# Indirect response model

From: Modi, Nishit [ALZUS] <NMODI>
Date: Tue, 15 May 2007 12:21:19 -0400

I am conducting a sequential pharmacokinetic-pharmacodynamic model. The
pharmacokinetic fits look good and I was using an indirect response model.
The PD model is that the drug inhibits clearance of the analyte (PD
response), thus one expects that the response increases with increasing drug
(Model II). There is a baseline measured (=Kfor/Kcl) and a dummy dose=1
unit given. It seems despite trying various permutations of the model, eta1
seems to be very small and no covariance step is conducted. The model and
data for the first 3 subjects are reproducted below. Any assistance would
be appreciated. Note that since conc (COP) are read in, the model only
requires a single differential equation. Any insight would be appreciated.

Nishit

\$DATA C:\PDDATA.CSV
\$INPUT ID TIME DV AMT=DOSE COP MDV
; data are subject ID, Time, DV=PD response, Amt (dummy dose of 1 inserted),
COP=plasma conc which drive PD model, MDV
\$MODEL
COMP=(EFFECT, DEFDOSE, DEFOBS)

\$PK
KFOR = THETA(1)
KCL = THETA(2)*EXP(ETA(1))
IC50 = THETA(3)
IMAX = THETA(4)
F1 = KFOR/KCL
COEF = IMAX*COP/(IC50+COP)

\$DES
\$ERROR
W = F
Y = F*EXP(ERR(1))
IPRED = F
IRES = DV-IPRED
IF (W.LE.0.) W=1
IWRES = IRES/W

\$THETA (0,0.3)
\$THETA (0, 0.003)
\$THETA (0,10)
\$THETA (0, 0.3, 1)

\$OMEGA 0.01
\$SIGMA 0.5

\$ESTIMATION METHOD=1 MAXEVAL=5000 PRINT=20
\$COVR
\$TABLE ID TIME PRED IPRED IRES KFOR KCL IC50 IMAX
FILE=C:\PD.TAB

1001 0 . 1 0 1
1001 0 98.3 . 0 0
1001 168 90.6 . 122.44 0
1001 840 92.8 . 183.69 0
1002 0 . 1 0 1
1002 0 105.1 . 0 0
1002 840 88.5 . 61.253 0
1002 842 106.7 . 106.8 0
1002 844 122.1 . 116.4 0
1002 1848 129.1 . 121.46 0
1002 1850 160.4 . 212.63 0
1002 1852 157.1 . 231.89 0
1101 0 . 1 0 1
1101 0 68.1 . 0 0
1101 840 88.1 . 0.13884 0
1101 842 105.5 . 0.12987 0
1101 844 108.8 . 0.12147 0
1101 1848 113.3 . 227.79 0
1101 1850 62.6 . 379.54 0
1101 1852 138.7 . 412.18 0

Received on Tue May 15 2007 - 12:21:19 EDT

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