lognormalEB {DCluster}

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

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)