# Longitudinal model over time
# Emax time-course function
# Fixed treatment effects for ET50 with treatment effects exchangeable around a single mean effect
# Fixed treatment effects for Emax
# Reference treatment effect for ET50 exchangeable across studies (Equation [12] in manuscript)

model{ 			# Begin Model Code
 
for(i in 1:NS){ # Run Through all NS trials
    
	mu.Emax[i] ~ dnorm(0,0.0001)
	mu.ET50[i] ~ dnorm(m.mu,tau.mu)	# Exchangeable baseline effect for ET50 (Equation [12] in manuscript)
	delta.Emax[i,1] <- 0
	delta.ET50[i,1] <- 0
	
    for (k in 1:narm[i]){
		for (m in 1:fups[i]) {	# Run through all observations within a study	
			
			y[i,k,m] ~ dnorm(theta[i,k,m], prec[i,k,m])	# Normal likelihood
			prec[i,k,m] <- pow(se[i,k,m], -2)			
		
			theta[i,k,m] <- exp(l.E0[i,k]) + ((Emax[i,k] * time[i,m]) / (exp(l.ET50[i,k]) + time[i,m]))	# Time-course function
						
			resdev[i,k,m] <- pow((y[i,k,m] - theta[i,k,m]),2) * prec[i,k,m] # residual deviance for normal likelihood			
			dev[i,k,m] <- -2* (log(pow((prec[i,k,m]/(2*3.14159)),0.5) * exp(-0.5*(pow((y[i,k,m]-theta[i,k,m]),2)*prec[i,k,m])))) # deviance for normal likelihood
			
		}
		
		armdev[i,k] <- sum(dev[i,k,1:fups[i]])
		resarmdev[i,k] <- sum(resdev[i,k,1:fups[i]])
		
		# Relative effects for time-course parameters
		Emax[i,k] <- mu.Emax[i] + delta.Emax[i,k]
		l.ET50[i,k] <- mu.ET50[i] + delta.ET50[i,k]
		
		l.E0[i,k] ~ dnorm(0,0.0001)	# priors for baseline nuisance parameter
		
	}
	
	studydev[i] <- sum(armdev[i, 1:narm[i]])
	resstudydev[i] <- sum(resarmdev[i, 1:narm[i]])
		
	# Consistency equations
	for(k in 2:narm[i]){		
		delta.Emax[i,k] <- d.Emax[treat[i,k]] - d.Emax[treat[i,1]]
		delta.ET50[i,k] <- d.ET50[treat[i,k]] - d.ET50[treat[i,1]]
		}
		
	}
	
	d.Emax[1] <- 0
	d.ET50[1] <- 0
		
	for (k in 2:NT){
		d.Emax[k] ~ dnorm(0,0.001)	# Priors on relative treatment effects	
		d.ET50[k] ~ dnorm(m.ET50, tau.ET50)	# Exchangeable ET50 treatment effects around a single mean effect
		}

	m.ET50 ~ dnorm(0,0.001) # Prior	for mean ET50 treatment effect
	
	m.mu ~ dnorm(0,0.001)	# Prior for mean reference treatment ET50
	
	# Between-study SD for reference treatment ET50
	tau.mu <- pow(sd.mu, -2)
	sd.mu ~ dunif(0,5)
	
	# SD for all treatment effects
	tau.ET50 <- pow(sd.ET50,-2)
	sd.ET50 ~ dunif(0,5)
	
	totdev <- sum(studydev[])
	totresdev <- sum(resstudydev[])

	# Model ends
}