From: Jocelyn Leu - josniko@hotmail.com
Subject: [NMusers] Question re: indirect model
Date: 1/5/2004 10:38 AM

I am forwarding this message for Dr. Xu who is joining
the NM user group in case his email did not post yet.

Dear NM Users:

I encountered difficulty in coding a control file for
simultaneous PK/PD modeling using differential equations
(ADVAN6, one-compartment PK model with oral dosing, and
indirectPD modeling (inhibition of Kin) for endogenous
substance: In this case, both drug concentration and drug
response occur  in the central compartment-- for which I
guess that I have to treat them as two different types of
observations). You will be profoundly appreciated if you send
me a sample control stream file of NONMEM for a similar situation
(if something particular for the data file, please also indicate so).

I also enclose the data file and the model control stream for
you to revise it (though it may not be helpful at all). The dose
unit is mg, and the PK concentration is in ng/ml. When Type=0, DV
is drug concentration; while DV is PD marker when type is 1.

Again, thank you so much.

Michael Xu


Control Stream
;Model Desc: one-com PK/indirect PD DIFF
;Project Name: XUPPD700
;Project ID: PPD700 VERSUS EFFECT

$PROB RUN# 101 ADVAN6
$INPUT C ID AMT TIME DV TYPE CMT
$DATA 101.csv IGNORE=C
$SUBROUTINE ADVAN6 TRANS=1 TOL=3
$MODEL NCOMP=2
 COMP=(GUT)
 COMP=(CENTRAL)

$PK
KA=THETA(1)*EXP(ETA(1))
KE=THETA(2)*EXP(ETA(2))
V2=THETA(3)*EXP(ETA(3))
IF (TYPE.EQ.0) THEN
  S2=V2/1000
ELSE
  S2=1
ENDIF

KIN=THETA(4)*EXP(ETA(4))
KOUT=THETA(5)*EXP(ETA(5))
IC50=THETA(6)*EXP(ETA(6))

$DES
;PK MODEL
DADT(1)=-KA*A(1)
IF (TYPE.EQ.0) THEN
  DADT(2)=KA*A(1)-KE*A(2)
  CP=A(2)/S2

;PD MODEL
EFF=CP/(CP + IC50)
ELSE
  DADT(2)=KIN* (1-EFF)- KOUT*A(2)
ENDIF

$ERROR
;TYPE=0 FOR CP, TYPE=1 FOR E
Y=F*EXP(ERR(1))
IPRED=F

$THETA
(0,10)      ;KA
(0,0.5)     ;KE
(0,1000)    ;V2
(0,100)   ;KIN
(0,1)     ;KOUT
(0,100)   ;EC50

$OMEGA
0.01 ;[P]
0.01 ;[P]
0.01 ;[P]
0.01 ;[P]
0.04 ;[P]
0.04 ;[P]
$SIGMA
0.01 ;[P]
$ESTIMATION MAXEVAL=9999 PRINT=5 MSF=101.msf POSTHOC
$COV
$TABLE ID TIME DV PRED IPRED TYPE CMT FILE=101.tab NOPRINT 
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From: vgcasabo - vicente.casabo@uv.es
Subject: RE: [NMusers] Question re: indirect model
Date: 1/7/2004 1:20 PM

Dear Jocelyn and Michael

Your code and data file has the following problems:

You need three compartments to model your data
Gut, Pkcentral, Pdcentral

Code in CMT variable in your data file: 1(gut), 2(drug concentrations), 3
(biomarker concs.)

You do not need any of the IF,THEN,ELSE structures in your $DES model. You
have to write DADT(3) differential equation for the biomarker concentration.
You need to initialize the third compartment in the data file with AMT=1 at
time =0  CMT=3 in additional data records.
Then you need another parameter in $PK as F3=THETA(.) and its corresponding
ETA(.), KIN and KOUT are then interdependent

You need two residuals error models.

See the relevant part of model below, I haven't checked it..there might be
additional errors. 
Other parametrization are possible, 
Hope this helps you. 

Vicente

------------------------------------------------------------------
...
$MODEL NCOMP=3
  COMP=(GUT)
  COMP=(CENTRAL)
  COMP= (PDCEN)

$PK
KA=THETA(1)*EXP(ETA(1))
KE=THETA(2)*EXP(ETA(2))
V2=THETA(3)*EXP(ETA(3))
S2=V2/1000
S3=1 ;or the adequate scale factor
F3=THETA(.)*EXP(ETA(.)); To adequate amt to concentration at time cero
KIN=KOUT*F3
KOUT=THETA(.)*EXP(ETA(.)) 
IC50=THETA(6)*EXP(ETA(6))

$DES
;PK MODEL
DADT(1)=-KA*A(1)
DADT(2)=KA*A(1)-KE*A(2)
CP=A(2)/S2
;PD MODEL
EFF=CP/(CP + IC50); EMAX can be necessary, no total inhibition is possible
DADT(3)=KIN* (1-EFF)- KIN*A(3)

$ERROR
; two residual error models are used
IF(CMT.EQ.2) W=EXP(EPS(1))
W=EXP(EPS(2))
Y=F*W
IPRED=F
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