## 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.
## Evaluating with uncertainty around parameter values in the model
library(PopED)
sfg <- function(x,a,bpop,b,bocc){
## -- parameter definition function
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)
}
ff <- function(model_switch,xt,parameters,poped.db){
##-- Model: One comp first order absorption
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))
})
}
# Adding 10% Uncertainty to all fixed effects (not Favail)
bpop_vals <- c(CL=0.15, V=8, KA=1.0, Favail=1)
bpop_vals_ed <- 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["Favail",] <- c(0,1,0)
bpop_vals_ed
## -- Define initial design and design space
poped.db <- create.poped.database(ff_fun=ff,
fg_fun=sfg,
fError_fun=feps.add.prop,
bpop=bpop_vals_ed,
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_samp_size=20)
## ElnD: E(ln(det(FIM))) evaluate.
## result is inaccurate (run several times to see)
## increase ED_samp_size for a more accurate calculation
tic();evaluate_design(poped.db,d_switch=FALSE,ED_samp_size=20); toc()
## optimization with line search search
output_ls <- poped_optim(poped.db, opt_xt=T, parallel=T, method = "LS", d_switch=F, ED_samp_size=20)
## ED: E(det(FIM)) using Laplace approximation
## deterministic calculation, relatively fast
## can be more stable for optimization
tic(); evaluate_design(poped.db,d_switch=FALSE,use_laplace=TRUE); toc()
## optimization with Laplace
output_ls <- poped_optim(poped.db, opt_xt=T, parallel=T, method = "LS", d_switch=F, use_laplace=T)
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