Theophylline_PML

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 PML 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