Failing table step upon redefining ETAs as additive (or high correlations in $COV output)

From: J. Elassaiss-Schaap jeroen.elassaiss@organon.com Subject: [NMusers] Failing table step upon redefining ETAs as additive (or high correlations in $COV output) Date: Thu, 21 Jul 2005 16:15:19 +0200 Dear all, During development of a PK model I encountered distributions of ETAs that tailed towards negative values. 'Qqnorm' plots and evaluation of 'skewness' also suggested that at least some ETAs could benefit from specifying normal rather than lognormal distributions. I therefore reran the control stream with THETA(x)+ETA(x) instead of THETA(x)*EXP(ETA(X)). The additive model minimized succesfully with a reduction in objective function of about 5. However, the table step failed with the following message: 0PRED EXIT CODE =3D 1 0INDIVIDUAL NO. 4 ID=3D0.40000000E+01 (WITHIN-INDIVIDUAL) DATA = REC NO. 1 =20 THETA=3D 4.17E+00 2.03E+02 2.06E-02 3.17E+01 1.66E+02 OCCURS DURING SEARCH FOR ETA AT A NONZERO VALUE OF ETA ERROR IN TRANS4 ROUTINE: Q IS NEGATIVE 0PROGRAM TERMINATED BY FNLETA MESSAGE ISSUED FROM TABLE STEP The help guide gave no clues as on how to recover from such error. I tried to recover by requesting an exponential ETA for Q only. This model ran succesfully, including the table step. It did not result in a different objective function. The $COV step however provided very disappointing results, as all |correlations| were above 0.97 while many SEs were larger than their THETAs. Thereafter I tried various variations on this theme but those produced essentially the same; I summarized them at the end of my message. So my question basically is: how do/can I proceed from here? Which model development decision - if any at all - can I extract from these outcomes? Further information is appended at the end of my message, in three parts: (i) background PK info, (ii) additional runs, (iii) control stream and (iv) one individual extracted from the input datafile. Thank you for considering my question. Best regards, Jeroen J. Elassaiss-Schaap Scientist PK/PD Organon NV PO Box 20, 5340 BH Oss, Netherlands Phone: + 31 412 66 9320 Fax: + 31 412 66 2506 e-mail: jeroen.elassaiss@organon.com PS: this is my first posting to the nmusers list. Please let me know if I should rather limit the amount of information. ____________________________________ ************************************ ******* (i) background *********** ************************************ The PK samples were obtained as a function of time after administration of a subcutaneous dose. Clearance of the drug is much faster than the release from the formulation and therefore is not considered part of the model. The in vitro release of the formulation seems rather well described by a funcion "A - B ln(x)" but structural models build around that release resulted in biased population predictions. A 2-compartmental equation should describe such a release equally well or better, the model below consequently is ADVAN 3.=20 The dataset consists of 130 subjects most of whom have supplied 8 samples for PK (with measurable concentrations, that is). For most subjects the initial decrease (on a log scale) was visible in the first 3 to 5 samples.=20 In most subjects plasma concentrations increased transiently (1-3 samples) typically after the initial decrease. It was not possible for me to minimize a structural 2-dose compartment model with flexible lagtime/duration/bioavailability to a meaningful prediction, i.e. in such a way that the small and transient bias in prediction after the initial decrease was picked up by the second, flexible, dose compartment. The fluctuations thusly result in increased residuals after the ADVAN 3 fit. The additive residual component accordingly is much larger than the LLOQ (but still considerably lower