From: Ulrika Simonsson <*ulrika.simonsson*>

Date: Wed, 21 Oct 2009 12:56:53 +0200

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: owner-nmusers

On Behalf Of Leonid Gibiansky

Sent: den 2 oktober 2009 16:11

To: Ann Rigby-Jones

Cc: 'nmusers

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
*

*>
*

Received on Wed Oct 21 2009 - 06:56:53 EDT

Date: Wed, 21 Oct 2009 12:56:53 +0200

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: owner-nmusers

On Behalf Of Leonid Gibiansky

Sent: den 2 oktober 2009 16:11

To: Ann Rigby-Jones

Cc: 'nmusers

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:

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.

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.

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.

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).

_______________________________________________________________________

_______________________________________________________________________

effect

;POSTHOC;INTERACTION

Received on Wed Oct 21 2009 - 06:56:53 EDT