Implementation of LLOQ about poped HOT 2 CLOSED

## 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. 

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_d2 <- function(model_switch,xt,parameters,poped.db){
  ##-- Model: One comp first order absorption
  with(as.list(parameters),{
    y=xt
    LOQ = 2
    y=(DOSE*Favail*KA/(V*(KA-CL/V)))*(exp(-CL/V*xt)-exp(-KA*xt))
    y[y<LOQ] <- 0
    return(list(y=y,poped.db=poped.db))
  })
}

feps_d2 <- function(model_switch,xt,parameters,epsi,poped.db){
  ## -- Residual Error function
  ## -- Proportional + additive
  y <- do.call(poped.db$model$ff_pointer,list(model_switch,xt,parameters,poped.db))[[1]] 
  loq_obs <- y==0
  y = y*(1+epsi[,1]) + epsi[,2]
  y[loq_obs] <- 0
  return(list(y=y,poped.db=poped.db)) 
}

## -- Define initial design  and design space
poped_db <- create.poped.database(ff_fun=ff_d2,
                                  fg_file="sfg",
                                  fError_fun=feps_d2,
                                  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(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)


output <- poped_optim(poped_db, opt_xt = T, parallel = T)
plot_model_prediction(output$poped.db)