than the lowest concentrations measured - except for one predose outlier). As for subject 4, who causes the table step to fail: the initial 'distribution phase' is present in one sample only and immediately followed by a rather low concentration. So it is no surprise that an 1-cmpt fit suites the data from subject 4 rather well. ************************************ ******* (ii) additional runs ****** ************************************ I tried several runs with FOCE+INTER (to be sure, non-diag OMEGA) instead of FO. The 'EXP' run resulted in essentially the same GOFs, ETA distributions and parameters. FOCE runs with additive errors (with or without ETA on Q as 'EXP') did not minimize succesfully, e.g due to rounding errors or this one: 0MINIMIZATION TERMINATED DUE TO PROXIMITY OF LAST ITERATION EST. TO A VALUE AT WHICH THE OBJ. FUNC. IS INFINITE (ERROR=3D136) 0AT THE LAST COMPUTED INFINITE VALUE OF THE OBJ. FUNCT.: 0PRED EXIT CODE =3D 1 0INDIVIDUAL NO. 83 ID=3D0.11400000E+03 (WITHIN-INDIVIDUAL) DATA = REC NO. 1 THETA=3D 3.90E+00 2.43E+02 2.19E-02 1.26E+01 1.47E+02 OCCURS DURING SEARCH FOR ETA AT A NONZERO VALUE OF ETA PK SUBROUTINE: USER ERROR CODE =3D 4=20 (NB: Although I knew it should not make a difference I inserted PREDD recovery on THETAs just to be sure) Upon googling on Nonmem (01 may 2003; model diagnostics) I reran two FO models with $COV PRINT=3DE, the full additive and the full 'EXP' models: the eigenvalue ratios were roughly 100. As the OMEGA matrix was non-diagonal, I have tried models in which I separated the ETA on Q out of the block. The increase in obj.funct. (roughly 10) seemed to be - P-cut off dependently of course - counterbalanced by the reduction in parameters (2) but resulted in rather high POSTHOC correlations between the ETAs inside and outside the block. ************************************ ******* (iii) control stream ****** ************************************ $PROB Exp variation $INPUT ID TIME AMT CP=3DDV EVID RACE AGE WGT HGH BMI SMOK NSMO TRT PROT=3DDROP $DATA data.nmdat $SUBR ADVAN3 TRANS4 $PK TVCL=3DTHETA(1) CL=3DTVCL*EXP(ETA(1)) TVV1=3DTHETA(2) CAV1=3DTHETA(3) V1=3DTVV1*(1-CAV1*(AGE-31))*EXP(ETA(2)) K=3DCL/V1 TVQ=3DTHETA(4) Q=3DTVQ*EXP(ETA(4)) TVV2=3DTHETA(5) V2=3DTVV2*EXP(ETA(3)) K12=3DQ/V1 K21=3DQ/V2 S1=3DV1/1000 $ERROR Y=3DF+F*EPS(1)+EPS(2) IPRED=3DF $THETA (0,4.26,10000) (0,207,900000) (0,0.05,.07692) (0,28.7,100000) (0,155,900000) $OMEGA 0 FIX $OMEGA BLOCK(3)=20 0.18 0.0657 0.157 0.05 0.1 0.421 $SIGMA 0.0412 331 $EST METHOD=3D0 PRINT=3D5 MAXEVAL=3D9999 SIG=3D3 POSTHOC NOABORT $COV $TABLE ID TIME CL V1 V2 Q CAV1 IPRED TRT ETA1 ETA2 ETA3 ETA4 RACE=20 AGE WGT HGH BMI SMOK NSMO NOPRINT ONEHEADER FILE=3Dtab.txt ___________ NB: as the PK parameters do not have a standard phsyiological meaning I did not reject the AGE covariate on theoretical grounds; perhaps AGE does (cor)relate to the condition of the subcutaneous compartment. The population median of AGE was 31. Only one dose was given. TRT described a co-medication but did not correlate visually with any ETA. PRDERR file was empty unless specified above. I did not remove any outlier from the data set. I used the obj. function as a decision criterium only when I did not see (rather) clear differences in GOF or other plots. ************************************ ******* (iv) example data ******** ************************************ #1 0.00 . A 0 2 39 76.5 175 25.0 1 15 1 1 1 0.00 200 . 1 2 39 76.5 175 25.0 1 15 1 1 1 0.98 . 1196 0 2 39 76.5 175 25.0 1 15 1 1 #1 2.00 . C 0 2 39 76.5 175 25.0 1 15 1 1 1 4.15 . 594 0 2 39 76.5 175 25.0 1 15 1 1 1 8.01 . 397 0 2 39 76.5 175 25.0 1 15 1 1 1 12.00 . 571 0 2 39 76.5 175 25.0 1 15 1 1 1 24.01 . 532 0 2 39 76.5 175 25.0 1 15 1 1 1 36.29 . 288 0 2 39 76.5 175 25.0 1 15 1 1 1 48.00 . 308 0 2 39 76.5 175 25.0 1 15 1 1 (A: <LLOQ, C: no sample)