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