DCluster (version 0.2-10)

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)

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.

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.

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

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)