epi.empbayes {epiR} | R Documentation |
Computes empirical Bayes estimates of observed event counts using the method of moments.
epi.empbayes(obs, pop)
obs |
a vector representing the observed disease counts in each region of interest. |
pop |
a vector representing the population count in each region of interest. |
The gamma distribution is sometimes parameterised in terms of shape and rate parameters. The rate parameter equals the inverse of the scale parameter. The mean of the distribution equals delta / α. The variance of the distribution equals delta / α^{2}. The empirical Bayes estimate of the proportion affected in each area equals (obs + delta) / (pop + α).
A data frame with four elements: gamma
: mean observed event count, phi
: variance of observed event count, alpha
: shape parameter of gamma distribution, and delta
: scale parameter of gamma distribution.
Bailey TC, Gatrell AC (1995). Interactive Spatial Data Analysis. Longman Scientific & Technical. London.
Langford IH (1994). Using empirical Bayes estimates in the geographical analysis of disease risk. Area 26: 142 - 149.
data(epi.SClip) obs <- epi.SClip$cases pop <- epi.SClip$population est <- epi.empbayes(obs, pop) empbayes.prop <- (obs + est[4]) / (pop + est[3]) raw.prop <- (obs) / (pop) rank <- rank(raw.prop) dat <- as.data.frame(cbind(rank, raw.prop, empbayes.prop)) plot(dat$rank, dat$raw.prop, type = "n", xlab = "Rank", ylab = "Proportion") points(dat$rank, dat$raw.prop, pch = 16, col = "red") points(dat$rank, dat$empbayes.prop, pch = 16, col = "blue") legend(5, 0.00025, legend = c("Raw estimate", "Bayes adjusted estimate"), col = c("red","blue"), pch = c(16,16), bty = "n")