Hi All,
I am having trouble understanding an aspect of NONMEM FOCEI estimation and I
didn’t find anything in the documentation to get me started.
When I add an ETA() on residual error everything estimates as I expect. I call
this "composite error model", I dont know if there is another terminology. But,
looking at the the PHI file all of the off-diagonal ETC() associated with the
ETA() are all zero. I don’t know why NONMEM thinks these must be uncorrelated.
If something special is being done in this case then:
1) how is this detected? I suppose the gradients of IPRED vs ETA() would give a
hint.
2) what is being done? Is it doing the posthoc phase twice? Or is it possible
to indicate to the posthoc estimate code to have zeros in ETC()?
As an example:
$PROB THEOPHYLLINE POPULATION DATA
$INPUT ID DOSE=AMT TIME CP=DV WT
$DATA THEOPP
$SUBROUTINES ADVAN2
$PK
CALLFL=1
KA=THETA(1)+ETA(1)
K=THETA(2)+ETA(2)
CL=THETA(3)*WT+ETA(3)
SC=CL/K/WT
$THETA (.1,3,5) (.008,.08,.5) (.004,.04,.9)
$OMEGA 1 1 1 1
$SIGMA .4
$ERROR
Y=F+EPS(1)*EXP(ETA(4))
$ESTM SIG=3 MAX=9000 METHOD=1 INTERACT SORT NOABORT POSTHOC PRINT=1
When running this, then in the PHI file has:
TABLE NO. 1: First Order Conditional Estimation with Interaction: Problem=1
Subproblem=0 Superproblem1=0 Iteration1=0 Superproblem2=0 Iteration2=0
SUBJECT_NO ID ETA(1) ETA(2) ETA(3) ETA(4) ETC(1,1) ETC(2,1) ETC(2,2) ETC(3,1)
ETC(3,2) ETC(3,3) ETC(4,1) ETC(4,2) ETC(4,3) ETC(4,4) OBJ
1 1 -3.94107E-01 -1.14325E-02 -1.17881E+00 2.58616E-01 4.90380E-02 -7.58020E-04
5.58386E-05 -5.71202E-03 9.37606E-04 2.12825E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 22.616364023850441
2 2 1.58715E-01 2.88530E-03 7.78218E-02 3.74587E-01 1.55438E-01 -1.16001E-03
6.89000E-05 3.53243E-03 1.34549E-03 4.87804E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 17.502311674928425
…
As you can see the off-diagonals for ETA(4, XXX) are all zero.
warm regards,
Douglas Eleveld
________________________________
Question about ETA on residual error
Hello Douglas:
The off-diagonals of ETA(4, XXX) should be zero, as the variance-covariance of
etas (phc) is the inverse of the information matrix that is calculated as:
Ey(2nd derivative partial -log posterior density of individual wrt partial
etax,etay))
Specifically,
-log(posterior density) =
[(y-f)^2/sigma^2*exp(-2eta4)+2*log(sigma*exp(eta4))+eta'*OMEGA-1eta]/2
Ey(2nd derivative partial posterior density of individual wrt partial eta4,etax
(not 4)))
= Ey( eta4*partial f wrt partial etax )*(y-f)/sigma^2*exp(-2eta4) +
omega_inveta4,etax)
Given that
Ey(y-f)=0
And off-diagonals of omega are 0,
Then
Ey(2nd derivative partial posterior density of individual wrt partial eta4,etax
(not 4)))=0
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
731 Arbor way, suite 100
Blue Bell, PA 19422
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com/
Quoted reply history
From: [email protected] <[email protected]> On Behalf Of
Eleveld, DJ
Sent: Saturday, February 1, 2025 2:23 AM
To: nonmem usersgroup <[email protected]>
Subject: [EXTERNAL] [NMusers] Question about ETA on residual error
Hi All,
I am having trouble understanding an aspect of NONMEM FOCEI estimation and I
didn't find anything in the documentation to get me started.
When I add an ETA() on residual error everything estimates as I expect. I call
this "composite error model", I dont know if there is another terminology. But,
looking at the the PHI file all of the off-diagonal ETC() associated with the
ETA() are all zero. I don't know why NONMEM thinks these must be uncorrelated.
If something special is being done in this case then:
1) how is this detected? I suppose the gradients of IPRED vs ETA() would give a
hint.
2) what is being done? Is it doing the posthoc phase twice? Or is it possible
to indicate to the posthoc estimate code to have zeros in ETC()?
As an example:
$PROB THEOPHYLLINE POPULATION DATA
$INPUT ID DOSE=AMT TIME CP=DV WT
$DATA THEOPP
$SUBROUTINES ADVAN2
$PK
CALLFL=1
KA=THETA(1)+ETA(1)
K=THETA(2)+ETA(2)
CL=THETA(3)*WT+ETA(3)
SC=CL/K/WT
$THETA (.1,3,5) (.008,.08,.5) (.004,.04,.9)
$OMEGA 1 1 1 1
$SIGMA .4
$ERROR
Y=F+EPS(1)*EXP(ETA(4))
$ESTM SIG=3 MAX=9000 METHOD=1 INTERACT SORT NOABORT POSTHOC PRINT=1
When running this, then in the PHI file has:
TABLE NO. 1: First Order Conditional Estimation with Interaction: Problem=1
Subproblem=0 Superproblem1=0 Iteration1=0 Superproblem2=0 Iteration2=0
SUBJECT_NO ID ETA(1) ETA(2) ETA(3) ETA(4) ETC(1,1) ETC(2,1) ETC(2,2) ETC(3,1)
ETC(3,2) ETC(3,3) ETC(4,1) ETC(4,2) ETC(4,3) ETC(4,4) OBJ
1 1 -3.94107E-01 -1.14325E-02 -1.17881E+00 2.58616E-01 4.90380E-02 -7.58020E-04
5.58386E-05 -5.71202E-03 9.37606E-04 2.12825E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 22.616364023850441
2 2 1.58715E-01 2.88530E-03 7.78218E-02 3.74587E-01 1.55438E-01 -1.16001E-03
6.89000E-05 3.53243E-03 1.34549E-03 4.87804E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 17.502311674928425
...
