bayes.cluster: Bayesian Cluster Detection

Description

Implementation of the Bayesian Cluster detection model of Wakefield and Kim for a study region with n areas. The prior and posterior probabilities of each of the n.zones single zones being a cluster/anti-cluster are estimated using Markov chain Monte Carlo.

Usage

bayes.cluster(E, cases, population, centroids, map, max.prop, k, shape, rate, J, pi0, n.sim.imp, n.sim.prior, n.sim.post)

Arguments

vector of length n of the expected number of disease in each area

cases

vector of length n of the observed number of disease in each area

population

vector of length n of the population in each area

centroids

an n x 2 table of the (x,y)-coordinates of the area centroids. The coordinate system must be grid-based

map

an object of class SpatialPolygons (See SpatialPolygons-class) representing the study region

max.prop

maximum proportion of study region's population each single zone can contain

parameter to tune the prior probability of each single zone being a cluster/anti-cluster as a function of geographical area size

shape

narrow/wide shape parameter for gamma prior on relative risk

rate

narrow/wide rate parameter for gamma prior on relative risk

maximum number of clusters/anti-clusters considered

pi0

prior probability of no clusters/anti-clusters i.e. probability that J=0

n.sim.imp

number of importance sampling iterations to estimate lambda

n.sim.prior

number of MCMC iterations to estimate prior probabilities associated with each single zone

n.sim.post

number of MCMC iterations to estimate posterior probabilities associated with each single zone

Value

List containing
prior.mapA sublist containing, for each area: 1) high.area the prior probability of cluster membership, 2) low.area anti-cluster membership, and 3) RR.est.area smoothed prior estimate of relative risk
post.mapA sublist containing, for each area: 1) high.area the posterior probability of cluster membership, 2) low.area anti-cluster membership, and 3) RR.est.area smoothed posterior estimates of the relative risk
pj.yposterior probability of j clusters/anti-clusters given y

References

Wakefield, J. and Kim, A.y. (2012) A Bayesian Model for Cluster Detection

Examples

Run this code

## Note for the NYleukemia example, 4 census tracts were completely surrounded by another 
## unique census tract; when applying the Bayesian cluster detection model in 
## \code{\link{bayes.cluster}}, we merge them with the surrounding census tracts yielding 
## \code{n=277} areas.

## Load data and convert coordinate system from latitude/longitude to grid
data(NYleukemia)
map <- NYleukemia$spatial.polygon
population <- NYleukemia$data$population
cases <- NYleukemia$data$cases
centroids <- latlong2grid(NYleukemia$geo[, 2:3])

## Identify the 4 census tract to be merged into their surrounding census tracts.  
remove <- NYleukemia$surrounded
add <- NYleukemia$surrounding

## Merge population and case counts and geographical objects accordingly
population[add] <- population[add] + population[remove]
population <- population[-remove]
cases[add] <- cases[add] + cases[remove]
cases <- cases[-remove]
map <- SpatialPolygons(map@polygons[-remove], proj4string=CRS("+proj=longlat"))
centroids <- centroids[-remove, ]

## Expected numbers
E <- expected(population, cases, 1)

## Set Parameters
max.prop <- 0.15
k <- 0.00005
shape <- c(2976.3, 2.31); rate <- c(2977.3, 1.31)
J <- 7
pi0 <- 0.95
n.sim.imp <- 0.5*10^4
n.sim.prior <- 0.5*10^4
n.sim.post <- 0.5*10^5

## (Uncomment first) Compute output
# output <- bayes.cluster(E, cases, population, centroids, map, max.prop, k, 
# 	shape, rate, J, pi0, n.sim.imp, n.sim.prior, n.sim.post)
# plotmap(output$prior.map$high.area, map)
# plotmap(output$post.map$high.area, map)
# plotmap(output$post.map$RR.est.area, map, log=TRUE)
# barplot(output$pj.y, names.arg=0:J, xlab="j", ylab="P(j|y)")