PopED (version 0.1.1)

ed_mftot: Evaluate the expectation of the Fisher Information Matrix (FIM) and the expectation of the OFV(FIM).

Description

Compute the expectation of the FIM given the model, parameters, distributions of parameter uncertainty, design and methods defined in the PopED database.

Usage

ed_mftot(model_switch, groupsize, ni, xtoptn, xoptn, aoptn, bpopdescr, ddescr,
  covd, sigma, docc, poped.db)

Arguments

xtoptn

The xtoptn value

xoptn

The xoptn

aoptn

The aoptn value

model_switch

A matrix that is the same size as xt, specifying which model each sample belongs to.

groupsize

A vector of the numer of individuals in each group.

ni

A vector of the number of samples in each group.

poped.db

A PopED database.

bpopdescr

Matrix defining the fixed effects, per row (row number = parameter_number) we should have:

• column 1 the type of the distribution for E-family designs (0 = Fixed, 1 = Normal, 2 = Uniform, 3 = User Defined Distribution, 4 = lognormal and 5 = trunca

ddescr

Matrix defining the diagnonals of the IIV (same logic as for the bpopdescr).

covd

Matrix defining the covariances of the IIV variances. Set to zero if not defined.

sigma

Matrix defining the variances can covariances of the residual variability terms of the model. can also just supply the diagnonal parameter values (variances) as a c().

docc

Matrix defining the IOV, the IOV variances and the IOV distribution

Value

• A list containing the E(FIM) and E(OFV(FIM)) and the a poped.db.

See Also

Other E-family: calc_ofv_and_fim; ed_laplace_ofv; evaluate.e.ofv.fim

Other FIM: LinMatrixH; LinMatrixLH; LinMatrixL_occ; calc_ofv_and_fim; ed_laplace_ofv; evaluate.e.ofv.fim; evaluate.fim; gradf_eps; mf3; mf5; mf6; mf7; mf8; mftot0; mftot1; mftot2; mftot3; mftot4; mftot5; mftot6; mftot7; mftot; mf; ofv_criterion; ofv_fim

Examples

## 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 samoples).
library(PopED)

## 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) 
}

# Adding 10\% log-normal Uncertainty to fixed effects (not Favail)
bpop_vals <- c(CL=0.15, V=8, KA=1.0, Favail=1)
bpop_vals_ed_ln <- cbind(ones(length(bpop_vals),1)*4, # log-normal distribution
                         bpop_vals,
                         ones(length(bpop_vals),1)*(bpop_vals*0.1)^2) # 10\% of bpop value
bpop_vals_ed_ln["Favail",]  <- c(0,1,0)
bpop_vals_ed_ln

## -- Define initial design  and design space
poped.db <- create.poped.database(ff_file="ff.PK.1.comp.oral.sd.CL",
                                  fg_file="sfg",
                                  fError_file="feps.add.prop",
                                  bpop=bpop_vals_ed_ln, 
                                  notfixed_bpop=c(1,1,1,0),
                                  d=c(CL=0.07, V=0.02, KA=0.6), 
                                  sigma=c(0.01,0.25),
                                  groupsize=32,
                                  xt=c( 0.5,1,2,6,24,36,72,120),
                                  minxt=0,
                                  maxxt=120,
                                  a=70,
                                  mina=0,
                                  maxa=100)
# warfarin ed model

# very few samples
poped.db$ED_samp_size=10
ed_mftot(model_switch=poped.db$global_model_switch,
         groupsize=poped.db$groupsize,
         ni=poped.db$gni,
         xtoptn=poped.db$gxt,
         xoptn=poped.db$gx,
         aoptn=poped.db$ga,
         bpopdescr=poped.db$gbpop,
         ddescr=poped.db$gd,
         covd=poped.db$covd,
         sigma=poped.db$sigma,
         docc=poped.db$docc, 
         poped.db)["ED_ofv"]