gradf_eps: Model linearization with respect to epsilon.
In PopED: Population (and Individual) Optimal Experimental Design

gradf_eps

R Documentation

Model linearization with respect to epsilon.

Description

The function performs a linearization of the model with respect to the residual variability. Derivative of model w.r.t. eps evaluated at eps=0 and b=b_ind.

Usage

gradf_eps(model_switch, xt_ind, x, a, bpop, b_ind, bocc_ind, num_eps, poped.db)

Arguments

`model_switch`	A matrix that is the same size as xt, specifying which model each sample belongs to.
`xt_ind`	A vector of the individual/group sample times
`x`	A matrix for the discrete design variables. Each row is a group.
`a`	A matrix of covariates. Each row is a group.
`bpop`	The fixed effects parameter values. Supplied as a vector.
`b_ind`	vector of individual realization of the BSV terms b
`bocc_ind`	Vector of individual realizations of the BOV terms bocc
`num_eps`	The number of `eps()` in the model.
`poped.db`	A PopED database.

Value

A matrix of size (samples per individual x number of epsilons)

Examples

library(PopED)

############# START #################
## Create PopED database
## (warfarin model for optimization)
#####################################

## Warfarin example from software comparison in:
## Nyberg et al., "Methods and software tools for design evaluation 
##   for population pharmacokinetics-pharmacodynamics studies", 
##   Br. J. Clin. Pharm., 2014. 

## Optimization using an additive + proportional reidual error  
## to avoid sample times at very low concentrations (time 0 or very late samples).

## find the parameters that are needed to define from the structural model
ff.PK.1.comp.oral.sd.CL

## -- parameter definition function 
## -- names match parameters in function ff
sfg <- function(x,a,bpop,b,bocc){
  parameters=c(CL=bpop[1]*exp(b[1]),
               V=bpop[2]*exp(b[2]),
               KA=bpop[3]*exp(b[3]),
               Favail=bpop[4],
               DOSE=a[1])
  return(parameters) 
}

## -- Define initial design  and design space
poped.db <- create.poped.database(ff_fun=ff.PK.1.comp.oral.sd.CL,
                                  fg_fun=sfg,
                                  fError_fun=feps.add.prop,
                                  bpop=c(CL=0.15, V=8, KA=1.0, Favail=1), 
                                  notfixed_bpop=c(1,1,1,0),
                                  d=c(CL=0.07, V=0.02, KA=0.6), 
                                  sigma=c(prop=0.01,add=0.25),
                                  groupsize=32,
                                  xt=c( 0.5,1,2,6,24,36,72,120),
                                  minxt=0.01,
                                  maxxt=120,
                                  a=c(DOSE=70),
                                  mina=c(DOSE=0.01),
                                  maxa=c(DOSE=100))

############# END ###################
## Create PopED database
## (warfarin model for optimization)
#####################################


#for the FO approximation
ind=1
gradf_eps(model_switch=t(poped.db$design$model_switch[ind,,drop=FALSE]),
          xt_ind=t(poped.db$design$xt[ind,,drop=FALSE]),
          x=zeros(0,1),
          a=t(poped.db$design$a[ind,,drop=FALSE]),
          bpop=poped.db$parameters$bpop[,2,drop=FALSE],
          b_ind=zeros(poped.db$parameters$NumRanEff,1),
          bocc_ind=zeros(poped.db$parameters$NumDocc,1),
          num_eps=size(poped.db$parameters$sigma,1),
          poped.db)["dfeps_de0"]

PopED documentation built on Oct. 8, 2024, 1:07 a.m.