problem with PK fit in a PKPD model

Dear NMusers group: I am puzzled by the result of a NONMEM analysis I am working on. I have modeled plasma conc versus effect data using ADVAN5 (simultaneous link, comp3=effect) and can get a reasonable fit for the PD but the PK IPRED versus observed plot has a very unusual S-shape. Fitting the same plasma conc independently using ADVAN3 with the same error structure does not produce such pattern. I log transform the plasma concentration data to obtain a better PK fit. Also I have built a non-linear binding equation into the error structure of the PKPD model. I have included the code below. Do you know what is wrong? Many thanks in advance and I look forward to hear from you. Fatemeh Akhlaghi $PROBLEM ;MODEL DESC:PKPDLINKWITH BINDING PARAMETERS ;PROJECT NAME: EXAMPLE1 ;PROJECT ID: PKPDLINK MODEL ; MODEL: C = BIEXP; CE = C*KEO.EXP(-KEO.T); E = SIGM_EMX(CE) ; NOTE: MAY BE MORE ETAS HERE THAN REASONABLE ; NOTE: MODEL FOR C CAN BE MORE COMPLEX BY ADDING CMPTS ; ; THE DATA FILE CONTAINS BOTH CP AND EFFECT OBSERVATIONS. ; WHEN DV IS A CP OBSERVATION, CMT = 1 (OR 0), ; WHEN DV IS AN EFFECT OBSERVATION, CMT =2. $DATA ..\PKPDLINK1ADDDOSE.CSV IGNORE=C $INPUT ID OCC TIME AMT DV DV1 MDV CMT EVID WT TPRO ALB DOSE HT SEX AST TBIL UREA CREA WBC DROP=RBC $SUBROUTINES ADVAN=5 $MODEL COMP=(CENTRAL,DEFDOSE,DEFOBS) COMP=PERIPH COMP=EFFECT $PK K10=THETA(1) TVK12=THETA(2) K12=TVK12*EXP(ETA(1)) K13= .001*K10 ; TRIVIAL LOSS TO EFFECT COMPT K21=THETA(3) TVS1=THETA(4) S1=TVS1 ; V1 FOR DRUG K30=THETA(5) ; KEO E0=THETA(6)*EXP(ETA(2)) EMAX=THETA(7) C50=THETA(8)*EXP(ETA(3)) HILL=THETA(9) TVBMAX=THETA(10)*EXP(ETA(4)) BMAX=TVBMAX KD=THETA(11) KNS=THETA(12) W=THETA(13) S3=S1*K13/K30 ; PRESERVES CESS = CPSS $ERROR FLAG=0 IF(AMT.GT.0) FLAG=1 ;DOSING RECORD ONLY CP1=1 IF(F.NE.0) CP1=F LNCP=LOG(CP1+FLAG) ;TRANFORM THE PREDICTION TO THE LOG OF PRED Y1=LNCP+W*ERR(1) CP=0 IF(LNCP.GT.-4) CP=EXP(LNCP) CB=HT*((CP*BMAX/(CP+KD))+KNS*CP)+CP*(1-HT) E=E0*(1-(EMAX*(CB**HILL))/((C50**HILL)+(CB**HILL))) Y2=E+E*(ERR(2))+ERR(3) Q=1 IF(CMT.EQ.2) Q=0 ; CMT = 3 = EFFECT OBS Y=Q*Y1+(1-Q)*Y2 F1=Q*LNCP+(1-Q)*E IPRE=F1 DEL=0 IF(IPRE.EQ.0) DEL=1 W=IPRE+DEL IRES=IPRE-DV IWRES=IRES/W $THETA (0.01,0.5,1) ;K10 1 $THETA (0.1,1,2) ;K12 2 $THETA (0.01,0.05,0.5) ;K21 3 $THETA (0.1,4,10) ;V1 OR S1 4 $THETA (0.1,0.5,) ;K30 5 $THETA (0.1,0.2,) ;E0 6 $THETA (0.01,0.1,) ;EMAX 7 $THETA (0.1,150,) ;EC50 8 $THETA (2,4,6) ;HILL 9 $THETA (200,250,350) ;BMAX 10 $THETA (0.1,0.6,12) ;KD 11 $THETA (0.01,0.1,2) ;KNS 12 $THETA (0.001,0.1,) ;PRO RES ERR 13 $OMEGA BLOCK(3) 0.001 ;k12 0.0001 0.001 ;e0 0.0001 0.0001 0.01 ;ec50 $OMEGA 0.2 ;BMAX 4 $SIGMA 0.17 ;[A] SIGMA(1,1) 