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 ________________________________ 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]> www.iconplc.com<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 ________________________________ De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadresseerde(n). 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