# Longitudinal model over time
# Emax time-course function
# Fixed treatment effects for ET50
# Random treatment effects for Emax with multi-arm correction

model{ 			# Begin Model Code
 
for(i in 1:NS){ # Run Through all NS trials
    
	l.E0[i] ~ dnorm(0,0.0001)	# prior for baseline nuisance parameter
	mu.Emax[i] ~ dnorm(0,0.0001)
	mu.ET50[i] ~ dnorm(0,0.0001)
	delta.Emax[i,1] <- 0
	w.Emax[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]) + (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]
	}
	
	studydev[i] <- sum(armdev[i, 1:narm[i]])
	resstudydev[i] <- sum(resarmdev[i, 1:narm[i]])
	
	# Consistency equations
	for(k in 2:narm[i]){
		
		# Random effects for Emax
		delta.Emax[i,k] ~ dnorm(md.Emax[i,k], taud.Emax[i,k])
		md.Emax[i,k] <- d.Emax[treat[i,k]] - d.Emax[treat[i,1]]	+ sw.Emax[i,k]
		
		# Fixed effects for ET50
		delta.ET50[i,k] <- d.ET50[treat[i,k]] - d.ET50[treat[i,1]]
		
		# Multi-arm correction
		taud.Emax[i,k] <- tau.Emax * 2*(k-1)/k 
		w.Emax[i,k] <- (delta.Emax[i,k] - d.Emax[treat[i,k]] + d.Emax[treat[i,1]])
		sw.Emax[i,k] <- sum(w.Emax[i,1:(k-1)])/(k-1)
			
		}
		
	}
	
	d.Emax[1] <- 0
	d.ET50[1] <- 0
	
	# Priors on relative treatment effects	
	for (k in 2:NT){
		d.Emax[k] ~ dnorm(0,0.001)
		d.ET50[k] ~ dnorm(0,0.001)
		}
	
	# Priors on between-study SD
	sd.Emax ~ dunif(0,2)
	tau.Emax <- pow(sd.Emax, -2)
	
	totdev <- sum(studydev[])
	totresdev <- sum(resstudydev[])
		
	# Model ends
}