0.002 ;[A] SIGMA(2,2) 0.0001 ;[A] SIGMA(3,3) $COV PRINT=E $ESTIMATION METHOD=1 INTER PRINT=10 MAXEVAL=9999 SIGDIG=6 NOABORT Fatemeh Akhlaghi, PharmD, PhD Associate Professor in Pharmacokinetics Biomedical and Pharmaceutical Sciences (BPS) University of Rhode Island 125 Fogarty Hall, 41 Lower College Road Kingston, RI 02881, USA Phone/Fax: (401) 874 9205/(401) 874 2181 Email: [EMAIL PROTECTED] Laboratory Website: http://www.uri.edu/pharmacy/faculty/aps/akhlaghi/index

Fatemeh, It is better to start with the sequential fit: first fit PK (you seems to indicate that you can get a good fit), then fix individual PK parameters and use the PK individual predictions to drive the PK-PD part. If and when you get the good PK-PD model, you can try to free the PK part to get simultaneous fit. From your description it looks like incorrect PD affects your PK fit. You need to correct PD model but it is difficult to do when your PK is biased. It will be easier when you have PK fixed to correct values: the bias will shift to PD part that can be explored graphically and using various PK-PD models. Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Fatemeh Akhlaghi, PhD wrote: > Dear NMusers group: > > I am puzzled by the result of a NONMEM analysis I am working on. I have > modeled plasma conc versus effect data using ADVAN5 (simultaneous link, > comp3fect) and can get a reasonable fit for the PD but the PK IPRED versus > observed plot has a very unusual S-shape. Fitting the same plasma conc > independently using ADVAN3 with the same error structure does not produce such > pattern. I log transform the plasma concentration data to obtain a better PK > fit. Also I have built a non-linear binding equation into the error structure > of the PKPD model. I have included the code below. Do you know what is > wrong? > > Many thanks in advance and I look forward to hear from you. > > > Fatemeh Akhlaghi > > > $PROBLEM > ;MODEL DESC:PKPDLINKWITH BINDING PARAMETERS > ;PROJECT NAME: EXAMPLE1 > ;PROJECT ID: PKPDLINK MODEL > ; MODEL: C = BIEXP; CE = C*KEO.EXP(-KEO.T); E = SIGM_EMX(CE) > ; NOTE: MAY BE MORE ETAS HERE THAN REASONABLE > ; NOTE: MODEL FOR C CAN BE MORE COMPLEX BY ADDING CMPTS > ; > ; THE DATA FILE CONTAINS BOTH CP AND EFFECT OBSERVATIONS. > ; WHEN DV IS A CP OBSERVATION, CMT = 1 (OR 0), > ; WHEN DV IS AN EFFECT OBSERVATION, CMT =2. > > $DATA ..