Evaluate the expectation of determinant the Fisher Information Matrix (FIM) using the Laplace approximation.
Source:R/ed_laplace_ofv.R
ed_laplace_ofv.RdCompute the expectation of the det(FIM) using the Laplace
approximation to the expectation. Computations are made based on the model,
parameters, distributions of parameter uncertainty, design and methods
defined in the PopED database or as arguments to the function.
Usage
ed_laplace_ofv(
model_switch,
groupsize,
ni,
xtopto,
xopto,
aopto,
bpopdescr,
ddescr,
covd,
sigma,
docc,
poped.db,
method = 1,
return_gradient = FALSE,
optxt = poped.db$settings$optsw[2],
opta = poped.db$settings$optsw[4],
x = c(),
...
)Arguments
- model_switch
A matrix that is the same size as xt, specifying which model each sample belongs to.
- groupsize
A vector of the number of individuals in each group.
- ni
A vector of the number of samples in each group.
- xtopto
the sampling times
- xopto
the discrete design variables
- aopto
the continuous design variables
- bpopdescr
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 = truncated normal)
column 2 defines the mean.
column 3 defines the variance of the distribution (or length of uniform distribution).
- ddescr
Matrix defining the diagonals of the IIV (same logic as for the
bpopdescr).- covd
Column major vector defining the covariances of the IIV variances. That is, from your full IIV matrix
covd <- IIV[lower.tri(IIV)].- sigma
Matrix defining the variances can covariances of the residual variability terms of the model. can also just supply the diagonal parameter values (variances) as a
c().- docc
Matrix defining the IOV, the IOV variances and the IOV distribution as for d and bpop.
- poped.db
A PopED database.
- method
If 0 then use an optimization routine translated from PopED code written in MATLAB to optimize the parameters in the Laplace approximation. If 1 then use
optimto compute both k and the hessian of k (see Dodds et al, JPP, 2005 for more information). If 2 then usefdHessto compute the hessian.- return_gradient
Should the gradient be returned.
- optxt
If sampling times are optimized
- opta
If continuous design variables are optimized
- x
The design parameters to compute the gradient on.
- ...
Arguments passed through from other functions, does not pass anything to another function.
Details
This computation follows the method outlined in Dodds et al, "Robust Population Pharmacokinetic Experiment Design" JPP, 2005, equation 16.
Typically this function will not be run by the user. Instead use evaluate.e.ofv.fim.
See also
Other FIM:
LinMatrixH(),
LinMatrixLH(),
LinMatrixL_occ(),
calc_ofv_and_fim(),
ed_mftot(),
efficiency(),
evaluate.e.ofv.fim(),
evaluate.fim(),
gradf_eps(),
mf3(),
mf7(),
mftot(),
ofv_criterion(),
ofv_fim()
Other E-family:
calc_ofv_and_fim(),
ed_mftot(),
evaluate.e.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
#> 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)
}
######################
# Normal distribution
######################
bpop_vals <- c(CL=0.15, V=8, KA=1.0, Favail=1)
bpop_vals_ed_n <- cbind(ones(length(bpop_vals),1)*1, # normal distribution
bpop_vals,
ones(length(bpop_vals),1)*(bpop_vals*0.1)^2) # 10% of bpop value
bpop_vals_ed_n["Favail",] <- c(0,1,0)
bpop_vals_ed_n
#> bpop_vals
#> CL 1 0.15 0.000225
#> V 1 8.00 0.640000
#> KA 1 1.00 0.010000
#> Favail 0 1.00 0.000000
## -- Define initial design and design space
poped.db.n <- create.poped.database(ff_fun=ff.PK.1.comp.oral.sd.CL,
fg_fun=sfg,
fError_fun=feps.add.prop,
bpop=bpop_vals_ed_n,
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)
## ED evaluate using LaPlace approximation
tic(); output <- evaluate.e.ofv.fim(poped.db.n,use_laplace=TRUE); toc()
#> Elapsed time: 0.857 seconds.
output$E_ofv
#> [1] 1.331515e+24
if (FALSE) { # \dontrun{
## ED value using MC integration (roughly)
tic();e_ofv_mc_n <- evaluate.e.ofv.fim(poped.db.n,ED_samp_size=500,ofv_calc_type = 1);toc()
e_ofv_mc_n$E_ofv
## Using ed_laplce_ofv directly
ed_laplace_ofv(model_switch=poped.db.n$design$model_switch,
groupsize=poped.db.n$design$groupsize,
ni=poped.db.n$design$ni,
xtopto=poped.db.n$design$xt,
xopto=poped.db.n$design$x,
aopto=poped.db.n$design$a,
bpopdescr=poped.db.n$parameters$bpop,
ddescr=poped.db.n$parameters$d,
covd=poped.db.n$parameters$covd,
sigma=poped.db.n$parameters$sigma,
docc=poped.db.n$parameters$docc,
poped.db.n)
######################
# Log-normal distribution
######################
# 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.ln <- create.poped.database(ff_fun=ff.PK.1.comp.oral.sd.CL,
fg_fun=sfg,
fError_fun=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)
## ED evaluate using LaPlace approximation
tic()
output <- evaluate.e.ofv.fim(poped.db.ln,use_laplace=TRUE)
toc()
output$E_ofv
## expected value (roughly)
tic()
e_ofv_mc_ln <- evaluate.e.ofv.fim(poped.db.ln,ED_samp_size=500,ofv_calc_type = 1)[["E_ofv"]]
toc()
e_ofv_mc_ln
## Using ed_laplce_ofv directly
ed_laplace_ofv(model_switch=poped.db.ln$design$model_switch,
groupsize=poped.db.ln$design$groupsize,
ni=poped.db.ln$design$ni,
xtopto=poped.db.ln$design$xt,
xopto=poped.db.ln$design$x,
aopto=poped.db.ln$design$a,
bpopdescr=poped.db.ln$parameters$bpop,
ddescr=poped.db.ln$parameters$d,
covd=poped.db.ln$parameters$covd,
sigma=poped.db.ln$parameters$sigma,
docc=poped.db.ln$parameters$docc,
poped.db.ln)
} # }