# RE: PD modelling problem - Emax at lower bound?

From: Joseph Standing <joseph.standing>
Date: Fri, 2 Oct 2009 17:03:12 +0200

Ann,
Are you sure you have observed Emax in your data? The physician attending a
recently deceased American singer probably has a better insight than myself,
but it seems clear that high enough doses of propofol are fatal (and which
point presumably BIS score is 0?). Why don't you try having Emax as a
fractional decrease (constrained between 0 and 1) in E0. If Emax goes
towards 1 (i.e. a BIS of 0) then you could remove it from the model, and
just have the maximum drop in BIS to be E0. If you do estimate an Emax in
this way, I suggest a LOGIT transformation of the IIV.
Good luck,
Joe

-----Original Message-----
From: owner-nmusers
Behalf Of Ann Rigby-Jones
Sent: den 2 oktober 2009 15:20
To: 'nmusers
Cc: 'Bachman, William'
Subject: [NMusers] PD modelling problem - Emax at lower bound?

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=#
\$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

\$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