\PKPDLINK1ADDDOSE.CSV IGNORE=C > $INPUT ID OCC TIME AMT DV DV1 MDV CMT EVID WT TPRO ALB DOSE HT SEX AST TBIL > UREA CREA WBC DROP=RBC > $SUBROUTINES ADVAN=5 > $MODEL > COMP=(CENTRAL,DEFDOSE,DEFOBS) > COMP=PERIPH > COMPFECT > $PK > K10=THETA(1) > TVK12=THETA(2) > K12=TVK12*EXP(ETA(1)) > K13= .001*K10 ; TRIVIAL LOSS TO EFFECT COMPT > K21=THETA(3) > TVS1=THETA(4) > S1=TVS1 ; V1 FOR DRUG > K30=THETA(5) ; KEO > E0=THETA(6)*EXP(ETA(2)) > EMAX=THETA(7) > C50=THETA(8)*EXP(ETA(3)) > HILL=THETA(9) > TVBMAX=THETA(10)*EXP(ETA(4)) > BMAX=TVBMAX > KD=THETA(11) > KNS=THETA(12) > W=THETA(13) > S3=S1*K13/K30 ; PRESERVES CESS = CPSS > > $ERROR > FLAG=0 > IF(AMT.GT.0) FLAG=1 ;DOSING RECORD ONLY > > CP1=1 > IF(F.NE.0) CP1=F > > LNCP=LOG(CP1+FLAG) ;TRANFORM THE PREDICTION TO THE LOG OF PRED > > Y1=LNCP+W*ERR(1) > > CP=0 > IF(LNCP.GT.-4) CP=EXP(LNCP) > > CB=HT*((CP*BMAX/(CP+KD))+KNS*CP)+CP*(1-HT) > E*(1-(EMAX*(CB**HILL))/((C50**HILL)+(CB**HILL))) > Y2=E+E*(ERR(2))+ERR(3) > > Q=1 > IF(CMT.EQ.2) Q=0 ; CMT = 3 = EFFECT OBS > Y=Q*Y1+(1-Q)*Y2 > F1=Q*LNCP+(1-Q)*E > > IPRE > > DEL=0 > IF(IPRE.EQ.0) DEL=1 > W=IPRE+DEL > IRES=IPRE-DV > IWRES=IRES/W > > $THETA (0.01,0.5,1) ;K10 1 > $THETA (0.1,1,2) ;K12 2 > $THETA (0.01,0.05,0.5) ;K21 3 > $THETA (0.1,4,10) ;V1 OR S1 4 > $THETA (0.1,0.5,) ;K30 5 > $THETA (0.1,0.2,) ;E0 6 > $THETA (0.01,0.1,) ;EMAX 7 > $THETA (0.1,150,) ;EC50 8 > $THETA (2,4,6) ;HILL 9 > $THETA (200,250,350) ;BMAX 10 > $THETA (0.1,0.6,12) ;KD 11 > $THETA (0.01,0.1,2) ;KNS 12 > $THETA (0.001,0.1,) ;PRO RES ERR 13 > > $OMEGA BLOCK(3) > 0.001 ;k12 > 0.0001 0.001 ;e0 > 0.0001 0.0001 0.01 ;ec50 > > $OMEGA > 0.2 ;BMAX 4 > > $SIGMA > 0.17 ;[A] SIGMA(1,1) > 0.002 ;[A] SIGMA(2,2) > 0.0001 ;[A] SIGMA(3,3) > > $COV PRINT=E > > $ESTIMATION METHOD=1 INTER PRINT MAXEVAL99 SIGDIG=6 NOABORT > > Fatemeh Akhlaghi, PharmD, PhD > Associate Professor in Pharmacokinetics > Biomedical and Pharmaceutical Sciences (BPS) > University of Rhode Island > 125 Fogarty Hall, 41 Lower College Road > Kingston, RI 02881, USA > > Phone/Fax: (401) 874 9205/(401) 874 2181 > Email: fatemeh > Laboratory Website: http://www.uri.edu/pharmacy/faculty/aps/akhlaghi/index > >

Dear Fatemeh, I second Leonid's suggestion. If your PD model has some degree of misspecification, this may reflect negatively on the PK fit. Sequential fit with FOCE should be as good. The following paper helps making a decision for sequential vs. (the gold standard) simultaneous fitting. Once you can get a decent fit for both PK and PD using the sequential model, you can try the simultaneous fit. Zhang L, Beal SL, Sheiner LB. Simultaneous vs. sequential analysis for population PK/PD data I: best-case performance.J Pharmacokinet Pharmacodyn. 