User-defined_logistic_model_PML

User-defined logistic model PML example

This example illustrates a repeated measures logistic response. It is adapted from a logistic example in the NONMEM archives. The data consist of the number of successes in 1000 simulated trials at a given dose.

Data

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

logistic1000a.dat 
  ## id   dose     frac   ntrial
      1 0.200000 0.269010  1000
      1 0.600000 0.499010  1000
      1 1.000000 0.625010  1000
      1 1.400000 0.690010  1000
      1 1.800000 0.735010  1000

Column mappings

The ASCII file containing column mappings reads as follows.

   colslogistic.txt 
   id(id)
   covr(dose <- dose)
   covr(ntrial <- ntrial)
   obs(cObs <- frac)

The model

The PML model file reads as follows.

logistic.mdl 
  logist2(){
     covariate(dose,ntrial)
     fixef(
          gamma=c(0, 1,)
          tvd50=c(0, 1,)
          )
     ranef(
        diag(neta1)=c(0.1) 
        )
     stparm(
        d50=tvd50*exp(neta1)
        )
     a=gamma*log(dose/d50)
     prob=exp(a)/(1+exp(a))
  #note cObs is the fraction of successes observed in ntrial
  #trials - corresponding count is ntrial*cObs
     LL(cObs, ntrial*cObs*log(prob)+ntrial*(1-cObs)*
     log(1-prob))
     }

NONMEM control file

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

  $PROB Repeated measures logistic response
  $DATA logistic1000a.dat
  $INPUT ID DOSE DV NT 
  $PRED
     GAMMA=THETA(1)
     D50=THETA(2)*EXP(ETA(1))
     LDOS= LOG(DOSE)
     A=GAMMA*LDOS-GAMMA*LOG(D50)
     B=EXP(A)
     P=B/(1+B)
     Y=-2*NT*(DV*LOG(P)+(1-DV)*LOG(1-P))
  $THETA (0,1.) (0,1.)
  $OMEGA .1 
  $EST NOABORT METH=1 LAPLACE -2LL PRINT=1
  $COV