Kulldorff spatial cluster detection method for a study region with n
areas. The method constructs zones by consecutively aggregating nearestneighboring areas until a proportion of the total study population is included. Given the observed number of cases, the likelihood of each zone is computed using either binomial or poisson likelihoods. The procedure reports the zone that is the most likely cluster and generates significance measures via Monte Carlo sampling. Further, secondary clusters, whose Monte Carlo pvalues are below the αthreshold, are reported as well.
1 2 
geo 
an 
cases 
aggregated case counts for all 
population 
aggregated population counts for all 
expected.cases 
expected numbers of disease for all 
pop.upper.bound 
the upper bound on the proportion of the total population each zone can include 
n.simulations 
number of Monte Carlo samples used for significance measures 
alpha.level 
alphalevel threshold used to declare significance 
plot 
flag for whether to plot histogram of Monte Carlo samples of the loglikelihood of the most likely cluster 
If expected.cases
is specified to be NULL
, then the binomial likelihood is used. Otherwise, a Poisson model is assumed. Typical values of n.simulations
are 99
, 999
, 9999
...
List containing:
most.likely.cluster 
information on the most likely cluster 
secondary.clusters 
information on secondary clusters, if none 
type 
type of likelihood 
log.lkhd 
loglikelihood of each zone considered 
simulated.log.lkhd 

The most.likely.cluster
and secondary.clusters
list elements are themselves lists reporting:
location.IDs.included  ID's of areas in cluster, in order of distance 
population  population of cluster 
number.of.cases  number of cases in cluster 
expected.cases  expected number of cases in cluster 
SMR  estimated SMR of cluster 
log.likelihood.ratio  loglikelihood of cluster 
monte.carlo.rank  rank of lkhd of cluster within Monte Carlo simulated values 
p.value  Monte Carlo pvalue 
Albert Y. Kim
SatScan: Software for the spatial, temporal, and spacetime scan statistics http://www.satscan.org/ Kulldorff, M. (1997) A spatial scan statistic. Communications in Statistics: Theory and Methods, 26, 1481–1496.
Kulldorff M. and Nagarwalla N. (1995) Spatial disease clusters: Detection and Inference. Statistics in Medicine, 14, 799–810.
pennLC
, expected
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 32 33 34 35 36 37 38 39 40 41  ## Load Pennsylvania Lung Cancer Data
data(pennLC)
data < pennLC$data
## Process geographical information and convert to grid
geo < pennLC$geo[,2:3]
geo < latlong2grid(geo)
## Get aggregated counts of population and cases for each county
population < tapply(data$population,data$county,sum)
cases < tapply(data$cases,data$county,sum)
## Based on the 16 strata levels, computed expected numbers of disease
n.strata < 16
expected.cases < expected(data$population, data$cases, n.strata)
## Set Parameters
pop.upper.bound < 0.5
n.simulations < 999
alpha.level < 0.05
plot < TRUE
## Kulldorff using Binomial likelihoods
binomial < kulldorff(geo, cases, population, NULL, pop.upper.bound, n.simulations,
alpha.level, plot)
cluster < binomial$most.likely.cluster$location.IDs.included
## plot
plot(pennLC$spatial.polygon,axes=TRUE)
plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red")
title("Most Likely Cluster")
## Kulldorff using Poisson likelihoods
poisson < kulldorff(geo, cases, population, expected.cases, pop.upper.bound,
n.simulations, alpha.level, plot)
cluster < poisson$most.likely.cluster$location.IDs.included
## plot
plot(pennLC$spatial.polygon,axes=TRUE)
plot(pennLC$spatial.polygon[cluster],add=TRUE,col="red")
title("Most Likely Cluster Controlling for Strata")

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