model { for (i in 1 : N) { y[i] ~ dpois(mu[i]) # Poisson likelihood for observed counts log(mu[i]) <- log(e[i])+alpha+beta[smoke[i]]+phi[i]+nu[i] phi[i] ~ dnorm(0, tau.phi) # normal prior for spatially unstructured effects rho[i] <- exp(alpha+beta[smoke[i]]+phi[i]+nu[i]) # relative risks compared to reference rate rholocaladj[i] <- exp(phi[i]+nu[i]) # relative risks compared to overall risk in study area after adjusting for smoking } nu[1:N] ~ car.normal(adj[],weights[],num[],tau.nu) #CAR prior for spatially structured effects alpha ~ dflat() # locally uniform prior for mean log relative risk beta[1] <- 0 # set level 1 of smoking to be the reference category beta[2] ~ dnorm(0, 0.0001) # diffuse normal prior for beta[2] beta[3] ~ dnorm(0, 0.0001) # diffuse normal prior for beta[3] tau.phi ~ dgamma(0.5, 0.0005) # diffuse gamma hyperprior for tau.phi tau.nu ~ dgamma(0.5, 0.0005) # diffuse gamma hyperprior for tau.nu sigma.phi <- sqrt(1/tau.phi) # st dev of prior for spatially unstructured effects sigma.nu <- sqrt(1/tau.nu) # st dev of prior for spatially structured effects mu.pred53 <- exp(log(e[53])+alpha+beta[1]+phi[53]+nu[53]) # predict mean in 53 with smoking level 1 y.pred53 ~ dpois(mu.pred53) # predict individual value in 53 with smoking level 1 y.diff53 <- y[53] - y.pred53 # predict excess cases in 53 due to smoking P.diff53 <- step(y.diff53-15) # predict probability that reducing smoking in 53 would reduce cases by 15 or more }