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PD modelling problem - Emax at lower bound?

From: Ann Rigby-Jones <ann.rigby-jones>
Date: Fri, 2 Oct 2009 14:20:05 +0100

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 - 09:20:05 EDT

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