psi-methods function

Functions to extract the individual estimates of the parameters and random effects

These three functions are used to access the estimates of individual parameters and random effects. methods

psi(object, type = c("mode", "mean"))

phi(object, type = c("mode", "mean"))

eta(object, type = c("mode", "mean"))

## S4 method for signature 'SaemixObject'
psi(object, type = c("mode", "mean"))

## S4 method for signature 'SaemixObject'
phi(object, type = c("mode", "mean"))

## S4 method for signature 'SaemixObject'
eta(object, type = c("mode", "mean"))

Arguments

• object: an SaemixObject object returned by the saemix function
• type: a string specifying whether to use the MAP (type="mode") or the mean (type="mean") of the conditional distribution of the individual parameters. Defaults to mode

Returns

a matrix with the individual parameters (psi/phi) or the random effects (eta). These functions are used to access and output the estimates of parameters and random effects. When the object passed to the function does not contain these estimates, they are automatically computed. The object is then returned (invisibly) with these estimates added to the results.

Details

The psi_i represent the individual parameter estimates. In the SAEM algorithm, these parameters are assumed to be a transformation of a Gaussian random vector phi_i, where the phi_i can be written as a function of the individual random effects (eta_i), the covariate matrix (C_i) and the vector of fixed effects (mu):

phi_i = C_i mu + eta_i

More details can be found in the PDF documentation.

Methods

• list("signature(object = "SaemixObject")"): please refer to the PDF documentation for the models

Examples

data(theo.saemix)

saemix.data<-saemixData(name.data=theo.saemix,header=TRUE,sep=" ",na=NA, 
  name.group=c("Id"),name.predictors=c("Dose","Time"),
  name.response=c("Concentration"),name.covariates=c("Weight","Sex"),
  units=list(x="hr",y="mg/L",covariates=c("kg","-")), name.X="Time")

model1cpt<-function(psi,id,xidep) { 
          dose<-xidep[,1]
          tim<-xidep[,2]  
          ka<-psi[id,1]
          V<-psi[id,2]
          CL<-psi[id,3]
          k<-CL/V
          ypred<-dose*ka/(V*(ka-k))*(exp(-k*tim)-exp(-ka*tim))
          return(ypred)
}

saemix.model<-saemixModel(model=model1cpt,
  description="One-compartment model with first-order absorption", 
  psi0=matrix(c(1.,20,0.5,0.1,0,-0.01),ncol=3, byrow=TRUE,
  dimnames=list(NULL, c("ka","V","CL"))),transform.par=c(1,1,1),
  covariate.model=matrix(c(0,1,0,0,0,0),ncol=3,byrow=TRUE),fixed.estim=c(1,1,1),
  covariance.model=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3,byrow=TRUE),
  omega.init=matrix(c(1,0,0,0,1,0,0,0,1),ncol=3,byrow=TRUE),error.model="constant")

saemix.options<-list(algorithm=c(1,0,0),seed=632545,save=FALSE,save.graphs=FALSE, 
displayProgress=FALSE)

# Not run (strict time constraints for CRAN)

saemix.fit<-saemix(saemix.model,saemix.data,saemix.options)
psi(saemix.fit)
phi(saemix.fit)
eta(saemix.fit,type="mean")

References

E Comets, A Lavenu, M Lavielle M (2017). Parameter estimation in nonlinear mixed effect models using saemix, an R implementation of the SAEM algorithm. Journal of Statistical Software, 80(3):1-41.

E Kuhn, M Lavielle (2005). Maximum likelihood estimation in nonlinear mixed effects models. Computational Statistics and Data Analysis, 49(4):1020-1038.

E Comets, A Lavenu, M Lavielle (2011). SAEMIX, an R version of the SAEM algorithm. 20th meeting of the Population Approach Group in Europe, Athens, Greece, Abstr 2173.

See Also

SaemixData,SaemixModel, SaemixObject, saemixControl, plot.saemix

Author(s)

Emmanuelle Comets emmanuelle.comets@inserm.fr, Audrey Lavenu, Marc Lavielle.