Re: Indirect response model
Dear Nishit,
Jurgen is correct, you are using concentration (COP) as a forcing function.
But, in ID 1101, for example, the COP has a value of 0 from TIME=0 to 840 and
then values around 0.12 until TIME 1848. Unless this is what you had in mind,
I would suggest two steps: 1. Include more time points for COP. These need
not coincide with TIMEs were you have DV values. 2. Create a linear
interpolation of COP to be used in the $DES block.
One way to do this linear interpolation is to add two columns to your data
file: PTME (previous time) and PCOP (previous concentration). Then, compute
SLOPE = (COP-PCOP)/(TIME-PTME) and use a linear interpolation of conc: PCOP +SLOPE*(T-PTME) in place of COP in computing your COEF parameter (must be in $DES block).
I hope this helps,
David Salinger
RFPK, Univ. of Washington
Quoted reply history
On Tue, 15 May 2007, Jurgen Bulitta wrote:
> Dear Nishit,
>
> If I understand correctly, you are using concentration (COP) of
> your drug as a time dependent covariate which is then used as
> forcing function for your PD model.
>
> As concentrations change over time, you probably need the
> CALLFL = 0 option ($PK CALLFL=0) to read in the concentration
> at every new time. I would write out COP in $TABLE in order to
> check, if COP changes over time as it should.
>
> This should work much better, but it will still give you a piecewise
> constant concentration profile. This may cause numerical problems.
> Instead, I would include the differential equations for your PK
> model. This should give you better numerical stability and more
> correct concentration predictions. You could start with reading in
> the individual PK parameters (IPP approach, see reference below)
> and then go to more complex PKPD analyses.
>
> You might try the MATRIX=S statement in $COV, if you like to get
> the covariance step to work.
>
> Hope some of this works.
>
> Best regards
> Juergen
>
> Reference:
> Zhang, L., S. L. Beal, and L. B. Sheiner. 2003. Simultaneous vs.
> sequential analysis for population PK/PD data I: best-case performance.
> J Pharmacokinet Pharmacodyn 30:387-404.
>
> -----------------------------------------------
> Juergen Bulitta, PhD, Post-doctoral Fellow
> Pharmacometrics, University at Buffalo, NY, USA
> Phone: +1 716 645 2855 ext. 281, [EMAIL PROTECTED]
> -----------------------------------------------
>
> -----Ursprüngliche Nachricht-----
> Von: "Modi, Nishit [ALZUS]" <[EMAIL PROTECTED]>
> Gesendet: 15.05.07 18:31:57
> An: [EMAIL PROTECTED]
> CC: [email protected]
> Betreff: [NMusers] Indirect response model
>
> 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
>
> $PROBLEM PD - ADVAN6
>
> $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
>
> $SUBROUTINES ADVAN6 TOL=6
>
> $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
>
> DADT(1) = KFOR-KCL*(1-COEF)*A(1)
>
> $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
>
> NOPRINT ONEHEADER
>
> 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