Administrative Censoring in Ecological Analyses of Autism and a Bayesian Solution

Algorithm 1

WinBUGS code.

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])

}