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 Phoenix 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