Evaluate a criterion of the Fisher Information Matrix (FIM)

Compute a criterion of the FIM given the model, parameters, design and methods defined in the PopED database.

Usage

ofv_fim(
  fmf,
  poped.db,
  ofv_calc_type = poped.db$settings$ofv_calc_type,
  ds_index = poped.db$parameters$ds_index,
  use_log = TRUE,
  ...
)

Arguments

fmf

The FIM

poped.db

A poped database

ofv_calc_type

OFV calculation type for FIM

1 = "D-optimality". Determinant of the FIM: det(FIM)
2 = "A-optimality". Inverse of the sum of the expected parameter variances: 1/trace_matrix(inv(FIM))
4 = "lnD-optimality". Natural logarithm of the determinant of the FIM: log(det(FIM))
6 = "Ds-optimality". Ratio of the Determinant of the FIM and the Determinant of the uninteresting rows and columns of the FIM: det(FIM)/det(FIM_u)
7 = Inverse of the sum of the expected parameter RSE: 1/sum(get_rse(FIM,poped.db,use_percent=FALSE))

ds_index

Ds_index is a vector set to 1 if a parameter is uninteresting, otherwise 0. size=(1,num unfixed parameters). First unfixed bpop, then unfixed d, then unfixed docc and last unfixed sigma. Default is the fixed effects being important, everything else not important. Used in conjunction with ofv_calc_type=6.

use_log

Should the criterion be in the log domain?

...

arguments passed to evaluate.fim and ofv_fim.

Value

The specified criterion value.

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
#> function (model_switch, xt, parameters, poped.db) 
#> {
#>     with(as.list(parameters), {
#>         y = xt
#>         y = (DOSE * Favail * KA/(V * (KA - CL/V))) * (exp(-CL/V * 
#>             xt) - exp(-KA * xt))
#>         return(list(y = y, poped.db = poped.db))
#>     })
#> }
#> <bytecode: 0x557079188b38>
#> <environment: namespace:PopED>

## -- 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)
#####################################


## evaluate initial design 
FIM <- evaluate.fim(poped.db) 
FIM
#>             [,1]      [,2]      [,3]         [,4]         [,5]        [,6]
#> [1,] 17141.83891 20.838375 10.011000 0.000000e+00     0.000000  0.00000000
#> [2,]    20.83837 17.268051 -3.423641 0.000000e+00     0.000000  0.00000000
#> [3,]    10.01100 -3.423641 49.864697 0.000000e+00     0.000000  0.00000000
#> [4,]     0.00000  0.000000  0.000000 2.324341e+03     9.770352  0.03523364
#> [5,]     0.00000  0.000000  0.000000 9.770352e+00 19083.877564 11.72131703
#> [6,]     0.00000  0.000000  0.000000 3.523364e-02    11.721317 38.85137516
#> [7,]     0.00000  0.000000  0.000000 7.268410e+02  9656.158553 64.78095548
#> [8,]     0.00000  0.000000  0.000000 9.062739e+01   266.487127  2.94728469
#>              [,7]        [,8]
#> [1,]      0.00000    0.000000
#> [2,]      0.00000    0.000000
#> [3,]      0.00000    0.000000
#> [4,]    726.84097   90.627386
#> [5,]   9656.15855  266.487127
#> [6,]     64.78096    2.947285
#> [7,] 192840.20092 6659.569867
#> [8,]   6659.56987  475.500111
get_rse(FIM,poped.db)
#>        CL         V        KA      d_CL       d_V      d_KA  sig_prop   sig_add 
#>  5.096246  3.031164 14.260384 29.761226 36.681388 26.748640 32.011719 25.637971 

det(FIM)
#> [1] 1.143859e+24
ofv_fim(FIM,poped.db,ofv_calc_type=1) # det(FIM)
#> [1] 1.143859e+24
ofv_fim(FIM,poped.db,ofv_calc_type=2) # 1/trace_matrix(inv(FIM))
#> [1] 9.127328
ofv_fim(FIM,poped.db,ofv_calc_type=4) # log(det(FIM)) 
#> [1] 55.39645
ofv_fim(FIM,poped.db,ofv_calc_type=6) # Ds with fixed effects as "important"
#> [1] 16.49204
ofv_fim(FIM,poped.db,ofv_calc_type=6,
        ds_index=c(1,1,1,0,0,0,1,1)) # Ds with random effects as "important"
#> [1] 21.23143
ofv_fim(FIM,poped.db,ofv_calc_type=7) # 1/sum(get_rse(FIM,poped.db,use_percent=FALSE))
#> [1] 0.5772714

Evaluate a criterion of the Fisher Information Matrix (FIM)

Usage

Arguments

Value

See also

Examples