Research Article
Administrative Censoring in Ecological Analyses of Autism and a Bayesian Solution
model { | for (i in 1:counties) { | b0[i] ~ dnorm(0,tau) | } | for (j in 1:districts){ | zeros[j] < − 0 | phiobs[j] < − lam[j] − y[j] * log(lam[j]) + 10000 | phicens[j] < − lam[j] − log(pow(lam[j],4)/24 + pow(lam[j],3)/6 + pow(lam[j],2)/2 | + lam[j] ) + 10000 | # use zeros method for censored for counts between 1 and 4 (see WinBUGS manual) | # y[j] is autism count for district j. Note that censored values are recorded as − 999. | phi[j] < − step(y[j]) * phiobs[j] + (1− step(y[j])) * phicens[j] | zeros[j] ~ dpois(phi[j]) | lam[j] < − exp(mu + b0[county[j]] + b[1]*airChem[j] + b[2]*white[j] + b[3]*taxbase[j] + | b[4]*econ[j] + b[5]*urban[j] + b[6]*suburban[j] + b[7]*other[j] + log(students[j])) | } | # Note that WinBUGS uses precision not variance to define normal distributions | mu ~ dnorm(− 6,0.1) | b[1] ~ dnorm(0,0.01) | b[2] ~ dnorm(0,0.01) | b[3] ~ dnorm(0,0.01) | b[4] ~ dnorm(0,0.01) | b[5] ~ dnorm(0,0.01) | b[6] ~ dnorm(0,0.01) | b[7] ~ dnorm(0,0.01) | tau < − 1/var | var ~ dunif(0,50) | RR < − exp(b[1]) |
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