lognormalEB: Empirical Bayes Smoothing Using a log-Normal Model
In DCluster: Functions for the Detection of Spatial Clusters of Diseases

Description Usage Arguments Value References Examples

Smooth relative risks from a set of expected and observed number of cases using a log-Normal model as proposed by Clayton and Kaldor (1987). There are estimated by betatilde_i =log((O_i+1/2)/E_i) in order to prevent taking the logarithm of zero.

If this case, the log-relative risks are assumed be independant and to have a normal distribution with mean \varphi and variance sigma2. Clayton y Kaldor (1987) use the EM algorithm to develop estimates of these two parameters which are used to compute the Empirical Bayes estimate of b_i. The formula is not listed here, but it can be consulted in Clayton and Kaldor (1987).

1	lognormalEB(Observed, Expected, maxiter = 20, tol = 1e-05)

`Observed`	Vector of observed cases.
`Expected`	Vector of expected cases.
`maxiter`	Maximum number of iterations allowed.
`tol`	Tolerance used to stop the iterative procedure.

A list of four elements:

`n`	Number of regions.
`phi`	Estimate of phi.
`sigma2`	Estimate of sigma2.
`smthrr`	Vector of smoothed relative risks.

Clayton, David and Kaldor, John (1987). Empirical Bayes Estimates of Age-standardized Relative Risks for Use in Disease Mapping. Biometrics 43, 671-681.

library(spdep)

data(nc.sids)

sids<-data.frame(Observed=nc.sids$SID74)
sids<-cbind(sids, Expected=nc.sids$BIR74*sum(nc.sids$SID74)/sum(nc.sids$BIR74))

smth<-lognormalEB(sids$Observed, sids$Expected)