2003 Dec;30(6):387-404. I hope this helps. *Murad Melhem, PhD * *Assistant Director PK/PD* *Cognigen Corporation* On Fri, Jul 25, 2008 at 7:04 PM, Fatemeh Akhlaghi, PhD < fak4939u > Dear NMusers group: > > I am puzzled by the result of a NONMEM analysis I am working on. I have > modeled plasma conc versus effect data using ADVAN5 (simultaneous link, > comp3fect) and can get a reasonable fit for the PD but the PK IPRED > versus > observed plot has a very unusual S-shape. Fitting the same plasma conc > independently using ADVAN3 with the same error structure does not produce > such > pattern. I log transform the plasma concentration data to obtain a better > PK > fit. Also I have built a non-linear binding equation into the error > structure > of the PKPD model. I have included the code below. Do you know what is > wrong? > > Many thanks in advance and I look forward to hear from you. > > > Fatemeh Akhlaghi > > > $PROBLEM > ;MODEL DESC:PKPDLINKWITH BINDING PARAMETERS > ;PROJECT NAME: EXAMPLE1 > ;PROJECT ID: PKPDLINK MODEL > ; MODEL: C = BIEXP; CE = C*KEO.EXP(-KEO.T); E = SIGM_EMX(CE) > ; NOTE: MAY BE MORE ETAS HERE THAN REASONABLE > ; NOTE: MODEL FOR C CAN BE MORE COMPLEX BY ADDING CMPTS > ; > ; THE DATA FILE CONTAINS BOTH CP AND EFFECT OBSERVATIONS. > ; WHEN DV IS A CP OBSERVATION, CMT = 1 (OR 0), > ; WHEN DV IS AN EFFECT OBSERVATION, CMT =2. > > $DATA ..\PKPDLINK1ADDDOSE.CSV IGNORE=C > $INPUT ID OCC TIME AMT DV DV1 MDV CMT EVID WT TPRO ALB DOSE HT SEX AST TBIL > UREA CREA WBC DROP=RBC > $SUBROUTINES ADVAN=5 > $MODEL > COMP=(CENTRAL,DEFDOSE,DEFOBS) > COMP=PERIPH > COMPFECT > $PK > K10=THETA(1) > TVK12=THETA(2) > K12=TVK12*EXP(ETA(1)) > K13= .001*K10 ; TRIVIAL LOSS TO EFFECT > COMPT > K21=THETA(3) > TVS1=THETA(4) > S1=TVS1 ; V1 FOR DRUG > K30=THETA(5) ; KEO > E0=THETA(6)*EXP(ETA(2)) > EMAX=THETA(7) > C50=THETA(8)*EXP(ETA(3)) > HILL=THETA(9) > TVBMAX=THETA(10)*EXP(ETA(4)) > BMAX=TVBMAX > KD=THETA(11) > KNS=THETA(12) > W=THETA(13) > S3=S1*K13/K30 ; PRESERVES CESS = CPSS > > $ERROR > FLAG=0 > IF(AMT.GT.0) FLAG=1 ;DOSING RECORD ONLY > > CP1=1 > IF(F.NE.0) CP1=F > > LNCP=LOG(CP1+FLAG) ;TRANFORM THE PREDICTION TO THE LOG OF PRED > > Y1=LNCP+W*ERR(1) > > CP=0 > IF(LNCP.GT.-4) CP=EXP(LNCP) > > CB=HT*((CP*BMAX/(CP+KD))+KNS*CP)+CP*(1-HT) > E*(1-(EMAX*(CB**HILL))/((C50**HILL)+(CB**HILL))) > Y2=E+E*(ERR(2))+ERR(3) > > Q=1 > IF(CMT.EQ.2) Q=0 ; CMT = 3 = EFFECT OBS > Y=Q*Y1+(1-Q)*Y2 > F1=Q*LNCP+(1-Q)*E > > IPRE > > DEL=0 > IF(IPRE.EQ.0) DEL=1 > W=IPRE+DEL > IRES=IPRE-DV > IWRES=IRES/W > > $THETA (0.01,0.5,1) ;K10 1 > $THETA (0.1,1,2) ;K12 2 > $THETA (0.01,0.05,0.5) ;K21 3 > $THETA (0.1,4,10) ;V1 OR S1 4 > $THETA (0.1,0.5,) ;K30 5 > $THETA (0.1,0.2,) ;E0 6 > $THETA (0.01,0.1,) ;EMAX 7 > $THETA (0.1,150,) ;EC50 8 > $THETA (2,4,6) ;HILL 9 > $THETA (200,250,350) ;BMAX 10 > $THETA (0.1,0.6,12) ;KD 11 > $THETA (0.01,0.1,2) ;KNS 12 > $THETA (0.001,0.1,) ;PRO RES ERR 13 > > $OMEGA BLOCK(3) > 