EBpostthresh {SpatialEpi}

Produce the probabilities of exceeding a threshold given a posterior gamma distribution.

Description

This function produces the posterior probabilities of exceeding a threshold given a gamma distributions with parameters (alpha+Y, (alpha+E*mu)/mu) where mu = exp(x beta). This model arises from Y being Poisson with mean theta times E where theta is the relative risk and E are the expected numbers. The prior on theta is gamma with parameters alpha and beta. The parameters alpha and beta may be estimated using empirical Bayes.

Usage

EBpostthresh(Y, E, alpha, beta, Xrow = NULL, rrthresh)

Arguments

Y

observed disease counts

E

expected disease counts

alpha

x

beta

x

Xrow

x

rrthresh

x

Value

Posterior probabilities of exceedence are returned.

Author(s)

Jon Wakefield

See Also

eBayes()

Examples

data(scotland)
Y <- scotland$data$cases
E <- scotland$data$expected
ebresults <- eBayes(Y,E)
#Find probabilities of exceedence of 3
thresh3 <- EBpostthresh(Y, E, alpha=ebresults$alpha, beta=ebresults$beta, rrthresh=3)
mapvariable(thresh3, scotland$spatial.polygon)