#Functions for modified power prior and conditional power prior

Prior<-function(logHR,alpha){  
  tempRes<-dunif(alpha,min=0,max=10)* prod(dnorm(logHR,mean=0,sd=100))
  if (tempRes==0){ #Set prior to almost zero when it is zero, to prevent numerical problems when taking logarithms.
    tempRes<- 10^-300    
  }
  Prior<-tempRes
}

LikelihoodCPPPooledPiecewise<-function(parameters,theta,minTrial,maxTrial,P,K,N,Trial,X,dataset){
  #Log-likelihood function for pooled analysis of conditional power prior, with piecewise constant baseline hazard.
  alpha<-parameters[1:K]
  par<-parameters[(K+1):(K+P)]
  sigma<-parameters[K+P+1]
  
  Prior<-0
  mu<-matrix(0,N,K)
  for (k in 1:K){mu[,k] <- dataset$TimeIntervals[,k]*exp(alpha[k]+X%*%par)}
  vector<-theta*(Trial<maxTrial)+1*(Trial==maxTrial)
  # define the likelihood        
  Likl<-sum(vector%*%dpois(dataset$EventsIntervals,mu,log=TRUE))
 
  eta <- 1/(sigma*sigma);
  if (sigma>0.01 & sigma<100){
    Prior <- Prior + log(1/(100-0.01))
    #Commensurate Priors on Current Log-Hazards
    for (j in 1:P){
      Prior <- Prior+ dnorm(par[j],mean=0,sd=100,log=TRUE)
    }
    Prior <- Prior+ dnorm(alpha[1],mean=0,sd=100,log=TRUE)
    for (k in 2:K) {
      Prior<- Prior +  dnorm(alpha[k],mean=alpha[k-1],sd=sigma,log=TRUE)
    }
  }else{
    Prior <- -10^300
  }
  LikelihoodCPPPooledPiecewise<- Prior + Likl
}

LikelihoodMPPPooledPiecewise<-function(parameters,minTrial,maxTrial,P,K,N,Trial,X,a,b,dataset,ScalingConstant){
  #Log-likelihood function for pooled analysis of modified power prior, with piecewise constant baseline hazard.
  
  alpha<-parameters[1:K]
  par<-parameters[(K+1):(K+P)]
  sigma<-parameters[K+P+1]
  theta<-parameters[K+P+2]
  Prior<-0
  mu<-matrix(0,N,K)
  for (k in 1:K){mu[,k] <- dataset$TimeIntervals[,k]*exp(alpha[k]+X%*%par)}
  vector<-theta*(Trial<maxTrial)+1*(Trial==maxTrial)
  # define the likelihood        
  Likl<-sum(vector%*%dpois(dataset$EventsIntervals,mu,log=TRUE))

  eta <- 1/(sigma*sigma);
  if (sigma>0.01 & sigma<100 & theta>0 & theta<1){
    Prior <- Prior + log(1/(100-0.01))  
    
    #Commensurate Priors on Current Log-Hazards
    for (j in 1:P){
      Prior <- Prior+ dnorm(par[j],mean=0,sd=100,log=TRUE)
    }
    Prior <- Prior+ dnorm(alpha[1],mean=0,sd=100,log=TRUE)
    for (k in 2:K) {
      Prior<- Prior +  dnorm(alpha[k],mean=alpha[k-1],sd=sigma,log=TRUE)
    }
    Prior<- Prior + log(dbeta(theta,a,b))
    
    ScalingConstantTemp <-  -(theta*length(ScalingConstant)-floor(theta*length(ScalingConstant)))*ScalingConstant[floor(theta*length(ScalingConstant))+1]
    if ((theta*length(ScalingConstant))>1){    
      ScalingConstantTemp<- ScalingConstantTemp - (-theta*length(ScalingConstant)+floor(theta*length(ScalingConstant)+1))*ScalingConstant[floor(theta*length(ScalingConstant))]
    }  
    
  }else{
    Prior <- -10^200
    ScalingConstantTemp<- 0
  }
  LikelihoodMPPPooledPiecewise<- Prior + Likl + ScalingConstantTemp

}

LikelihoodMPPPooledPiecewiseScalingConstant<-function(parameters,theta,minTrial,maxTrial,P,K,N,Trial,X,dataset){
  #Log-likelihood function for pooled analysis of modified power prior, with piecewise constant baseline hazard. 
  #Only for calculating the scaling constant, so current trial is not included in calculation!
  
  alpha<-parameters[1:K]
  par<-parameters[(K+1):(K+P)]
  sigma<-parameters[K+P+1]
  
  Prior<-0
  mu<-matrix(0,N,K)
  for (k in 1:K){mu[,k] <- dataset$TimeIntervals[,k]*exp(alpha[k]+X%*%par)}
  vector<-theta*(Trial<maxTrial)
  # define the likelihood        
  Likl<-sum(vector%*%dpois(dataset$EventsIntervals,mu,log=TRUE))
  
  eta <- 1/(sigma*sigma);
  if (sigma>0.01 & sigma<100){
    Prior <- Prior + log(1/(100-0.01))    
    
    #Commensurate Priors on Current Log-Hazards
    for (j in 1:P){
      Prior <- Prior+ dnorm(par[j],mean=0,sd=100,log=TRUE)
    }
    Prior <- Prior+ dnorm(alpha[1],mean=0,sd=100,log=TRUE)
    for (k in 2:K) {
      Prior<- Prior +  dnorm(alpha[k],mean=alpha[k-1],sd=sigma,log=TRUE)
    }    
    
  }else{
    Prior <- -10^300
  }
  if(is.nan(Likl)){
    Likl<- -10^300
  }
  LikelihoodMPPPooledPiecewiseScalingConstant<- Prior + Likl
}

LikelihoodMPPPooledPiecewiseScalingConstantWithoutPrior<-function(parameters,minTrial,maxTrial,P,K,N,Trial,X,dataset){
  #Log-likelihood function (excluding prior) for pooled analysis of modified power prior, with piecewise constant baseline hazard. 
  #Only for calculating the scaling constant, so current trial is not included in calculation!
  
  alpha<-parameters[1:K]
  par<-parameters[(K+1):(K+P)]
  sigma<-parameters[K+P+1]  
  Prior<-0
  mu<-matrix(0,N,K)
  for (k in 1:K){mu[,k] <- dataset$TimeIntervals[,k]*exp(alpha[k]+X%*%par)}
  vector<-1*(Trial<maxTrial)
  # define the likelihood        
  Likl<-sum(vector%*%dpois(dataset$EventsIntervals,mu,log=TRUE))
  LikelihoodMPPPooledPiecewiseScalingConstantWithoutPrior<- Likl
}