################
#  Model 1(a)  #
################
# N ~ POI(theta)

######################
#  First Activation  #
######################

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]  # Regression on eta
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))  # Weibull survival function
		L1[i] <- -theta*(1-s[i])  # Loglikelihood part 1 = log(S*(t))
		L2[i] <- (log(theta)+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]  # Loglikelihood part 2 = delta*log(h*(t))
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dgamma(2, 0.001)
	fraction <- exp(-theta)  # Cure rate

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#####################
#  Last Activation  #
#####################

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		temp[i] <- 1+exp(-theta)*(1-exp(theta*(1-s[i])))
		L1[i] <- log(temp[i])
		L2[i] <- (log(theta)-theta*s[i]-log(temp[i])+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dgamma(2, 0.001)
	fraction <- exp(-theta)  # Cure rate

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#############
#  Mixture  #
#############

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		logf[i] <- log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i], rho)  # Logarithm of Weibull probability density function
		
		temp[i] <- 1+exp(-theta)-exp(-theta*s[i])
		Sstar[i] <- p*exp(-theta*(1-s[i])) + (1-p)*temp[i]
		L1[i] <- log(Sstar[i])
		L2FA[i] <- exp(-theta*(1-s[i]))
		L2LA[i] <- exp(-theta*s[i])
		L2[i] <- (log(theta)-L1[i]+log(p*L2FA[i]+(1-p)*L2LA[i])+logf[i])*d[i]

		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dgamma(2, 0.001)
	fraction <- exp(-theta)  # Cure rate
	p ~ dunif(0, 1)  # Only for Mixtrue model

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0, p=0.5)


################
#  Model 1(b)  #
################
# N ~ BER(theta)

model 
{

	c <- 100000

	for (i in 1:284)
	{
		# All the activation schemes collide for this model
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]  # Regression on eta
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))  # Weibull survival function
		temp[i] <- 1 - theta*(1 - s[i])
		L1[i] <- log(temp[i])  # Loglikelihood part 1 = log(S*(t))
		L2[i] <- (log(theta)-log(temp[i])+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]  # Loglikelihood part 2 = delta*log(h*(t))
		
		# Poisson trick adopted from Minhui Chen's codes
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- 1-theta  # Cure rate
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)


################
#  Model 1(c)  #
################
# N ~ BIN(K, theta)

######################
#  First Activation  #
######################

model 
{
	
	c <- 100000
	K <- 10

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]  # Regression on eta
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))  # Weibull survival function
		temp[i] <- 1 - theta*(1 - s[i])
		L1[i] <- K*log(temp[i])  # Loglikelihood part 1 = log(S*(t))
		L2[i] <- (log(K)+log(theta)-log(temp[i])+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]  # Loglikelihood part 2 = delta*log(h*(t))
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- pow(1-theta, K)  # Cure rate
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#####################
#  Last Activation  #
#####################

model 
{
	
	c <- 100000
	K <- 10

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		temp[i] <- 1+pow(1-theta,K)-pow(1-theta*s[i],K)
		L1[i] <- log(temp[i])
		L2[i] <- (log(K)+log(theta)+(K-1)*log(1-theta*s[i])-log(temp[i])+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- pow(1-theta, K)  # Cure rate
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#############
#  Mixture  #
#############

model 
{
	
	c <- 100000
	K <- 10

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		logf[i] <- log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i], rho)  # Logarithm of Weibull probability density function
		
		tempFA[i] <- 1-theta*(1-s[i])
		tempLA[i] <- 1+pow(1-theta, K)-pow(1-theta*s[i], K)
		Sstar[i] <- p*pow(tempFA[i], K) + (1-p)*tempLA[i]
		L1[i] <- log(Sstar[i])
		L2FA[i] <- pow(tempFA[i], K-1)
		L2LA[i] <- pow(1-theta*s[i], K-1)
		L2[i] <- (log(K)+log(theta)-L1[i]+log(p*L2FA[i]+(1-p)*L2LA[i])+logf[i])*d[i]

		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- pow(1-theta, K)  # Cure rate
	p ~ dunif(0, 1)  # Only for Mixtrue model
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0, p=0.5)


################
#  Model 1(d)  #
################
# N ~ GEO(1-theta)

