Description Usage Arguments Details Value References Examples

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

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

`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. |

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.

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.

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.

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[4]) / (pop + est[3])) * 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)
``` |

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