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 robert.ba...@iconplc.com<mailto:robert.ba...@iconplc.com> www.iconplc.com<http://www.iconplc.com/> From: owner-nmus...@globomaxnm.com <owner-nmus...@globomaxnm.com> On Behalf Of Eleveld, DJ Sent: Saturday, February 1, 2025 2:23 AM To: nonmem usersgroup <nmusers@globomaxnm.com> 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). Anderen dan de geadresseerde(n) mogen geen gebruik maken van dit bericht, het niet openbaar maken of op enige wijze verspreiden of vermenigvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomplete aankomst of vertraging van dit verzonden bericht. The contents of this message are confidential and only intended for the eyes of the addressee(s). Others than the addressee(s) are not allowed to use this message, to make it public or to distribute or multiply this message in any way. The UMCG cannot be held responsible for incomplete reception or delay of this transferred message. <br /><br /> ICON plc made the following annotations. ------------------------------------------------------------------------------ This e-mail transmission may contain confidential or legally privileged information that is intended only for the individual or entity named in the e-mail address. If you are not the intended recipient, you are hereby notified that any disclosure, copying, distribution, or reliance upon the contents of this e-mail is strictly prohibited. If you have received this e-mail transmission in error, please reply to the sender, so that ICON plc can arrange for proper delivery, and then please delete the message. Thank You, ICON plc South County Business Park Leopardstown Dublin 18 Ireland Registered number: 145835
