Compute the Bayesian Fisher information matrix

Computation of the Bayesian Fisher information matrix for individual parameters of a population model based on Maximum A Posteriori (MAP) estimation of the empirical Bayes estimates (EBEs) in a population model

Usage

evaluate_fim_map(
  poped.db,
  use_mc = FALSE,
  num_sim_ids = 1000,
  use_purrr = FALSE,
  shrink_mat = F
)

Arguments

poped.db

A PopED database

use_mc

Should the calculation be based on monte-carlo simulations. If not then then a first order approximation is used

num_sim_ids

If use_mc=TRUE, how many individuals should be simulated to make the computations.

use_purrr

If use_mc=TRUE then should the method use the package purrr in calculations? This may speed up computations (potentially).

shrink_mat

Should the shrinkage matrix be returned. Calculated as the inverse of the Bayesian Fisher information matrix times the inverse of the omega matrix (variance matrix of the between-subject variability).

Value

The Bayesian Fisher information matrix for each design group

References

1. Combes, F. P., Retout, S., Frey, N., & Mentre, F. (2013). Prediction of shrinkage of individual parameters using the Bayesian information matrix in non-linear mixed effect models with evaluation in pharmacokinetics. Pharmaceutical Research, 30(9), 2355-67. doi:10.1007/s11095-013-1079-3 .

2. Hennig, S., Nyberg, J., Fanta, S., Backman, J. T., Hoppu, K., Hooker, A. C., & Karlsson, M. O. (2012). Application of the optimal design approach to improve a pretransplant drug dose finding design for ciclosporin. Journal of Clinical Pharmacology, 52(3), 347-360. doi:10.1177/0091270010397731 .

Examples

library(PopED)

############# START #################
## Create PopED database
## (warfarin example)
#####################################

## 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. 

## 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: 0x564e4be77e58>
#> <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 model, parameters, initial design
poped.db <- create.poped.database(ff_fun=ff.PK.1.comp.oral.sd.CL,
                                  fg_fun=sfg,
                                  fError_fun=feps.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),
                                  groupsize=32,
                                  xt=c( 0.5,1,2,6,24,36,72,120),
                                  a=c(DOSE=70))

############# END ###################
## Create PopED database
## (warfarin example)
#####################################

shrinkage(poped.db)
#> # A tibble: 3 × 5
#>     d_CL    d_V   d_KA type       group
#>    <dbl>  <dbl>  <dbl> <chr>      <chr>
#> 1 0.0244 0.174  0.0301 shrink_var grp_1
#> 2 0.0123 0.0910 0.0152 shrink_sd  grp_1
#> 3 0.0413 0.0590 0.134  se         grp_1