Bayesian Cluster Detection Method

Description

Implementation of the Bayesian Cluster detection model of Wakefield and Kim (2013) 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. Furthermore, the posterior probability of k clusters/anti-clusters is computed.

Usage

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bayes_cluster(y, E, population, sp.obj, centroids, max.prop, shape, rate, J, pi0,
         n.sim.lambda, n.sim.prior, n.sim.post, burnin.prop = 0.1,
         theta.init = vector(mode="numeric", length=0))

Arguments

y

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

E

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

population

vector of length n of the population in each area

sp.obj

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

centroids

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

max.prop

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

shape

vector of length 2 of narrow/wide shape parameter for gamma prior on relative risk

rate

vector of length 2 of narrow/wide rate parameter for gamma prior on relative risk

J

maximum number of clusters/anti-clusters

pi0

prior probability of no clusters/anti-clusters

n.sim.lambda

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

burnin.prop

proportion of MCMC samples to use as burn-in

theta.init

Initial configuration used for MCMC sampling

Value

List containing

prior.map

A list 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 estimates of relative risk

post.map

A list 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

pk.y

posterior probability of k clusters/anti-clusters given y for k=0,...,J

Author(s)

Albert Y. Kim

References

Wakefield J. and Kim A.Y. (2013) A Bayesian model for cluster detection. Biostatistics, 14, 752–765.

See Also

kulldorff

Examples

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## 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)
sp.obj <- 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]
sp.obj <-
  SpatialPolygons(sp.obj@polygons[-remove], proj4string=CRS("+proj=longlat +ellps=WGS84"))
centroids <- centroids[-remove, ]


## Set parameters
y <- cases
E <- expected(population, cases, 1)
max.prop <- 0.15
shape <- c(2976.3, 2.31)
rate <- c(2977.3, 1.31)
J <- 7
pi0 <- 0.95
n.sim.lambda <- 10^4
n.sim.prior <- 10^5
n.sim.post <- 10^5


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

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