Theophylline PML example

This example performs population PK modeling based on a one-compartment, first-order input PK model.

Data

The subject data are contained in an ASCII file (*.dat). The headers and the first subject data read as follows:

thbates.dat
## xid wt dose time yobs
     1 79.6 4.02     0 0.74
     1 79.6 4.02 0.25 2.84
     1 79.6 4.02 0.57 6.57
     1 79.6 4.02 1.12 10.5
     1 79.6 4.02 2.02 9.66
     1 79.6 4.02 3.82 8.58
     1 79.6 4.02 5.1 8.36
     1 79.6 4.02 7.03 7.47
     1 79.6 4.02 9.05 6.89
     1 79.6 4.02 12.12 5.94
     1 79.6 4.02 24.37 3.28

Column mappings

The ASCII file containing column mappings reads as follows.

colstheo.txt
id(xid)
covr(dose <- dose)
covr(time <- time)
obs(cObs <- yobs)

The model

The Phoenix model file reads as follows.

fm3theophx.mdl
  #One compartment model with first order absorption with a
#single dose at time=0
  #The use of an explicit prediction formula in the model text
  #requires that dose and time are entered as covariates, that
  #is, there is no defined compartment name in which to dose,
  #and there is no implicit continuous time structure as in an
#ODE model.
theo(){
    covariate(dose,time)
    fixef(
       tvlKe=c(, -2.5,)
       tvlKa=c(, 0.1,)
       tvlCl=c(, -3.0,)
       )
    ranef(
       diag(nlKa, nlCl)=c(1.0, 1.0,)
       )
    stparm(
       Ke=exp(tvlKe)
       Ka=exp(tvlKa+nlKa)
       Cl=exp(tvlCl+nlCl)
       )
    V=Cl/Ke
    cpred=dose*Ka/(V*(Ka-Ke))*(exp(-Ke*time)-exp(
    -Ka*time))
    error(eps1=0.5)
    observe(cObs=cpred+eps1)
    }

NONMEM control file

The equivalent model, written as a NONMEM control file (*.ctl), would read as follows.

$PROB THEOPHYLLINE POPULATION DATA
  $INPUT ID WT DOSE TIME CP=DV
  $DATA ThBates.dat
$PRED
     KE=EXP(THETA(1))
    KA=EXP(THETA(2)+ETA(1))
     CL=EXP(THETA(3)+ETA(2))
F=DOSE*KA*KE/(CL*(KA-KE))*(EXP(-KE*TIME)-EXP(-KA*TIME))
Y=F+EPS(1)
$THETA -2.5 0.1 -3.0
$OMEGA 1 1
$SIGMA .5
$EST METHOD=1 MAXEVAL=450 PRINT=5
$COV