PD1.saemix {saemix}

Data simulated according to an Emax response model, in SAEM format

Description

The PD1.saemix and PD2.saemix data frames were simulated according to an Emax dose-response model.

Usage

PD1.saemix

PD2.saemix

Format

This data frame contains the following columns:

subject

an variable identifying the subject on whom the observation was made. The ordering is by the dose at which the observation was made.

dose

simulated dose.

response

simulated response

gender

gender (0 for male, 1 for female)

Details

These examples were used by P. Girard and F. Mentre for the symposium dedicated to Comparison of Algorithms Using Simulated Data Sets and Blind Analysis, that took place in Lyon, France, September 2004. The datasets contain 100 individuals, each receiving 3 different doses:(0, 10, 90), (5, 25, 65) or (0, 20, 30). It was assumed that doses were given in a cross-over study with sufficient wash out period to avoid carry over. Responses (y_ij) were simulated with the following pharmacodynamic model: y_ij = E0_i + D_ij Emax_i/(D_ij + ED50_i) +epsilon_ij The individual parameters were simulated according to log (E0_i) = log (E0) + eta_i1 log (Emax_i) = log (Emax) + eta_i2 log (E50_i) = log (E50) + beta w_i + eta_i3

PD1.saemix contains the data simulated with a gender effect, beta=0.3. PD2.saemix contains the data simulated without a gender effect, beta=0.

References

P Girard, F Mentre (2004). Comparison of Algorithms Using Simulated Data Sets and Blind Analysis workshop, Lyon, France.

Examples

data(PD1.saemix)
saemix.data<-saemixData(name.data=PD1.saemix,header=TRUE,name.group=c("subject"),
      name.predictors=c("dose"),name.response=c("response"),
      name.covariates=c("gender"), units=list(x="mg",y="-",covariates=c("-")))

modelemax<-function(psi,id,xidep) {
# input:
#   psi : matrix of parameters (3 columns, E0, Emax, EC50)
#   id : vector of indices 
#   xidep : dependent variables (same nb of rows as length of id)
# returns:
#   a vector of predictions of length equal to length of id
  dose<-xidep[,1]
  e0<-psi[id,1]
  emax<-psi[id,2]
  e50<-psi[id,3]
  f<-e0+emax*dose/(e50+dose)
  return(f)
}

# Plotting the data
plot(saemix.data,main="Simulated data PD1")

# Compare models with and without covariates with LL by Importance Sampling
model1<-saemixModel(model=modelemax,description="Emax growth model", 
       psi0=matrix(c(20,300,20,0,0,0),ncol=3,byrow=TRUE,dimnames=list(NULL,
       c("E0","Emax","EC50"))), transform.par=c(1,1,1),
       covariate.model=matrix(c(0,0,0), ncol=3,byrow=TRUE),fixed.estim=c(1,1,1))

model2<-saemixModel(model=modelemax,description="Emax growth model", 
       psi0=matrix(c(20,300,20,0,0,0),ncol=3,byrow=TRUE,dimnames=list(NULL, 
       c("E0","Emax","EC50"))), transform.par=c(1,1,1),
       covariate.model=matrix(c(0,0,1), ncol=3,byrow=TRUE),fixed.estim=c(1,1,1))

# SE not computed as not needed for the test
saemix.options<-list(algorithms=c(0,1,1),nb.chains=3,seed=765754, 
       nbiter.saemix=c(500,300),save=FALSE,save.graphs=FALSE,displayProgress=FALSE)

fit1<-saemix(model1,saemix.data,saemix.options)
fit2<-saemix(model2,saemix.data,saemix.options)
wstat<-(-2)*(fit1["results"]["ll.is"]-fit2["results"]["ll.is"])

cat("LRT test for covariate effect on EC50: p-value=",1-pchisq(wstat,1),"\n")