0.001 ;k12 > 0.0001 0.001 ;e0 > 0.0001 0.0001 0.01 ;ec50 > > $OMEGA > 0.2 ;BMAX 4 > > $SIGMA > 0.17 ;[A] SIGMA(1,1) > 0.002 ;[A] SIGMA(2,2) > 0.0001 ;[A] SIGMA(3,3) > > $COV PRINT=E > > $ESTIMATION METHOD=1 INTER PRINT MAXEVAL99 SIGDIG=6 NOABORT > > Fatemeh Akhlaghi, PharmD, PhD > Associate Professor in Pharmacokinetics > Biomedical and Pharmaceutical Sciences (BPS) > University of Rhode Island > 125 Fogarty Hall, 41 Lower College Road > Kingston, RI 02881, USA > > Phone/Fax: (401) 874 9205/(401) 874 2181 > Email: fatemeh > Laboratory Website: http://www.uri.edu/pharmacy/faculty/aps/akhlaghi/index > >

Fatemeh, It is better to start with the sequential fit: first fit PK (you seems to indicate that you can get a good fit), then fix individual PK parameters and use the PK individual predictions to drive the PK-PD part. If and when you get the good PK-PD model, you can try to free the PK part to get simultaneous fit. From your description it looks like incorrect PD affects your PK fit. You need to correct PD model but it is difficult to do when your PK is biased. It will be easier when you have PK fixed to correct values: the bias will shift to PD part that can be explored graphically and using various PK-PD models. Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Fatemeh Akhlaghi, PhD wrote: > Dear NMusers group: > > I am puzzled by the result of a NONMEM analysis I am working on. I have modeled plasma conc versus effect data using ADVAN5 (simultaneous link, comp3=effect) and can get a reasonable fit for the PD but the PK IPRED versus observed plot has a very unusual S-shape. Fitting the same plasma conc independently using ADVAN3 with the same error structure does not produce such pattern. I log transform the plasma concentration data to obtain a better PK fit. Also I have built a non-linear binding equation into the error structure of the PKPD model. I have included the code below. Do you know what is wrong? > > Many thanks in advance and I look forward to hear from you. > > Fatemeh Akhlaghi > > $PROBLEM > ;MODEL DESC:PKPDLINKWITH BINDING PARAMETERS > ;PROJECT NAME: EXAMPLE1 > ;PROJECT ID: PKPDLINK MODEL > ; MODEL: C = BIEXP; CE = C*KEO.EXP(-KEO.T); E = SIGM_EMX(CE) > ; NOTE: MAY BE MORE ETAS HERE THAN REASONABLE > ; NOTE: MODEL FOR C CAN BE MORE COMPLEX BY ADDING CMPTS > ; > ; THE DATA FILE CONTAINS BOTH CP AND EFFECT OBSERVATIONS. > ; WHEN DV IS A CP OBSERVATION, CMT = 1 (OR 0), > ; WHEN DV IS AN EFFECT OBSERVATION, CMT =2. > > $DATA ..