######################
#  First Activation  #
######################

model 
{
	
	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]  # Regression on eta
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))  # Weibull survival function
		L1[i] <- log(1-theta)-log(1-theta*s[i])  # Loglikelihood part 1 = log(S*(t))
		L2[i] <- (log(theta)-log(1-theta*s[i])+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]  # Loglikelihood part 2 = delta*log(h*(t))
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- 1-theta  # Cure rate
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#####################
#  Last Activation  #
#####################

model 
{
	
	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		temp[i] <- 1-theta*(2-theta)*(1-s[i])
		L1[i] <- log(temp[i])-log(1-theta*(1-s[i]))
		L2[i] <- (log(theta)+log(1-theta)-log(temp[i])-log(1-theta*(1-s[i]))+log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i],rho))*d[i]
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- 1-theta  # Cure rate
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0)

#############
#  Mixture  #
#############

model 
{
	
	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(xb[i])*pow(y[i], rho))
		logf[i] <- log(rho)+(rho-1)*log(y[i])+xb[i]-exp(xb[i])*pow(y[i], rho)  # Logarithm of Weibull probability density function

		temp[i] <- 1-theta*(2-theta)*(1-s[i])
		Sstar[i] <- p*(1-theta) / (1-theta*s[i]) + (1-p)*temp[i] / (1-theta*(1-s[i]))
		L1[i] <- log(Sstar[i])
		L2FA[i] <- pow(1-theta*s[i], -2)
		L2LA[i] <- pow(1-theta*(1-s[i]), -2)
		L2[i] <- (log(theta)+log(1-theta)-L1[i]+log(p*L2FA[i]+(1-p)*L2LA[i])+logf[i])*d[i]
				
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}
	
	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	theta ~ dunif(0, 1)
	fraction <- 1-theta  # Cure rate
	p ~ dunif(0, 1)  # Only for Mixtrue model
	
}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, theta = 0.5, rho = 1.0, p=0.5)


#############
#  Model 2  #
#############
# N ~ POI(theta)

######################
#  First Activation  #
######################

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(eta)*pow(y[i], rho))  # Weibull survival function
		theta[i] <- exp(xb[i])  # Regression on theta
		fraction[i] <- exp(-theta[i])  # Cure rate
		L1[i] <- -theta[i]*(1-s[i])  # Loglikelihood part 1 = log(S*(t))
		L2[i] <- (xb[i]+log(rho)+(rho-1)*log(y[i])+eta-exp(eta)*pow(y[i],rho))*d[i]  # Loglikelihood part 2 = delta*log(h*(t))

		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	eta ~ dnorm(0, 0.0001)

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, rho = 1.0, eta = 0.0)

#####################
#  Last Activation  #
#####################

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(eta)*pow(y[i], rho))
		theta[i] <- exp(xb[i])
		fraction[i] <- exp(-theta[i])
		temp[i] <- 1+exp(-theta[i])*(1-exp(theta[i]*(1-s[i])))
		L1[i] <- log(temp[i])
		L2[i] <- (xb[i]-theta[i]*s[i]-log(temp[i])+log(rho)+(rho-1)*log(y[i])+eta-exp(eta)*pow(y[i],rho))*d[i]

		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	eta ~ dnorm(0, 0.0001)

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, rho = 1.0, eta = 0.0)

#############
#  Mixture  #
#############

model 
{

	c <- 100000

	for (i in 1:284) 
	{
		xb[i] <- beta0+beta[1]*age[i]+beta[2]*gender[i]+beta[3]*ps[i]
		s[i] <- exp(-exp(eta)*pow(y[i], rho))
		logf[i] <- log(rho)+(rho-1)*log(y[i])+eta-exp(eta)*pow(y[i], rho)  # Logarithm of Weibull probability density function
		theta[i] <- exp(xb[i])
		fraction[i] <- exp(-theta[i])
		
		temp[i] <- 1+exp(-theta[i])-exp(-theta[i]*s[i])
		Sstar[i] <- p*exp(-theta[i]*(1-s[i])) + (1-p)*temp[i]
		L1[i] <- log(Sstar[i])
		L2FA[i] <- exp(-theta[i]*(1-s[i]))
		L2LA[i] <- exp(-theta[i]*s[i])
		L2[i] <- (xb[i]-L1[i]+log(p*L2FA[i]+(1-p)*L2LA[i])+logf[i])*d[i]
		
		# Poisson trick adopted from Minhui Chen's codes		
		zeros[i] <- 0
		mu[i] <- -L1[i]-L2[i]+c
		zeros[i] ~ dpois(mu[i])		
	}

	# Priors for parameters	
	for (i in 1:3) { beta[i] ~ dnorm(0.0, 1.0E-6) }
	beta0 ~ dnorm(0.0, 1.0E-6)
	rho ~ dgamma(2, 0.001)
	eta ~ dnorm(0, 0.0001)
	p ~ dunif(0, 1)  # Only for Mixtrue model

