PopED (version 0.1.1)

mftot7: The reduced Fisher Information Matrix (FIM) parameterized with A,B,C matrices & using the derivative of variance.

Description

Compute the reduced FIM given specific model(s), parameters, design and methods. This computation assumes that there is no correlation in the FIM between the fixed and random effects, and set these elements in the FIM to zero. This computation parameterizes the FIM calculation using A,B,C matrices (as in Retout et al.) but uses the derivative of variances. Should give the same answer as mftot1 but computation times may be different.

Usage

mftot7(model_switch, groupsize, ni, xt, x, a, bpop, d, sigma, docc, poped.db)

Arguments

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.

xt

A matrix of sample times. Each row is a vector of sample times for a group.

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.

d

A between subject variability matrix (OMEGA in NONMEM).

sigma

A residual unexplained variability matrix (SIGMA in NONMEM).

docc

A between occasion variability matrix.

poped.db

A PopED database.

Value

• As a list:
• ret
  The FIM
• poped.db
  A PopED database

References

S. Retout and F. Mentre, "Further developments of the Fisher Information Matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics", J. of Biopharm. Stats., 13(2), 2003.

See Also

For an easier function to use, please see evaluate.fim.

Other FIM: LinMatrixH; LinMatrixLH; LinMatrixL_occ; calc_ofv_and_fim; ed_laplace_ofv; ed_mftot; evaluate.e.ofv.fim; evaluate.fim; gradf_eps; mf3; mf5; mf6; mf7; mf8; mftot0; mftot1; mftot2; mftot3; mftot4; mftot5; mftot6; 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) 
}

## -- 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=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(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 optimization model



mftot7(model_switch=poped.db$global_model_switch,
      groupsize=poped.db$groupsize,
      ni=poped.db$gni,
      xt=poped.db$gxt,
      x=poped.db$gx,
      a=poped.db$ga,
      bpop=poped.db$param.pt.val$bpop,
      d=poped.db$param.pt.val$d,
      sigma=poped.db$sigma,
      docc=poped.db$param.pt.val$docc,
      poped.db)["ret"]