#Tailrank depends on biobase, which is within bioconductor. You may need to run:
#if (!requireNamespace("BiocManager", quietly = TRUE))
#install.packages("BiocManager")
#BiocManager::install("Biobase")
#install.packages("TailRank",dependencies=T)

library(TailRank)

#simulatetrials generates niterations replicates of simulated trials. Currently written to only allow three stages/
#Used in conjunction with findtrialproperties
#Arguments: p0 - null response rate, p1 - alt response rate, a0,b0 - parameters for beta prior
#neachstage - number of patients recruited per stage (must be vector with three integers, e.g. c(6,3,3) for monotherapy or c(10,5,5) for combination)
#alpha - type I error rate used for final comparison in the futility stopping calculation
#niterations - number of simulation replicates
#printprogress - set to 1 if the progress in number of replicates simulated should be printed out, 0 for silent

simulatetrials=function(p0=0.3,
                        p1=0.6,
                        a0=0.3,
                        b0=0.7,
                        neachstage,
                        alpha=0.1,
                        niterations=25000,
                        printprogress=0)
{

totaln=sum(neachstage)

#define vectors/matrices to store results for each iteration
posteriormeanmorethanp0.null=matrix(0,niterations,3)
predictiveprobabilityoftrialsuccess.null=matrix(0,niterations,2)
finalteststatistic.null=rep(0,niterations)
finalteststatistic.alt=rep(0,niterations)
posteriormeanmorethanp0.alt=matrix(0,niterations,3)
predictiveprobabilityoftrialsuccess.alt=matrix(0,niterations,2)



#first simulate null situation with response rate equal to p0:

for(iteration in 1:niterations)
{
  if(iteration%%1000==0)
  {
    if(printprogress==1)
    {
    print(iteration)
    }
  }
  
  
  
  responses=0
  for(stage in 1:length(neachstage))
  {
    
    
    responses=responses+rbinom(1,neachstage[stage],p0)
    n=cumsum(neachstage)[stage]
    
    #Update prior beta parameters to posterior beta parameters using conjugate distribution
    an=a0+responses
    bn=b0+n-responses
    
    
    #efficacy check - if posterior mean that proportion is more than null value
    
    posteriormeanmorethanp0.null[iteration,stage]=1-pbeta(p0,an,bn)
    
    
    #futility assessment: if predictive probability of trial success is less than futility threshold, stop trial early
    #to declare significance at alpha level, need there to be a total of qbinom(1-alpha,totaln,p0) responses. 
    #Probability of this is beta-binomial (totaln-currentn,an,bn). Use pbb in tailrank package
    
    responsesneededforsignificance=qbinom(1-alpha,totaln,p0)
    if(stage<length(neachstage))
    {
      predictiveprobabilityoftrialsuccess.null[iteration,stage]=1-pbb(responsesneededforsignificance-responses,totaln-n,an,bn)
    }
    
  }
  finalteststatistic.null[iteration]=1-pbinom(responses,totaln,p0)
  
}


#next simulate alt situation:




for(iteration in 1:niterations)
{
  if(iteration%%1000==0)
  {   if(printprogress==1)
  {
    print(iteration)
  }
  }
  
  
  
  responses=0
  for(stage in 1:length(neachstage))
  {
    
    
    responses=responses+rbinom(1,neachstage[stage],p1)
    n=cumsum(neachstage)[stage]
    
    
    an=a0+responses
    bn=b0+n-responses
    
    
    #efficacy check - if posterior mean that proportion is more than null value is above efficacy threshold, stop early.
    
    posteriormeanmorethanp0.alt[iteration,stage]=1-pbeta(p0,an,bn)
    
    
    #futility assessment: if predictive probability of trial success is less than futility threshold, stop trial early
    
    
    #to declare significance at alpha level, need there to be more than qbinom(1-alpha,totaln,p0) responses. Probability of this is beta-binomial (totaln-currentn,an,bn)
    
    responsesneededforsignificance=qbinom(1-alpha,totaln,p0)
    if(stage<length(neachstage))
    {
      predictiveprobabilityoftrialsuccess.alt[iteration,stage]=1-pbb(responsesneededforsignificance-responses,totaln-n,an,bn)
    }
    
  }
  finalteststatistic.alt[iteration]=1-pbinom(responses,totaln,p0)
  
}

return(list(predictiveprobabilityoftrialsuccess.null=predictiveprobabilityoftrialsuccess.null,predictiveprobabilityoftrialsuccess.alt=predictiveprobabilityoftrialsuccess.alt,posteriormeanmorethanp0.null=posteriormeanmorethanp0.null,posteriormeanmorethanp0.alt=posteriormeanmorethanp0.alt,finalteststatistic.null=finalteststatistic.null,finalteststatistic.alt=finalteststatistic.alt))
}





