model 
   {
      for(j in 1 : N) {
         for(k in 1 : T) {
            log(mu[j, k]) <- a0 + alpha.Base * (log.Base4[j] - log.Base4.bar) 
   + alpha.Trt * (Trt[j] - Trt.bar) 
   + alpha.BT * (BT[j] - BT.bar) 
   + alpha.Age * (log.Age[j] - log.Age.bar) 
   + alpha.V4 * (V4[k] - V4.bar) 
   + b1[j] + b[j, k]
            y[j, k] ~ dpois(mu[j, k])
            b[j, k] ~ dnorm(0.0, tau.b); # subject*visit random effects
         }
         b1[j] ~ dnorm(0.0, tau.b1) # subject random effects
         BT[j] <- Trt[j] * log.Base4[j] # interaction
         log.Base4[j] <- log(Base[j] / 4) log.Age[j] <- log(Age[j])
      }
      
   # covariate means:
      log.Age.bar <- mean(log.Age[]) 
      Trt.bar <- mean(Trt[]) 
      BT.bar <- mean(BT[]) 
      log.Base4.bar <- mean(log.Base4[]) 
      V4.bar <- mean(V4[]) 
   # priors:
   
      a0 ~ dnorm(0.0,1.0E-4)       
      alpha.Base ~ dnorm(0.0,1.0E-4) 
      alpha.Trt ~ dnorm(0.0,1.0E-4); 
      alpha.BT ~ dnorm(0.0,1.0E-4) 
      alpha.Age ~ dnorm(0.0,1.0E-4) 
      alpha.V4 ~ dnorm(0.0,1.0E-4)
      tau.b1 ~ dgamma(1.0E-3,1.0E-3); sigma.b1 <- 1.0 / sqrt(tau.b1)
      tau.b ~ dgamma(1.0E-3,1.0E-3); sigma.b <- 1.0/ sqrt(tau.b)      
      
   # re-calculate intercept on original scale: 
      alpha0 <- a0 - alpha.Base * log.Base4.bar - alpha.Trt * Trt.bar 
      - alpha.BT * BT.bar - alpha.Age * log.Age.bar - alpha.V4 * V4.bar
   }