# Longitudinal model over time
# Exponential time-course function
# Random treatment effects

model{ 			# Begin Model Code
 
for(i in 1:NS){ # Run Through all NS trials
    
	mu[i] ~ dnorm(0,0.0001)
	delta[i,1] <- 0
	
	# Prior on baseline nuisance parameter
	lambda0[i] <- exp(loglambda0[i])
	loglambda0[i] ~ dnorm(0,0.0001)
	w[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] <- lambda0[i] * exp(lambda1[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
			
		}
		
		lambda1[i,k] <- mu[i] + delta[i,k]	# Relative effects for time-course parameters
		
		resarmdev[i,k] <- sum(resdev[i,k,1:fups[i]])
		armdev[i,k] <- sum(dev[i,k,1:fups[i]])
		
	}
	
	resstudydev[i] <- sum(resarmdev[i, 1:narm[i]])
	studydev[i] <- sum(armdev[i, 1:narm[i]])
		
	for(k in 2:narm[i]){
		
		# Random effects
		delta[i,k] ~ dnorm(md[i,k], taud[i,k])
		md[i,k] <- d[treat[i,k]] - d[treat[i,1]] + sw[i,k]		# Consistency equation
		
		# Multi-arm correction
		taud[i,k] <- tau * 2*(k-1)/k 
		w[i,k] <- (delta[i,k] - d[treat[i,k]] + d[treat[i,1]])
		sw[i,k] <- sum(w[i,1:(k-1)])/(k-1)
			
		}
		
	}
	
	d[1] <- 0
		
	for (k in 2:NT){
		d[k] ~ dnorm(0,0.0001)	# Priors on relative treatment effects	
		}
		
	totresdev <- sum(resstudydev[])
	totdev <- sum(studydev[])
	
	# Prior on between-study SD
	sd ~ dunif(0,10)
	tau <- pow(sd, -2)
	
	# Model ends
}