#findtrialproperties takes vectors of simulation results under the null and alternative, and determines the type I error rate and power for a particular critical value used for final test statistic
#Arguments:
#predictiveprobabilityoftrialsuccess.alt,posteriormeanmorethanp0.null,posteriormeanmorethanp0.alt, finalteststatistic.null, finalteststatistic.alt - output from simulatetrials
#futilitythreshold - threshold on predictive probability of trial success; if below this at an interim, then stop for futility
#efficacythreshold - threshold on posterior probability - if above this at interim then stop for efficacy
#criticalvalue - type I error rate to use if trial gets through to final stage
#neachstage - vector of sample sizes at each stage as in simulatetrials - used to calculate expected sample size

findtrialproperties=function(predictiveprobabilityoftrialsuccess.null,predictiveprobabilityoftrialsuccess.alt,posteriormeanmorethanp0.null,posteriormeanmorethanp0.alt,finalteststatistic.null,finalteststatistic.alt,futilitythreshold,efficacythreshold,criticalvalue,neachstage)
{
  #calculate at which stage the trial stops for efficacy and at which it stops for futility:
  
  
  #which stage does trial stop for futility (if any):
  
  futilitystopping.null=t(apply(predictiveprobabilityoftrialsuccess.null,1,function(x){ifelse(x<futilitythreshold,1,0)}))
  futilitystopping.alt=t(apply(predictiveprobabilityoftrialsuccess.alt,1,function(x){ifelse(x<futilitythreshold,1,0)}))
  
  #which stage does trial stop for efficacy (if any)
  efficacystopping.null=t(apply(posteriormeanmorethanp0.null[,-3],1,function(x){ifelse(x>efficacythreshold,1,0)}))
  
  efficacystopping.alt=t(apply(posteriormeanmorethanp0.alt[,-3],1,function(x){ifelse(x>efficacythreshold,1,0)}))
  
 
  whichstagestopforefficacy.null=apply(efficacystopping.null,1,function(x){return(min(which(x==1)))})
  whichstagestopforefficacy.alt=apply(efficacystopping.alt,1,function(x){return(min(which(x==1)))})
  
  whichstagestopforfutility.null=apply(futilitystopping.null,1,function(x){return(min(which(x==1)))})
  whichstagestopforfutility.alt=apply(futilitystopping.alt,1,function(x){return(min(which(x==1)))})
  
  #null hypothesis could be rejected if:
  #-efficacy stopping is equal to or smaller than futility stopping
  #no futility stopping and final teststatistic is significant
  
  typeIerror=ifelse((whichstagestopforefficacy.null<whichstagestopforfutility.null)|(is.infinite(whichstagestopforfutility.null) & finalteststatistic.null<criticalvalue),1,0)
  
  power=ifelse((whichstagestopforefficacy.alt<whichstagestopforfutility.alt)|(is.infinite(whichstagestopforfutility.alt) & finalteststatistic.alt<criticalvalue),1,0)
  
  whichstagestop.null=as.double(t(apply(cbind(whichstagestopforefficacy.null,whichstagestopforfutility.null),1,min)))
  whichstagestop.alt=as.double(t(apply(cbind(whichstagestopforefficacy.alt,whichstagestopforfutility.alt),1,min)))
  whichstagestop.null=replace(whichstagestop.null,is.infinite(whichstagestop.null),3)
  whichstagestop.alt=replace(whichstagestop.alt,is.infinite(whichstagestop.alt),3)
  samplesize.null=cumsum(neachstage)[whichstagestop.null]
  samplesize.alt=cumsum(neachstage)[whichstagestop.alt]
  
  
  return(list(typeIerror=mean(typeIerror),power=mean(power),ess.null=mean(samplesize.null),ess.alt=mean(samplesize.alt)))
  
}
set.seed(1)
neachstage=c(6,3,3)
  temp=simulatetrials(p0=0.2,p1=0.5,a0=0.3,b0=0.7,neachstage = neachstage,alpha = 0.1,niterations = 25000,printprogress=0)

  
  properties.monotherapy=findtrialproperties(temp$predictiveprobabilityoftrialsuccess.null,temp$predictiveprobabilityoftrialsuccess.alt,temp$posteriormeanmorethanp0.null,temp$posteriormeanmorethanp0.alt,temp$finalteststatistic.null,temp$finalteststatistic.alt,futilitythreshold=0.02,efficacythreshold=0.98,criticalvalue=0.1,neachstage=neachstage)

print(paste("Single arm properties, type I error rate = ",properties.monotherapy$typeIerror,", power = ",properties.monotherapy$power,sep=""))  
set.seed(1)
neachstage=c(10,5,5)
temp=simulatetrials(p0=0.3,p1=0.6,a0=0.3,b0=0.7,neachstage = neachstage,alpha = 0.05,niterations = 25000,printprogress=0)


properties.combination=findtrialproperties(temp$predictiveprobabilityoftrialsuccess.null,temp$predictiveprobabilityoftrialsuccess.alt,temp$posteriormeanmorethanp0.null,temp$posteriormeanmorethanp0.alt,temp$finalteststatistic.null,temp$finalteststatistic.alt,futilitythreshold=0.02,efficacythreshold=0.98,criticalvalue=0.05,neachstage=neachstage)

print(paste("Combination properties, type I error rate = ",properties.combination$typeIerror,", power = ",properties.combination$power,sep=""))