# Longitudinal model over time
# Piecewise linear time-course function
# Fixed treatment effects for beta.1
# Fixed treatment effects for beta.2

# "piece" is a variable that denotes which linear piece a time point belongs to, with values at each time point in each study that takes 1 if the time is before the knot and 2 if located after (calculated outside of JAGS using a predetermined knot)
# "knot" is a variable that contains the time point at which the knot between the two linear pieces is located

model{ 			# Begin Model Code
 
for(i in 1:NS){ # Run Through all NS trials
    
	mu.1[i] ~ dnorm(0,0.0001)
	delta.1[i,1] <- 0
	
	mu.2[i] ~ dnorm(0,0.0001)
	delta.2[i,1] <- 0	
	
	alpha.1[i] ~ dnorm(0,0.0001)	# prior for baseline nuisance parameter
	
    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] <- (equals(piece[i,m],1) * alpha.1[i]) + (equals(piece[i,m],1) * (beta.1[i,k]*time[i,m]))		+		(equals(piece[i,m],2) * (alpha.2[i,k])) + (equals(piece[i,m],2) * (beta.2[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
			
		}
		
		# Relative effects for time-course parameters
		beta.1[i,k] <- mu.1[i] + delta.1[i,k]
		beta.2[i,k] <- mu.2[i] + delta.2[i,k]
		
		alpha.2[i,k] <- alpha.2[i] + (beta.2[i,k]*knot)	# Intercept for second linear piece
		
		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]])
		
	# Consistency equations
	for(k in 2:narm[i]){
		delta.1[i,k] <- d.1[treat[i,k]] - d.1[treat[i,1]]
		delta.2[i,k] <- d.2[treat[i,k]] - d.2[treat[i,1]]
		}
		
	}
	
	d.1[1] <- 0
	d.2[1] <- 0
	
	# Priors on relative treatment effects	
	for (k in 2:NT){
		d.1[k] ~ dnorm(0,0.001)
		d.2[k] ~ dnorm(0,0.001)
		}
		
	totresdev <- sum(resstudydev[])
	totdev <- sum(studydev[])
	
	# Model ends
}