library(PopED)

##-- Model: One comp first order absorption + inhibitory imax
## -- works for both mutiple and single dosing  
ff <- function(model_switch,xt,parameters,poped.db){
  with(as.list(parameters),{
    
    y=xt
    MS <- model_switch
    
    # PK model
    N = floor(xt/TAU)+1
    CONC=(DOSE*Favail/V)*(KA/(KA - CL/V)) * 
      (exp(-CL/V * (xt - (N - 1) * TAU)) * (1 - exp(-N * CL/V * TAU))/(1 - exp(-CL/V * TAU)) - 
         exp(-KA * (xt - (N - 1) * TAU)) * (1 - exp(-N * KA * TAU))/(1 - exp(-KA * TAU)))  
    
    # PD model
    EFF = E0*(1 - CONC*IMAX/(IC50 + CONC))
    
    y[MS==1] = CONC[MS==1]
    y[MS==2] = EFF[MS==2]
    
    return(list( y= y,poped.db=poped.db))
  })
}

## -- parameter definition function 
sfg <- function(x,a,bpop,b,bocc){
  parameters=c( V=bpop[1]*exp(b[1]),
                KA=bpop[2]*exp(b[2]),
                CL=bpop[3]*exp(b[3]),
                Favail=bpop[4],
                DOSE=a[1],
                TAU = a[2],
                E0=bpop[5]*exp(b[4]),
                IMAX=bpop[6],
                IC50=bpop[7])
  return( parameters ) 
}


## -- Residual Error function
feps <- function(model_switch,xt,parameters,epsi,poped.db){
  returnArgs <- ff(model_switch,xt,parameters,poped.db) 
  y <- returnArgs[[1]]
  poped.db <- returnArgs[[2]]
  
  MS <- model_switch
  
  pk.dv <- y*(1+epsi[,1])+epsi[,2]
  pd.dv <-  y*(1+epsi[,3])+epsi[,4]
  
  y[MS==1] = pk.dv[MS==1]
  y[MS==2] = pd.dv[MS==2]
  
  return(list( y= y,poped.db =poped.db )) 
}

poped.db <- create.poped.database(ff_fun="ff",
                                  fError_fun="feps",
                                  fg_fun="sfg",
                                  groupsize=20,
                                  m=3,
                                  bpop=c(V=72.8,KA=0.25,CL=3.75,Favail=0.9,E0=1120,IMAX=0.807,IC50=0.0993),  
                                  notfixed_bpop=c(1,1,1,0,1,1,1),
                                  d=c(V=0.09,KA=0.09,CL=0.25^2,E0=0.09), 
                                  sigma=c(0.04,5e-6,0.09,100),
                                  notfixed_sigma=c(0,0,0,0),
                                  xt=c( 1,2,8,240,240,1,2,8,240,240),
                                  minxt=c(0,0,0,240,240,0,0,0,240,240),
                                  maxxt=c(10,10,10,248,248,10,10,10,248,248),
                                  discrete_xt = list(0:248),
                                  G_xt=c(1,2,3,4,5,1,2,3,4,5),
                                  bUseGrouped_xt=1,
                                  model_switch=c(1,1,1,1,1,2,2,2,2,2),
                                  a=list(c(DOSE=20,TAU=24),c(DOSE=40, TAU=24),c(DOSE=0, TAU=24)),
                                  maxa=c(DOSE=200,TAU=40),
                                  mina=c(DOSE=0,TAU=2),
                                  ourzero=0)

##  create plot of model and design 
plot_model_prediction(poped.db,facet_scales="free")
plot_model_prediction(poped.db,IPRED=T,DV=T,facet_scales="free",separate.groups=T)

## evaluate initial design
evaluate_design(poped.db)
shrinkage(poped.db)

# Optimization 
output <- poped_optim(poped.db, opt_xt = T, parallel = T)

summary(output)

get_rse(output$FIM,output$poped.db)
plot_model_prediction(output$poped.db,facet_scales="free")




