EBest function

Global Empirical Bayes estimator

The function computes global empirical Bayes estimates for rates "shrunk" to the overall mean.

EBest(n, x, family="poisson")

Arguments

• n: a numeric vector of counts of cases
• x: a numeric vector of populations at risk
• family: either "poisson" for rare conditions or "binomial" for non-rare conditions

Details

Details of the implementation for the "poisson" family are to be found in Marshall, p. 284--5, and Bailey and Gatrell p. 303--306 and exercise 8.2, pp. 328--330. For the "binomial" family, see Martuzzi and Elliott (implementation by Olaf Berke).

Returns

A data frame with two columns: - raw: a numerical vector of raw (crude) rates

• estmm: a numerical vector of empirical Bayes estimates

and a parameters attribute list with components:

• a: global method of moments phi value

• m: global method of moments gamma value

References

Marshall R M (1991) Mapping disease and mortality rates using Empirical Bayes Estimators, Applied Statistics, 40, 283--294; Bailey T, Gatrell A (1995) Interactive Spatial Data Analysis, Harlow: Longman, pp. 303--306, Martuzzi M, Elliott P (1996) Empirical Bayes estimation of small area prevalence of non-rare conditions, Statistics in Medicine 15, 1867--1873.

Author(s)

Roger Bivand Roger.Bivand@nhh.no and Olaf Berke, Population Medicine, OVC, University of Guelph, CANADA

See Also

EBlocal, probmap, EBImoran.mc

Examples

auckland <- st_read(system.file("shapes/auckland.gpkg", package="spData")[1], quiet=TRUE)
res <- EBest(auckland$M77_85, 9*auckland$Und5_81)
attr(res, "parameters")
auckland$estmm000 <- res$estmm*1000
plot(auckland[,"estmm000"], breaks=c(0,2,2.5,3,3.5,5),
 main="Infant mortality per 1000 per year")
data(huddersfield, package="spData")
res <- EBest(huddersfield$cases, huddersfield$total, family="binomial")
round(res[,1:2],4)*100