# epi.empbayes: Empirical Bayes estimates of observed event counts In epiR: Tools for the Analysis of Epidemiological Data

## Description

Computes empirical Bayes estimates of observed event counts using the method of moments.

## Usage

 `1` ```epi.empbayes(obs, pop) ```

## Arguments

 `obs` a vector representing the observed event counts in each unit of interest. `pop` a vector representing the population count in each unit of interest.

## Details

The gamma distribution is parameterised in terms of shape (α) and scale (ν) parameters. The mean of a given gamma distribution equals ν / α. The variance equals ν / α^{2}. The empirical Bayes estimate of event risk in each unit of interest equals (obs + ν) / (pop + α).

This technique performs poorly when your data contains large numbers of zero event counts. In this situation a Bayesian approach for estimating α and ν would be advised.

## Value

A data frame with four elements: `gamma` the mean event risk across all units, `phi` the variance of event risk across all units, `alpha` the estimated shape parameter of the gamma distribution, and `nu` the estimated scale parameter of the gamma distribution.

## References

Bailey TC, Gatrell AC (1995). Interactive Spatial Data Analysis. Longman Scientific & Technical. London, pp. 303 - 308.

Langford IH (1994). Using empirical Bayes estimates in the geographical analysis of disease risk. Area 26: 142 - 149.

Meza J (2003). Empirical Bayes estimation smoothing of relative risks in disease mapping. Journal of Statistical Planning and Inference 112: 43 - 62.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```## EXAMPLE 1: data(epi.SClip) obs <- epi.SClip\$cases; pop <- epi.SClip\$population est <- epi.empbayes(obs, pop) crude.p <- ((obs) / (pop)) * 100000 crude.r <- rank(crude.p) ebay.p <- ((obs + est) / (pop + est)) * 100000 dat.df01 <- data.frame(rank = c(crude.r, crude.r), Method = c(rep("Crude", times = length(crude.r)), rep("Empirical Bayes", times = length(crude.r))), est = c(crude.p, ebay.p)) ## Scatter plot showing the crude and empirical Bayes adjusted lip cancer ## incidence rates as a function of district rank for the crude lip ## cancer incidence rates: ## Not run: library(ggplot2) ggplot(dat = dat.df01, aes(x = rank, y = est, colour = Method)) + geom_point() + scale_x_continuous(name = "District rank", breaks = seq(from = 0, to = 60, by = 10), labels = seq(from = 0, to = 60, by = 10), limits = c(0,60)) + scale_y_continuous(limits = c(0,30), name = "Lip cancer incidence rates (cases per 100,000 person years)") ## End(Not run) ```

epiR documentation built on Oct. 11, 2021, 9:08 a.m.