#########################################################################
#                                    
#    This R Program is for the implmentation of the Non-parametric         
#    optimal design of O'Quigley, Paoletti, and Maccario (2002)* in
#    dose finding studies. The function 'npoptimal' returns a the 
#    distribution of the MTD recommendation according to a number of 
#    simulations, based on the target, the true toxicity probalities, 
#    and the sample size.                     
#                                    
#    *O’Quigley, J. , Paoletti, X. and Maccario, J. (2002) Non-        
#    parametric optimal design in dose finding studies. Biostatistics,    
#    3(1): 51-56.                            
#                                    
#########################################################################

npoptimal<-function(r,theta,n,B){
count<-rep(0,length(r))
for(i in 1:B){
v<<-rep(NA,n)
tox<<-matrix(nrow=n,ncol=length(r))
for(j in 1:n){
### Generates a toxicity threshold for the given patient
v[j]<<-runif(1)
### Assigns the complete information to the given patient based on
### the threshold generated above
for(l in 1:(length(r)-1)){
if(v[j]<=r[1]) {tox[j,]<<-rep(1,length(r))}
if(v[j]<=r[l+1] & v[j]>r[l]) {tox[j,]<<-c(rep(0,l),rep(1,length(r)-l))}
if(v[j]>=r[length(r)]) {tox[j,]<<-rep(0,length(r))}
}

}
### Calculates the estimates of the toxicity probabilities 
rhat<-colMeans(tox)
distance<-abs(rhat-theta)
library("nnet")
### Determines the MTD, randomly breaks ties if they arise
next.lev<-which.is.max(-distance)
### Outputs the estimated toxicity probabilities and the MTD
out<-list(ptox.est=round(rhat,2),MTD=next.lev)
count[out$MTD]<-count[out$MTD]+1
}
### Output the recommended dose allocation
out2<-list(MTD.rec=round(count/B,2),p.tox=r,Target=theta,Sample.size=n)
}
### Function npoptimal ends here

### Target DLT rate
theta<-0.25 
### sample size
n<-16
### True toxicity probabilities 
r<-c(0.01,0.05,0.10,0.15,0.45,0.60)
### Number of simulations
B=5000
fit<-npoptimal(r,theta,n,B)
### fit gives:
### 1) Dose allocation based on B simulations
### 2) True toxicity probabilites
### 3) Target toxicity rate
### 4) The sample size
fit