Re: OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
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
>
> (
>
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>
> 7
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> [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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