model 
    {
       for (i in 1 : N) {
         x[i] ~ dbern(q) # incidence of HSV
         logit(p[i]) <- beta0C + beta * x[i]   # logistic model
         d[i] ~ dbern(p[i]) # incidence of cancer
         x1[i] <- x[i] + 1 
         d1[i] <- d[i] + 1 
         w[i] ~ dbern(phi[x1[i], d1[i]])   # incidence of w
      } 
      q ~ dunif(0.0, 1.0) # prior distributions
      beta0C ~ dnorm(0.0, 0.00001);
      beta ~ dnorm(0.0, 0.00001);
      for(j in 1 : 2) {
         for(k in 1 : 2){
            phi[j, k] ~ dunif(0.0, 1.0)
         }
       }
    # calculate gamma1 = P(x=1|d=0) and gamma2 = P(x=1|d=1) 
       gamma1 <- 1 / (1 + (1 + exp(beta0C + beta)) / (1 + exp(beta0C)) * (1 - q) / q)
       gamma2 <- 1 / (1 + (1 + exp(-beta0C - beta)) / (1 + exp(-beta0C)) * (1 - q) / q)
   }