PopED (version 0.1.1)

evaluate.e.ofv.fim: Evaluate the expectation of the Fisher Information Matrix (FIM) and the expectation of the OFV(FIM).

Description

Compute the expectation of the FIM and OFV(FIM) given the model, parameters, distributions of parameter uncertainty, design and methods defined in the PopED database. Some of the arguments coming from the PopED database can be overwritten; by default these arguments are NULL in the function, if they are supplied then they are used instead of the arguments from the PopED database.

Usage

evaluate.e.ofv.fim(poped.db, fim.calc.type = NULL, bpop = poped.db$gbpop,
  d = poped.db$gd, covd = poped.db$covd, docc = poped.db$docc,
  sigma = poped.db$sigma, model_switch = NULL, ni = NULL, xt = NULL,
  x = NULL, a = NULL, groupsize = poped.db$design$groupsize,
  deriv.type = NULL, bLHS = poped.db$bLHS,
  ofv_calc_type = poped.db$ofv_calc_type,
  ED_samp_size = poped.db$ED_samp_size,
  use_laplace = poped.db$iEDCalculationType, laplace.fim = FALSE, ...)

Arguments

use_laplace

Should the Laplace method be used in calculating the expectation of the OFV?

laplace.fim

Should an E(FIM) be calculated when computing the Laplace approximated E(OFV). Typically the FIM does not need to be computed and, if desired, this calculation is done usng the standard MC integration technique, so can be slow.

poped.db

A PopED database.

fim.calc.type

The method used for calculating the FIM. Potential values:

• 0 = Full FIM. No assumption that fixed and random effects are uncorrelated. Seemftot0.
• 1 = Reduced FIM. Assume that there is no co

model_switch

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

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.

groupsize

A vector of the numer of individuals in each group.

deriv.type

A number indicating the type of derivative to use:

• 0=Complex difference
• 1=Central difference
• 20=Analytic derivative (placeholder)
• 30=Automatic differentiation (placeholder)

...

Other arguments passed to the function.

bpop

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

d

Matrix defining the diagnonals of the IIV (same logic as for the fixed efects). can also just supply the parameter values as a c().

covd

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

docc

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

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().

bLHS

How to sample from distributions in E-family calculations. 0=Random Sampling, 1=LatinHyperCube --

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

ED_samp_size

Sample size for E-family sampling

Value

• A list containing the E(FIM) and E(OFV(FIM)) and the a poped.db updated according to the function arguments.

See Also

Other E-family: calc_ofv_and_fim; ed_laplace_ofv; ed_mftot

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

Other evaluate_FIM: calc_ofv_and_fim; evaluate.fim; 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

## ED evaluate (with very few samples)
output <- evaluate.e.ofv.fim(poped.db,ED_samp_size=10)
output$E_ofv

## API evaluate (with very few samples)
output <- evaluate.e.ofv.fim(poped.db,ED_samp_size=10,ofv_calc_type=4)
output$E_ofv

## ED evaluate using Laplace approximation 
tic()
output <- evaluate.e.ofv.fim(poped.db,use_laplace=TRUE)
toc()
output$E_ofv

## ED expected value with more precision. 
  ## Compare time and value to Laplace approximation.
  ## Run a couple of times to see stochasticity of calculation.
  tic()
  e_ofv_mc <- evaluate.e.ofv.fim(poped.db,ED_samp_size=500)
  toc()
  e_ofv_mc$E_ofv
  
  # If you want to get an E(FIM) from the laplace approximation you have to ask for it
  # and it will take more time.
  output <- evaluate.e.ofv.fim(poped.db,use_laplace=TRUE,laplace.fim=TRUE)
  output$E_fim