# Longitudinal model over time
# Emax time-course function
# Random treatment effects for ET50
# Random treatment effects for Emax
# Bivariate correlation between ET50 and Emax treatment effects 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)
		
		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
				
			}
			
			resarmdev[i,k] <- sum(resdev[i,k,1:fups[i]])
			armdev[i,k] <- sum(dev[i,k,1:fups[i]])
		}
		
		# Reference treatment effects
		Emax[i,1] <- mu.Emax[i] 
		l.ET50[i,1] <- mu.ET50[i]
		
		for (k in 2:narm[i]) {
			# Relative effects for time-course parameters
			Emax[i,k] <- mu.Emax[i] + delta[i,(k-1)]
			l.ET50[i,k] <- mu.ET50[i] + delta[i,((k-1)*2)]
			
			# Consistency equations
			md[i,(k-1)] <- d.Emax[treat[i,k]] - d.Emax[treat[i,1]]
			md[i,((narm[i]-1)+k-1)] <- d.ET50[treat[i,k]] - d.ET50[treat[i,1]]
		}
		
		resstudydev[i] <- sum(resarmdev[i, 1:narm[i]])
		studydev[i] <- sum(armdev[i, 1:narm[i]])
		
		# Generate matrix of relative effects (uses dmnorm.vcov function from JAGS 4.3.0)
		delta[i,1:((narm[i]-1)*2)] ~ dmnorm.vcov(md[i,1:((narm[i]-1)*2)], cov.mat[i,1:((narm[i]-1)*2),1:((narm[i]-1)*2)])
		
		# Covariance matrix diagonals
		for (r in 1:(narm[i]-1)) {
			cov.mat[i,r,r] <- pow(sd.Emax,2)
		}

		for (r in (1+(narm[i]-1)):((narm[i]-1)*2)) {
			cov.mat[i,r,r] <- pow(sd.ET50,2)
		}
		
	}

	
	#### Covariance matrix for 2-arm studies
	for (i in (NS.mult+1):NS) {	
		cov.mat[i,1,2] <- sd.Emax * sd.ET50 * rho		# Upper triangle
		cov.mat[i,2,1] <- cov.mat[i,1,2]				# Lower triangle
	}
	
	#### Covariance matrix upper triangle for multi-arm studies
	for (i in 1:NS.mult) {

		# Upper triangle - Covariances within outcome between arms (multi-arm correction)
		for (c in 1:(narm[i]-2)) {
			for (r in (c+1):(narm[i]-1)) {
				cov.mat[i,c,r] <- pow(sd.Emax,2) * 0.5
			}
		}
		
		for (c in (narm[i]):((2*narm[i])-3)) {
			for (r in (c+1):((narm[i]-1)*2)) {
				cov.mat[i,c,r] <- pow(sd.ET50,2) * 0.5
			}
		}
		
		
		# Upper triangle - Covariances between-outcome within-arms
		for (c in 1:(narm[i]-1)) {
			cov.mat[i,c,(c+narm[i]-1)] <- 2* rho * sd.Emax * sd.ET50
		}
		
		
		# Upper triangle - Covariances between-outcome between-arms
		for (c in 1:(narm[i]-2)) {
			for (r in (c+narm[i]):((narm[i]-1)*2)) {
				cov.mat[i,c,r] <- rho * sd.Emax * sd.ET50 # Top upper diagonal
			}
		}

		for (c in 2:(narm[i]-1)) {
			for (r in (narm[i]):(narm[i]-2+c)) {
				cov.mat[i,c,r] <- rho * sd.Emax * sd.ET50 # Bottom upper diagonal
			}
		}
		
		
		# Lower triangle
		for (c in 1:((2*narm[i])-3)) {
			for (r in (c+1):((narm[i]-1)*2)) {
				cov.mat[i,r,c] <- cov.mat[i,c,r]
			}
		}
			
	}
		
		
	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 SDs
	sd.Emax ~ dunif(0,2)
	tau.Emax <- pow(sd.Emax, -2)
	
	sd.ET50 ~ dunif(0,2)
	tau.ET50 <- pow(sd.ET50, -2)
	
	# Prior on correlation between Emax and ET50
	rho ~ dunif(-1,1)
	
	totresdev <- sum(resstudydev[])
	totdev <- sum(studydev[])

	# Model ends
}