Manuscript entitled: "Bayesian meta-analysis models for microarray data: a 
comparative study"

Authors: Erin M Conlon, Joon J Song, Anna Liu

The following is the WinBUGS code for the standardized expression integration
(SEI) model for two studies. The parameter T corresponds to the parameter D in 
the manuscript. The posterior mean of T is used as the basis for inference. The 
dgamma(alpha, beta) distribution for the precision of the Normal distribution 
is equivalent to a scaled inverse chi-squared distribution for the variance 
with parameters (alpha = nu/2, beta = nu/2 * s.squared), where nu = degrees 
of freedom and s.squared = scale parameter.


model
        {
		for ( i in 1:N ) {		
		
		y[1,i] ~ dnorm(xi[1,i], phi1.squared[i])

		y[2,i] ~ dnorm(xi[1,i], phi1.squared[i])
		y[3,i] ~ dnorm(xi[1,i], phi1.squared[i])
		xi[1,i] ~ dnorm(theta1[i], sigma1.squared[i])
		
		y[4,i] ~ dnorm(xi[2,i], phi1.squared[i])
		xi[2,i] ~ dnorm(theta1[i], sigma1.squared[i])
		
		y[5,i] ~ dnorm(xi[3,i], phi1.squared[i])
		xi[3,i] ~ dnorm(theta1[i], sigma1.squared[i])
		
		y[6,i] ~ dnorm(xi[4,i], phi2.squared[i])
		y[7,i] ~ dnorm(xi[4,i], phi2.squared[i])
		xi[4,i] ~ dnorm(theta2[i], sigma2.squared[i])
		
		y[8,i] ~ dnorm(xi[5,i], phi2.squared[i])
		xi[5,i] ~ dnorm(theta2[i], sigma2.squared[i])
		
		y[9,i] ~ dnorm(xi[6,i], phi2.squared[i])
		xi[6,i] ~ dnorm(theta2[i], sigma2.squared[i])		
		
                theta1[i] ~ dnorm(mu[i], tau.squared[i])
                theta2[i] ~ dnorm(mu[i], tau.squared[i])
 	
                tau.squared[i] <- 1/taus.squared[T1[i],i]	 
	
                taus.squared[1,i] ~ dunif(lower1, upper1)
                taus.squared[2,i] ~ dunif(lower2, upper2)
	
                mu[i] ~ dnorm(0, eta.squared[i])
	
                eta.squared[i] <- etas.squared[T1[i]]  
       
                T[i] ~ dbern(p)
                T1[i] <- T[i] + 1
                 
                }
  
                p~dbeta(1,1)

		for ( i in 1:N ){

		phi1.squared[i] ~ dgamma(h/2, h/2 * phi1.tilde.squared) 
		phi2.squared[i] ~ dgamma(h/2, h/2 * phi2.tilde.squared) 

		sigma1.squared[i] ~ dgamma(k/2, k/2 * sigma1.tilde.squared) 
		sigma2.squared[i] ~ dgamma(k/2, k/2 * sigma2.tilde.squared) 

		}
			 
                eta1.squared ~ dgamma(a/2, a/2 * s1.squared)
  
                etas.squared[1] <- eta1.squared
                etas.squared[2] <- eta1.squared * c
                c ~ dgamma(b/2, b/2 * s2.squared)

        }


The following are sample data, where the rows = slides and
the columns = genes.  The first 5 slides are for Study 1 as 
follows: slides 1-3 are for experiment 1, slide 4 is for 
experiment 2 and slide 5 is for experiment 3. Slides 6-9 are 
for Study 2 as follows: slides 6 and 7 are for experiment 1, 
slide 8 is for experiment 2 and slide 9 is for experiment 3.


         y[ ,1]    y[ ,2]    y[ ,3]    y[ ,4]   ...   y[ ,N]

y[1, ]  0.702716  1.151031  1.033856  1.385349  ...  1.043028
y[2, ]  1.095491  0.976146  1.350054  1.368257  ...  0.845897
y[3, ]  1.354985  1.358365  1.158088  1.041808	...  1.224347
y[4, ]  0.749297  1.018893  1.146190  1.489410	...  0.997665
y[5, ]  1.026909  1.153235  1.270153  1.397205	...  1.462478
y[6, ]  1.234977  1.049516  1.014355  0.298656	...  1.889275
y[7, ]  1.118606  1.287329  0.827385  0.669852  ...  1.492056
y[8, ]  1.293059  1.079623  0.776515  0.609285	...  1.238171
y[9, ]  1.408793  1.324384  0.613495  0.091526	...  1.362053