\PKPDLINK1ADDDOSE.CSV IGNORE=C > > $INPUT ID OCC TIME AMT DV DV1 MDV CMT EVID WT TPRO ALB DOSE HT SEX AST TBIL UREA CREA WBC DROP=RBC > > $SUBROUTINES ADVAN=5 > $MODEL > COMP=(CENTRAL,DEFDOSE,DEFOBS) > COMP=PERIPH > COMP=EFFECT > $PK > K10=THETA(1) > TVK12=THETA(2) > K12=TVK12*EXP(ETA(1)) > K13= .001*K10 ; TRIVIAL LOSS TO EFFECT COMPT > K21=THETA(3) > TVS1=THETA(4) > S1=TVS1 ; V1 FOR DRUG > K30=THETA(5) ; KEO > E0=THETA(6)*EXP(ETA(2)) > EMAX=THETA(7) > C50=THETA(8)*EXP(ETA(3)) > HILL=THETA(9) > TVBMAX=THETA(10)*EXP(ETA(4)) > BMAX=TVBMAX > KD=THETA(11) > KNS=THETA(12) > W=THETA(13) > S3=S1*K13/K30 ; PRESERVES CESS = CPSS > > $ERROR > FLAG=0 > IF(AMT.GT.0) FLAG=1 ;DOSING RECORD ONLY > > CP1=1 > IF(F.NE.0) CP1=F > > LNCP=LOG(CP1+FLAG) ;TRANFORM THE PREDICTION TO THE LOG OF PRED > > Y1=LNCP+W*ERR(1) > > CP=0 > IF(LNCP.GT.-4) CP=EXP(LNCP) > > CB=HT*((CP*BMAX/(CP+KD))+KNS*CP)+CP*(1-HT) > E=E0*(1-(EMAX*(CB**HILL))/((C50**HILL)+(CB**HILL))) > Y2=E+E*(ERR(2))+ERR(3) > > Q=1 > IF(CMT.EQ.2) Q=0 ; CMT = 3 = EFFECT OBS > Y=Q*Y1+(1-Q)*Y2 > F1=Q*LNCP+(1-Q)*E > > IPRE=F1 > > DEL=0 > IF(IPRE.EQ.0) DEL=1 > W=IPRE+DEL > IRES=IPRE-DV > IWRES=IRES/W > > $THETA (0.01,0.5,1) ;K10 1 > $THETA (0.1,1,2) ;K12 2 > $THETA (0.01,0.05,0.5) ;K21 3 > $THETA (0.1,4,10) ;V1 OR S1 4 > $THETA (0.1,0.5,) ;K30 5 > $THETA (0.1,0.2,) ;E0 6 > $THETA (0.01,0.1,) ;EMAX 7 > $THETA (0.1,150,) ;EC50 8 > $THETA (2,4,6) ;HILL 9 > > $THETA (200,250,350) ;BMAX 10 $THETA (0.1,0.6,12) ;KD 11 > > $THETA (0.01,0.1,2) ;KNS 12 > $THETA (0.001,0.1,) ;PRO RES ERR 13 > > $OMEGA BLOCK(3) > 0.001 ;k12 > 0.0001 0.001 ;e0 > 0.0001 0.0001 0.01 ;ec50 > > $OMEGA > 0.2 ;BMAX 4 > > $SIGMA > 0.17 ;[A] SIGMA(1,1) > 0.002 ;[A] SIGMA(2,2) > 0.0001 ;[A] SIGMA(3,3) > > $COV PRINT=E > > $ESTIMATION METHOD=1 INTER PRINT=10 MAXEVAL=9999 SIGDIG=6 NOABORT > > Fatemeh Akhlaghi, PharmD, PhD > Associate Professor in Pharmacokinetics > Biomedical and Pharmaceutical Sciences (BPS) > University of Rhode Island > 125 Fogarty Hall, 41 Lower College Road > Kingston, RI 02881, USA > > Phone/Fax: (401) 874 9205/(401) 874 2181 > Email: [EMAIL PROTECTED] > Laboratory Website: http://www.uri.edu/pharmacy/faculty/aps/akhlaghi/index

Dear Fatemeh, I second Leonid's suggestion. If your PD model has some degree of misspecification, this may reflect negatively on the PK fit. Sequential fit with FOCE should be as good. The following paper helps making a decision for sequential vs. (the gold standard) simultaneous fitting. Once you can get a decent fit for both PK and PD using the sequential model, you can try the simultaneous fit. Zhang L, Beal SL, Sheiner LB. Simultaneous vs. sequential analysis for population PK/PD data I: best-case performance.J Pharmacokinet Pharmacodyn. 2003 Dec;30(6):387-404. I hope this helps. *Murad Melhem, PhD * *Assistant Director PK/PD* *Cognigen Corporation*