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