural” part of your drug-effects model right, you
may then be able to estimate correlation (or conclude with the new structure
these two etas are no longer correlated).
Best regards
Jakob
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Jules Heuberger
Sent: 17 September 2013 11:42
To: [email protected]
Subject: [NMusers] OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Dear NM Users,
I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an
error message saying the parameter estimate is near its boundary (See also the
discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS
BOUNDARY ). After digging through the documentation I am still unsure where the
problem is originating from. What I figured out is that the problem lies in the
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is
only introduced since NM7.2. The estimate in this matrix that is giving
problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a
boundary).
Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV
MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA
BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs,
is related to the OMEGA - CORR MATRIX value. What does this value actually
mean, and what does it mean for my error message, as the correlation estimate
itself seems to be fine? In the print below you can see the model and resulting
estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2)
and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an
proportional error model,
Thanks in advance for any insights and help,
Best,
Jules Heuberger
Hi Sven, Jules,
Nonmem 7.3 beta allows you to code the off-diagonal elements by correlation
rather than covariance in $OMEGA, from its help:
[
CORRELATON indicates that all initial estmates given for off-
diagonal elements are understood to be initial estimates of cor-
relations of etas.
]
This will be an improvement in developing full omega blocks, assuming this
functionality makes it into the actual release.
Best regards,
Jeroen
J. Elassaiss-Schaap Senior Principal
Scientist Phone: + 31 412 66 9320
MSD | PK, PD and Drug Metabolism | Clinical PK-PD Mail stop KR
4406 | PO Box 20, 5340 BH Oss, NL
Quoted reply history
From: [email protected] [mailto:[email protected]] On
Behalf Of Sven Mensing
Sent: Tuesday, September 17, 2013 13:44
To: Jules Heuberger
Cc: [email protected]
Subject: Re: [NMusers] OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Hi Jules,
it seems that your two ETAs are heavily correlated (1.00) and this causes
problems for NONMEM. Next to evaluating if you really need two destinct ETAs or
should use just one as in e.g.
E0= THETA(1)*EXP(ETA(1))
EMAX = E0+THETA(2)
I would suggest to re-code your Emax and E0 in logit space if you are trying to
model a DV that is between 0 and 1.
E0 = EXP(THETA(1) + ETA(1))/(1+EXP(THETA(1)+ETA(1))
EMAX =
EXP(THETA(1)+THETA(2)+ETA(1)+ETA(2))/(1+EXP(THETA(1)+THETA(2)+ETA(1)+ETA(2)))
again check if ETA(2) (or ETA(1)) is really necessary. THETA(2) should be
positive in all examples.
Kind Regards
Sven Mensing
2013/9/17 Jules Heuberger <[email protected]<mailto:[email protected]>>
Dear NM Users,
I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an
error message saying the parameter estimate is near its boundary (See also the
discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS
BOUNDARY ). After digging through the documentation I am still unsure where the
problem is originating from. What I figured out is that the problem lies in the
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is
only introduced since NM7.2. The estimate in this matrix that is giving
problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a
boundary).
Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV
MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA
BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs,
is related to the OMEGA - CORR MATRIX value. What does this value actually
mean, and what does it mean for my error message, as the correlation estimate
itself seems to be fine? In the print below you can see the model and resulting
estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2)
and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an
proportional error model,
Thanks in advance for any insights and help,
Best,
Jules Heuberger
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