epi.empbayes {epiR} R Documentation

## Empirical Bayes estimates of observed event counts

### Description

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

### Usage

```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

```## 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)
```

[Package epiR version 2.0.31 Index]