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Re: PD modelling problem - Emax at lower bound?

From: Leonid Gibiansky <LGibiansky>
Date: Fri, 02 Oct 2009 10:10:44 -0400

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
>
Received on Fri Oct 02 2009 - 10:10:44 EDT

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