ofv_criterion: Normalize an objective function by the size of the FIM matrix

In PopED: Population (and Individual) Optimal Experimental Design

Description

Compute a normalized OFV based on the size of the FIM matrix. This value can then be used in efficiency calculations. This is NOT the OFV used in optimization, see ofv_fim.

Usage

ofv_criterion(
  ofv_f,
  num_parameters,
  poped.db,
  ofv_calc_type = poped.db$settings$ofv_calc_type
)

Arguments

ofv_f	An objective function
num_parameters	The number of parameters to use for normalization
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))

Value

The specified criterion value.

See Also

Other FIM: LinMatrixH(), LinMatrixLH(), LinMatrixL_occ(), calc_ofv_and_fim(), ed_laplace_ofv(), ed_mftot(), efficiency(), evaluate.e.ofv.fim(), evaluate.fim(), gradf_eps(), mf3(), mf7(), mftot(), ofv_fim()

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)
#####################################


## evaluate initial design 
FIM <- evaluate.fim(poped.db) # new name for function needed
FIM
get_rse(FIM,poped.db)

ofv_criterion(ofv_fim(FIM,poped.db,ofv_calc_type=1),
              length(get_unfixed_params(poped.db)[["all"]]),
              poped.db,
              ofv_calc_type=1) # det(FIM)

ofv_criterion(ofv_fim(FIM,poped.db,ofv_calc_type=2),
              length(get_unfixed_params(poped.db)[["all"]]),
              poped.db,
              ofv_calc_type=2) 

ofv_criterion(ofv_fim(FIM,poped.db,ofv_calc_type=4),
              length(get_unfixed_params(poped.db)[["all"]]),
              poped.db,
              ofv_calc_type=4)

ofv_criterion(ofv_fim(FIM,poped.db,ofv_calc_type=6),
              length(get_unfixed_params(poped.db)[["all"]]),
              poped.db,
              ofv_calc_type=6)

ofv_criterion(ofv_fim(FIM,poped.db,ofv_calc_type=7),
              length(get_unfixed_params(poped.db)[["all"]]),
              poped.db,
              ofv_calc_type=7) 

PopED documentation built on May 21, 2021, 5:08 p.m.