echepoi {echelon}

Echelon spatial scan statistic based on Poisson model

Description

echepoi detects spatial clusters using echelon spatial scan statistic based on Poisson model.

Usage

echepoi(echelon.obj, cas, pop = NULL, ex = NULL, K = length(cas)/2, n.sim = 99,
        cluster.type = "high", cluster.legend.pos = "bottomleft",
        dendrogram = TRUE, cluster.info = FALSE, coo = NULL, ...)

Arguments

echelon.obj

An object of class echelon. See echelon.

cas

A numeric (integer) vector of case counts. NAs are not allowed.

pop

A numeric (integer) vector for population. NAs are not allowed.

ex

A numeric vector for expected cases. NAs are not allowed.

K

Maximum cluster size. if K >= 1 (integer), the cluster size is limit to less than or equal to number of regions K. On the other hand, if 0 < K < 1, the cluster size is limit to less than or equal to K * 100% of the total population.

n.sim

Number of Monte Carlo replications used for significance testing of detected clusters. If 0, the significance is not assessed.

cluster.type

A character string specifying the cluster type. If "high", the detected clusters have high rates (hotspot clusters). On the other hand, If "low", the detected clusters have low rates (coldspot cluster).

cluster.legend.pos

A location of the legend on the dendrogram. (See the help for legend)

dendrogram

Logical. if TRUE, draw an echelon dendrogram with detected clusters.

cluster.info

Logical. if TRUE, return the result of detected clusters for detail.

coo

An array of (x,y)-coordinates of the region centroid to draw a cluster map.

...

Related to dendrogram drawing. (See the help for echelon)

Value

clusters

Each detected cluster.

scanned.regions

A region list of all scanning processes.

simulated.LLR

Monte Carlo samples of the log-likelihood ratio.

Note

echepoi requires either pop or ex.

Typical values of n.sim are 99, 999, 9999, ...

Author(s)

Fumio Ishioka

References

[1] Kulldorff M. (1997). A spatial scan statistic. Communications in Statistics: Theory and Methods, 26, 1481–1496.

[2] Ishioka F, Kawahara J, Mizuta M, Minato S, and Kurihara K. (2019) Evaluation of hotspot cluster detection using spatial scan statistic based on exact counting. Japanese Journal of Statistics and Data Science, 2, 241–262.

See Also

echelon for the echelon analysis.

echebin for cluster detection based on echelons using Binomial model.

Examples

##Hotspot detection for SIDS data of North Carolina using echelon scan

#Mortality rate per 1,000 live births from 1974 to 1984
library(spData)
data("nc.sids")
SIDS.cas <- nc.sids$SID74 + nc.sids$SID79
SIDS.pop <- nc.sids$BIR74 + nc.sids$BIR79
SIDS.rate <- SIDS.cas * 1000 / SIDS.pop

#Hotspot detection based on Poisson model
SIDS.echelon <- echelon(x = SIDS.rate, nb = ncCR85.nb, name = row.names(nc.sids))
echepoi(SIDS.echelon, cas = SIDS.cas, pop = SIDS.pop, K = 20,
  main = "Hgih rate clusters", ens = FALSE)
text(SIDS.echelon$coord, labels = SIDS.echelon$regions.name,
  adj = -0.1, cex = 0.7)

#Detected clusters and neighbors map
#XY coordinates of each polygon centroid point
NC.coo <- cbind(nc.sids$lon, nc.sids$lat)
echepoi(SIDS.echelon, cas = SIDS.cas, pop = SIDS.pop, K = 20,
  coo = NC.coo, dendrogram = FALSE)


##Detected clusters map
#Here is an example using the sf class "sf"
SIDS.clusters <- echepoi(SIDS.echelon, cas = SIDS.cas,
  pop = SIDS.pop, K = 20, dendrogram = FALSE)
MLC <- SIDS.clusters$clusters[[1]]
Secondary <- SIDS.clusters$clusters[[2]]
cluster.col <- rep(0,times=length(SIDS.rate))
cluster.col[MLC$regionsID] <- 2
cluster.col[Secondary$regionsID] <- 3

library(sf)
nc <- st_read(system.file("shape/nc.shp", package = "sf"))
plot(nc$geometry, col = cluster.col,
main = "Detected high rate clusters")
text(st_coordinates(st_centroid(st_geometry(nc))),
  labels = nc$CRESS_ID, cex =0.75)
legend("bottomleft",
  c(paste("1- p-value:", MLC$p),
  paste("2- p-value:", Secondary$p)),
  text.col = c(2,3))