Dear NMUsers,
I am investigating a model with between-occasion variability (BOV) and I experienced a weird behaviour of NONMEM 7 (I have version 7.1.2 installed).
The inclusion of a correlation between two parameters at BOV level caused a significant drop in the objective function value (-16 points). However, while the VPC of the original model (without correlation) was pretty satisfactory, the new one, with the correlation included, was completely skewed and did not superimpose with the real data.
All the parameter estimates were pretty much the same in the two models (expect obviously the newly included correlation which was just below 0.5), so the difference in the VPC was really striking.
I decided to investigate and I tried to run a simulation. The model and a portion of the dataset are pasted below. The structural model is not relevant at all, since all I am interested in is obtaining ETAs with BSV and BOV. I used 200 subjects and 4 occasions, so that I could obtain reasonably stable estimates of variance.
The model includes a VERY SMALL correlation (almost zero and thus expected to be irrelevant) at BOV level, I performed 5 simulations with the option SUBPROBLEMS=5, and I analysed the variance of the ETAs obtained in output. The OMEGA used for the simulation and therefore expected as an output are:
BSV
0.1
0 0.3
BOV
0.5
0.00001 0.7
It turns out that, if I analyse the results from the 1st simulation (out of 5), all behaves as expected: all the variances and covariances of the ETAs are almost the same as specified in OMEGA.
However, analysing the results of all other simulations (2 to 5), the covariance matrix of the ETAs for the BOV is very different from the OMEGAs given as input. For the 3rd simulation I got
BOV
0.287
0.0335 0.00392
Which also implies a very strong correlation (almost 1) between the 2 ETAs. Since all the simulations except the 1st one display the same trend, this would explain my crazy VPC.
I also tried running a model with correlation only in the BSV instead, and I obtained BOV values different from the OMEGA used in the simulation. Also in this case, the problem was there only for simulations after the first one.
If instead I either include correlation BOTH on BSV and BOV or NONE at all, everything looks in order.
The question is, do you see any mistakes in my model/dataset that would explain this? Is there something I am doing wrong in the modelling of the between occasion variability?
I should also mention that I tried this with NONMEM 6, and it does not happen. Any clues?
If it can be of help, please email me and I can send you the model files and dataset so that you can test this on a different machine/NONMEM installation.
Thank you and enjoy your weekend!
Paolo
Model:
> $PROBLEM test_corr | NO CORR BSV | WITH CORR BOV
> $INPUT ID DMID OCC TIME DV AMT EVID
>
> $DATA test_corr_200.csv IGNORE=@
>
> $SUBROUTINE ADVAN2 TRANS2
>
> $PK
> BSVCL=ETA(1)
> BSVV=ETA(2)
>
> IF (OCC.EQ.1) THEN
> BOVCL=ETA(3)
> BOVKA=ETA(4)
> ENDIF
> IF (OCC.EQ.2) THEN
> BOVCL=ETA(5)
> BOVKA=ETA(6)
> ENDIF
> IF (OCC.EQ.3) THEN
> BOVCL=ETA(7)
> BOVKA=ETA(8)
> ENDIF
> IF (OCC.EQ.4) THEN
> BOVCL=ETA(9)
> BOVKA=ETA(10)
> ENDIF
>
> TVCL=THETA(1)
> CL=TVCL*EXP(BSVCL+BOVCL)
>
> TVV=THETA(2)
> V=TVV*EXP(BSVV)
>
> TVKA=THETA(3)
> KA=TVKA*EXP(BOVKA)
>
> S2=V
> K=CL/V
>
> $ERROR
> IF (F.EQ.0) THEN
> IPRED=0
> ELSE
> IPRED=LOG(F)
> ENDIF
> W = THETA(4)
> IRES=DV-IPRED
> IWRES=IRES/W
> Y = IPRED + W*ERR(1)
>
> $THETA
> (0,0.45) ; POP_CL
> (0,10) ; POP_V
> (0,1) ; POP_KA
> (0,0.1) ; EXP err
>
> $OMEGA BLOCK(2)
> 0.1 ; BSV CL
> 0 ; COV CL~VOL
> 0.3 ; BSV VOL
>
> $OMEGA BLOCK(2)
> 0.5 ; BSV CL
> .00001 ; COV CL~VOL
> 0.7 ; BSV VOL
> $OMEGA BLOCK(2) SAME
> $OMEGA BLOCK(2) SAME
> $OMEGA BLOCK(2) SAME
>
> $SIGMA 1. FIX
>
> $SIMULATION (123) ONLYSIM SUBPROBLEMS=5
>
> $TABLE ID OCC TIME Y DV CL V KA K BSVCL BSVV BOVCL BOVKA ETA1 ETA2 ETA3 ETA4 ETA5 ETA6 ETA7 ETA8 ETA9 ETA10 NOPRINT NOAPPEND ONEHEADER FILE=sim1.tab
Dataset:
> #ID DMID OCC TIME DV AMT EVID
> 1 1 1 0 . . 3
> 1 1 1 0 . 100 1
> 1 1 1 12 . . 0
> 1 2 2 0 . . 3
> 1 2 2 0 . 100 1
> 1 2 2 12 . . 0
> 1 3 3 0 . . 3
> 1 3 3 0 . 100 1
> 1 3 3 12 . . 0
> 1 4 4 0 . . 3
> 1 4 4 0 . 100 1
> 1 4 4 12 . . 0
> 2 5 1 0 . . 3
> 2 5 1 0 . 100 1
> 2 5 1 12 . . 0
> 2 6 2 0 . . 3
> 2 6 2 0 . 100 1
> 2 6 2 12 . . 0
> 2 7 3 0 . . 3
> 2 7 3 0 . 100 1
> 2 7 3 12 . . 0
> 2 8 4 0 . . 3
> 2 8 4 0 . 100 1
> 2 8 4 12 . . 0
--
------------------------------------------------
Paolo Denti, PhD
Post-Doctoral Fellow
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]