}

# Initial values
#Inits 
list(beta = c(0.0,0.0,0.0), beta0 = 0.0, rho = 1.0, eta = 0.0, p=0.5)


# Data
#datainput 
y[]  d[]  age[]  gender[]  ps[]
1.57808 1 -0.849108219 0 0
1.48219 1 -0.394633018 0 0
7.33425 0 1.7839389673 1 0
0.65479 1 0.8574925353 1 1
2.23288 1 -1.024911705 0 0
9.38356 0 0.0724899159 0 0
3.27671 1 -1.170149838 1 0
0.80274 1 -0.48590749 1 0
9.64384 0 -1.083512868 0 0
1.66575 1 -0.854799698 0 0
0.94247 1 -0.501927952 1 0
1.68767 1 0.770012383 0 0
5.94247 1 1.2398756587 0 0
2.34247 1 1.1566114175 0 0
0.89863 1 0.7312260022 0 1
9.03288 0 -1.849333092 1 0
9.63014 0 -2.197356541 0 0
0.52603 1 -0.444591563 0 0
1.82192 1 -1.347428893 0 0
0.93425 1 0.924736315 1 0
8.9863 0 -1.134314594 0 0
1.8274 1 0.5474122847 0 0
9.3589 0 -1.562861943 0 0
3.35068 1 -1.58099036 0 0
8.67397 1 0.6163424288 0 0
6.09589 0 -0.025530014 0 0
0.41096 1 0.6226662952 1 0
2.7863 1 -1.894654135 1 0
2.56438 1 0.2936144453 0 0
8.75342 0 0.6922288259 0 0
8.7589 0 -0.691643944 0 0
0.56986 1 0.6498589209 0 0
8.4 0 -0.445434745 0 0
7.25205 0 -1.099322534 0 0
4.3863 1 -0.129452219 0 0
8.36712 0 -0.322119349 1 0
8.99178 0 0.3136400224 0 0
0.86575 1 -1.296416371 0 0
4.76986 0 0.8979652805 1 0
1.15616 1 0.3469457189 0 0
7.28767 0 -1.525972722 0 0
3.13151 1 1.5883206991 0 0
8.28767 0 1.4283268784 1 0
8.55068 0 1.3385279751 1 0
2.21918 1 1.7573787283 0 0
8.45753 0 -0.891688919 0 0
4.59452 1 -0.852902538 0 0
2.88219 1 0.0851376487 0 0
0.89589 1 0.8907982318 0 0
1.76164 1 -0.53987115 1 0
7.8137 0 -1.617668785 0 0
8.33425 0 -0.77469739 0 0
2.62192 1 -1.625257425 1 0
0.16164 1 1.2906773858 0 0
8.24658 0 -1.333516387 1 0
1.52603 1 1.1239381075 0 1
5.30959 1 0.2278462345 0 0
4.03014 1 -0.065159577 1 0
0.87123 1 -0.763525226 0 1
0.41644 1 0.4951349889 1 0
8.39452 0 -0.511413751 0 0
4.2411 1 0.8241868388 1 0
0.13699 1 -1.375886292 0 0
7.07671 1 0.9399135944 0 1
0.13151 1 1.1018045751 1 0
8.0274 0 -1.008680448 1 1
6.16164 0 -0.295348315 0 0
1.29863 1 -0.988022484 1 0
1.29041 1 0.8733022014 1 1
7.99726 0 -1.929856991 1 0
8.34795 0 -0.916773589 0 0
7.30137 0 -1.183429957 0 1
2.32877 1 0.7046657633 0 0
0.56438 1 1.0526892124 0 0
5.6274 1 0.9080834667 1 1
1.23014 1 -0.195852816 1 0
7.94521 0 0.3155371823 1 0
1.51507 1 1.1117119658 0 1
5.06301 1 -0.985914529 0 0
3.27671 1 -0.907920176 0 0
0.60822 0 -1.099322534 1 0
0.65753 1 -0.687217238 1 0
0.8411 1 -0.096989704 0 0
8.4 0 -0.217775553 0 0
7.96712 0 -0.929842913 1 1
0.18356 1 1.8693111641 0 0
2.62466 1 0.9270550661 0 0
2.55616 1 -0.150110182 1 0
7.96438 0 -0.896115626 1 0
7.77808 0 0.847374349 1 1
0.22192 1 -0.293451155 0 0
2.33973 1 1.0358255686 0 0
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END