Dear Ann, I would recommend you to investigate the possibility to model the BIS and propofol data using a two-effect site model instead of just a single effect site model. We presented a two-effect site model for BIS and propofol at PAGE this year (Reference: PAGE 18 (2009) Abstr 1590 [www.page-meeting.org/?abstract=1590]). This approach gave substantially better predictions than just using a single effect site model.
Best regards, Ulrika Simonsson Assoc Prof The Pharmacometrics Research Group Uppsala University, Sweden -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Leonid Gibiansky Sent: den 2 oktober 2009 16:11 To: Ann Rigby-Jones Cc: '[email protected]' Subject: Re: [NMusers] PD modelling problem - Emax at lower bound? Ann, When you do sequential PK-PD, do not touch PK portion, it should be fixed. Thus, this is the PK: DADT(1)=A(2)*K21+A(3)*K31-A(1)*(K10+K12+K13) DADT(2)=A(1)*K12-A(2)*K21 DADT(3)=A(1)*K13-A(3)*K31 This is propofol concentration: C=A(1)/V1 This is effect compartment: DADT(4)=KE0*(C-A(4)) This is EFF model: CONG=0 IF(C.GT.0) CONG=C**GAM EFF=E0+(EMAX-E0)*CONG/(C50**GAM+CONG); SIGMOID EMAX MODEL Now, the main problem, Y should be 100 minus effect, not the effect, that is why your EMAX tries to be negative. BIS vary from 0 to 100 with 100 being the baseline. Y=100-EFF + ERR(1) Initial conditions should be something like (0,50,100) ;EMAX (0, 2, 100) ;E0 Let me know of you have problem with this code, it should work. Leonid -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Ann Rigby-Jones wrote: > Dear NONMEM Users > > I’m struggling with a pharmacodynamic model for the intravenous anaesthetic, > propofol and I would really appreciate some opinions on what might be going > wrong. I have taken a sequential approach to the PK-PD modelling. PK are > described using a 3 compartment mamillary model. Bispectral Index (BIS), an > EEG derivative, was used as an effect measure. Drug was administered > intravenously (2mg/kg propofol over 1 minute) to healthy volunteers (n=6). > BIS was recorded every 15 seconds prior to drug administration and for about > an hour afterwards. BIS has a value of around 100 in an awake individual, > while a value of 40-60 indicates anaesthesia. > > The data are pretty clean so I don’t understand why I’m having such > difficulty. I’ve modelled much noisier data generated with a second > sedative-hypnotic drug from this same group of patients (cross-over study) > with fewer problems. However, for this data set I have yet to produce a > single run that minimises successfully without it having a final estimate at > the lower boundary for Emax (doesn’t seem to matter how low I set the > boundary). The observed Emax is pretty low so an estimate of 20-30 wouldn’t > be too unrealistic but if I set a lower bound of -10 (NB this was just to > prove the problem, I wouldn’t ordinarily set a negative bound), NONMEM is > happy to minimise with an Emax value of -9.9. I’m using NONMEM 6 v2, FOCE, > additive error. I’ve tried additive, constant CV and log error models (with > transformed data), same problem with all. > > When I model data from each subject individually, all but one (5/6) also > minimises at the lower bound for Emax so I don’t think data from anyone one > individual is causing the problem. I’ve checked for gross errors (dosing, PK > parameters). I’ve tried running with FO and the result of that is that > estimates for Emax sit on the upper boundary, rather than the lower one and > the models are strongly over-predicting. > > Really hoping that I’ve not overlooked something very obvious here :-S I’ve > attached an example control stream but not the data due to limitation on the > size this e-mail could be (very happy to e-mail the data directly to anyone > who is interested in taking a look at it). > > With all best wishes and very many thanks! :-) > > Ann > _______________________________________________________________________ > Ann Rigby-Jones PhD MRSC > Research Fellow in Pharmacokinetics & Pharmacodynamics > > Peninsula College of Medicine & Dentistry > Plymouth, UK > _______________________________________________________________________ > > $PROB propofol PD > $INPUT ID PER TIME DV AMT RATE EVID V1 K10 K12 K21 K13 K31 > $DATA BIS_Step_3_Propofol_smth.CSV IGNORE=# > $SUBROUTINES ADVAN6 TOL=3 > $MODEL > COMP(CENTRAL, DEFDOSE, DEFOBS) > COMP(PERIPH1) > COMP(PERIPH2) > COMP(EFFECT) > > $PK > > EMAX=THETA(1)*EXP(ETA(1)) ; maximum response > E0=THETA(2)*EXP(ETA(2)) ; baseline > C50=THETA(3)*EXP(ETA(3)) ; concentration associated with 50% peak effect > GAM=THETA(4)*EXP(ETA(4)) ; gamma > K41=THETA(5)*EXP(ETA(5)) ;ke0 > > > V4=0.00001 > K14=V4*K41/V1 > > $DES > DADT(1)=A(2)*K21+A(3)*K31+K41*A(4)-A(1)*(K10+K12+K13+K14) > DADT(2)=A(1)*K12-A(2)*K21 > DADT(3)=A(1)*K13-A(3)*K31 > DADT(4)=A(1)*K14-A(4)*K41 > > $ERROR > CON=A(4)/V4 > IF (CON.EQ.0) CON=0.0000001 > > TY=E0+(EMAX-E0)*(CON**GAM)/(C50**GAM+CON**GAM); SIGMOID EMAX MODEL > > Y=TY + ERR(1) > W=TY > IPRED=TY > ;IF(IPRED.LT.0.1) IPRED=0.1 > IRES=DV-IPRED > IWRES=IRES/W > > > $THETA > (15,45,60) ;EMAX > (90, 98, 100 ) ;E0 > (1000,2500, 8000) ;C50 > (1,4, 10) ;GAMMA > (0.0001,0.2, 3) ;K41(KE0) > > $SIGMA (15) > > $OMEGA (0 FIX) ;EMAX > $OMEGA (0 FIX) ;E0 > $OMEGA (0.01) ;C50 > $OMEGA (0 FIX) ;Gamma > $OMEGA (0.01) ;KeO > > $ESTIMATION METHOD=1 NOABORT MAXEVAL=9999 PRINT=5 SIGDIG=3 > ;POSTHOC;INTERACTION > $COV PRINT=E > $TABLE ID TIME DV RES WRES IWRES IRES PRED IPRED EVID > ONEHEADER NOPRINT FILE=sdtab100 > $TABLE ID C50 K41 EMAX E0 GAM > ONEHEADER NOPRINT FILE=patab100 >
