DCluster (version 0.2-7)

lognormalEB: Empirical Bayes Smoothing Using a log-Normal Model

Description

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 \(\tilde{\beta}_i =\log((O_i+1/2)/E_i)\) 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 \(\sigma^2\). 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).

Usage

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

Arguments

Observed

Vector of observed cases.

Expected

Vector of expected cases.

maxiter

Maximum number of iterations allowed.

tol

Tolerance used to stop the iterative procedure.

Value

A list of four elements:

n

Number of regions.

phi

Estimate of \(\varphi\).

sigma2

Estimate of \(\sigma^2\).

smthrr

Vector of smoothed relative risks.

References

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

Examples

# NOT RUN {
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)
# }