As you can see the off-diagonals for ETA(4, XXX) are all zero.
warm regards,
Douglas Eleveld
________________________________
Hi Robert,
Thank you very much, it will take me some time to try and understand this.
I have always visualized the ETC matrix as a measure of the uncertainty of the
ETA, capturing the ellipsoidal shape of the likelihood around the minimum. Is
this right? It seems likely to me that a different estimate of residual error
ETA(4) would result in a different ETA(XXX) estimate, so I expected to see
off-diagonals in the ETC(4,XXX). I'll study your equations for a while.
warm regards,
Douglas
________________________________
Quoted reply history
Van: Bauer, Robert <[email protected]>
Verzonden: dinsdag 4 februari 2025 19:45
Aan: Eleveld, DJ <[email protected]>; nonmem usersgroup
<[email protected]>
Onderwerp: RE: Question about ETA on residual error
Hello Douglas:
The off-diagonals of ETA(4, XXX) should be zero, as the variance-covariance of
etas (phc) is the inverse of the information matrix that is calculated as:
Ey(2nd derivative partial -log posterior density of individual wrt partial
etax,etay))
Specifically,
-log(posterior density) =
[(y-f)^2/sigma^2*exp(-2eta4)+2*log(sigma*exp(eta4))+eta’*OMEGA-1eta]/2
Ey(2nd derivative partial posterior density of individual wrt partial eta4,etax
(not 4)))
= Ey( eta4*partial f wrt partial etax )*(y-f)/sigma^2*exp(-2eta4) +
omega_inveta4,etax)
Given that
Ey(y-f)=0
And off-diagonals of omega are 0,
Then
Ey(2nd derivative partial posterior density of individual wrt partial eta4,etax
(not 4)))=0
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
731 Arbor way, suite 100
Blue Bell, PA 19422
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com/
From: [email protected] <[email protected]> On Behalf Of
Eleveld, DJ
Sent: Saturday, February 1, 2025 2:23 AM
To: nonmem usersgroup <[email protected]>
Subject: [EXTERNAL] [NMusers] Question about ETA on residual error
Hi All,
I am having trouble understanding an aspect of NONMEM FOCEI estimation and I
didn’t find anything in the documentation to get me started.
When I add an ETA() on residual error everything estimates as I expect. I call
this "composite error model", I dont know if there is another terminology. But,
looking at the the PHI file all of the off-diagonal ETC() associated with the
ETA() are all zero. I don’t know why NONMEM thinks these must be uncorrelated.
If something special is being done in this case then:
1) how is this detected? I suppose the gradients of IPRED vs ETA() would give a
hint.
2) what is being done? Is it doing the posthoc phase twice? Or is it possible
to indicate to the posthoc estimate code to have zeros in ETC()?
As an example:
$PROB THEOPHYLLINE POPULATION DATA
$INPUT ID DOSE=AMT TIME CP=DV WT
$DATA THEOPP
$SUBROUTINES ADVAN2
$PK
CALLFL=1
KA=THETA(1)+ETA(1)
K=THETA(2)+ETA(2)
CL=THETA(3)*WT+ETA(3)
SC=CL/K/WT
$THETA (.1,3,5) (.008,.08,.5) (.004,.04,.9)
$OMEGA 1 1 1 1
$SIGMA .4
$ERROR
Y=F+EPS(1)*EXP(ETA(4))
$ESTM SIG=3 MAX=9000 METHOD=1 INTERACT SORT NOABORT POSTHOC PRINT=1
When running this, then in the PHI file has:
TABLE NO. 1: First Order Conditional Estimation with Interaction: Problem=1
Subproblem=0 Superproblem1=0 Iteration1=0 Superproblem2=0 Iteration2=0
SUBJECT_NO ID ETA(1) ETA(2) ETA(3) ETA(4) ETC(1,1) ETC(2,1) ETC(2,2) ETC(3,1)
ETC(3,2) ETC(3,3) ETC(4,1) ETC(4,2) ETC(4,3) ETC(4,4) OBJ
1 1 -3.94107E-01 -1.14325E-02 -1.17881E+00 2.58616E-01 4.90380E-02 -7.58020E-04
5.58386E-05 -5.71202E-03 9.37606E-04 2.12825E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 22.616364023850441
2 2 1.58715E-01 2.88530E-03 7.78218E-02 3.74587E-01 1.55438E-01 -1.16001E-03
6.89000E-05 3.53243E-03 1.34549E-03 4.87804E-02 0.00000E+00 0.00000E+00
0.00000E+00 3.57535E-02 17.502311674928425
…
As you can see the off-diagonals for ETA(4, XXX) are all zero.
warm regards,
Douglas Eleveld
________________________________