Echelon spatial scan statistic based on Binomial model

Description

The echebin function detects spatial clusters using the echelon spatial scan statistic with a Binomial model.

Usage

echebin(echelon.obj, cas, ctl, K = length(cas)/2, Kmin = 1, n.sim = 99,
        cluster.type = "high", cluster.legend.pos = "bottomleft",
        dendrogram = TRUE, cluster.info = FALSE, coo = NULL, ...)

Arguments

Value

Note

The function echebin requires either cas or ctl.

Population is defined as the sum of cas and ctl.

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

Author(s)

Fumio Ishioka

References

[1] Kulldorff M, Nagarwalla N. (1995). Spatial disease clusters: Detection and inference. Statistics in Medicine, 14, 799–810.

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

See Also

echelon for the echelon analysis.

echepoi for cluster detection based on echelons using Poisson model.

echenor for cluster detection based on echelons using Normal model.

Examples

##Hotspot detection for non-white birth in North Carolina using echelon scan

#Load required packages and data
library(spData)
data("nc.sids")

#Non-white birth from 1974 to 1984 (case data)
nwb <- nc.sids$NWBIR74 + nc.sids$NWBIR79

#White birth from 1974 to 1984 (control data)
wb <- (nc.sids$BIR74 - nc.sids$NWBIR74) + (nc.sids$BIR79 - nc.sids$NWBIR79)

##Hotspot detection based on Binomial model
#Echelon analysis
SIDS.echelon <- echelon(x = nwb/wb, nb = ncCR85.nb, name = row.names(nc.sids))

#Basic cluster detection (significance not evaluated)
SIDS.clusters <- echebin(SIDS.echelon, cas = nwb, ctl = wb, K = 20,
  n.sim = 0, cluster.info = TRUE, main = "Hgih rate clusters", ens = FALSE)

#Significance assessment of clusters using Monte Carlo simulation
SIDS.clusters <- echebin(SIDS.echelon, cas = nwb, ctl = wb, K = 20,
  n.sim = 199, cluster.info = TRUE, 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)
echebin(SIDS.echelon, cas = nwb, ctl = wb, K = 20,
  n.sim = 0, coo = NC.coo, dendrogram = FALSE)

#Load geospatial information for North Carolina
nc <- sf::st_read(system.file("shape/nc.shp", package = "sf"))

#Extract detected clusters
MLC <- SIDS.clusters$clusters[[1]]
Secondary <- SIDS.clusters$clusters[[2]]

#Assign colors to clusters for plotting
cluster.col <- rep(0, length(nwb))
cluster.col[MLC$regionsID] <- 2
cluster.col[Secondary$regionsID] <- 3

#Plot detected high-rate clusters on a simple map
plot(nc$geom, col = cluster.col, 
  main = "Detected high rate clusters")
legend("bottomleft",
  legend = c(
    paste("1- p-value:", MLC$p),
    paste("2- p-value:", Secondary$p)
  ),
  text.col = c(2, 3)
)

#Interactive map visualization with mapview
library(mapview)
nc$cluster.col <- cluster.col
mapview(nc, zcol = "cluster.col", 
  col.regions=c("white", "red", "green"), 
  label = "NAME", legend=FALSE)

Echelon analysis for spatial data

Description

The echelon function divides the study area into structural entities, called 'echelons', based on neighbor information and draws a dendrogram.

Usage

echelon(x, nb, dendrogram = TRUE, name = NULL,
      main = NULL, ylab = NULL, yaxes = TRUE, ylim = NULL,
      xaxes = FALSE, xdper = c(0, 1), dmai = NULL,
      col = 1, lwd = 1, symbols = 4, cex.symbols = 1, col.symbols = 4,
      ens = TRUE, adj.ens = 1, cex.ens = 0.8, col.ens = 1,
      profiles = FALSE, nb.check = TRUE)

Arguments

Value

The echelon function returns an object of class echelon, which contains the following components:

Note

Any NA values in x are replaced with the minimum value of x.

The functions Sf::st_read and spdep::poly2nb are helpful for creating the object specified in the nb argument.

Author(s)

Fumio Ishioka

References

[1] Myers, W.L., Patil, G.P. and Joly, K. (1997). Echelon approach to areas of concern in synoptic regional monitoring. Environmental and Ecological Statistics, 4, 131–152.

[2] Kurihara, K., Myers, W.L. and Patil, G.P. (2000) Echelon analysis of the relationship between population and land cover patter based on remote sensing data. Community ecology, 1, 103–122.

See Also

echepoi, echebin and echenor for cluster detection based on echelons.

Examples

##Echelon analysis for one-dimensional data with 25 regions
#A weights matrix
one.nb <- matrix(0,25,25)
one.nb[1,2] <- 1
for(i in 2:24) one.nb[i,c(i-1,i+1)] <- c(1,1)
one.nb[25,24] <- 1

#25 random values
one.dat <- runif(25) * 10

#Echelon analysis
echelon(x = one.dat, nb = one.nb)


##Echelon analysis for SIDS data for North Carolina
#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

#Echelon analysis
SIDS.echelon <- echelon(x = SIDS.rate, nb = ncCR85.nb, name = row.names(nc.sids),
  symbols = 12, cex.symbols = 1.5, ens = FALSE)
text(SIDS.echelon$coord, labels = SIDS.echelon$regions.name,
  adj = -0.1, cex = 0.7)

#Echelon Profiles
echelon(x = SIDS.rate, nb = ncCR85.nb, profiles = TRUE)

Echelon spatial scan statistic based on Normal model

Description

The echenor function detects spatial clusters using the echelon spatial scan statistic with a Normal model.

Usage

echenor(echelon.obj, val, weight = NULL, K = length(val)/2, Kmin = 2, n.sim = 99,
        cluster.type = "high", cluster.legend.pos = "bottomleft",
        dendrogram = TRUE, cluster.info = FALSE, coo = NULL, ...)

Arguments

Value

Note

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

Author(s)

Fumio Ishioka

References

[1] Kulldorff M, Huang L, and Konty K. (2009). A scan statistic for continuous data based on the normal probability model. International Journal of Health Geographics, 8, 58.

[2] Huang L, Tiwari R, Zuo J, Kulldorff M, and Feuer E. (2009) Weighted normal spatial scan statistic for heterogeneous population data. Journal of the American Statistical Association, 104, 886–898.

See Also

echelon for the echelon analysis.

echepoi for cluster detection based on echelons using Poisson model.

echebin for cluster detection based on echelons using Binomial model.

Examples

##Hotspot detection for predicting SIDS rate in North Carolina using echelon scan

#Load required packages and data
library(spData)
data("nc.sids")
SIDS.cas <- nc.sids$SID74 + nc.sids$SID79
SIDS.pop <- nc.sids$BIR74 + nc.sids$BIR79
SIDS.nwpop <- nc.sids$NWBIR74 + nc.sids$NWBIR79
SIDS.rate <- SIDS.cas * 1000 / SIDS.pop

#Fit a linear model: SIDS rate explained by proportion of non-white births
res <- lm(SIDS.rate ~ I(SIDS.nwpop / SIDS.pop))
summary(res)

#Predicted values and reliability weights (inverse of standard error)
pred <- predict(res, newdata = nc.sids, se.fit = TRUE)
V <- res$fitted.values
W <- 1 / (pred$se.fit + 1e-6)

##Hotspot detection based on Normal model
#Echelon analysis
SIDS.echelon <- echelon(x = V, nb = ncCR85.nb, name = row.names(nc.sids))

#Basic cluster detection (significance not evaluated)
SIDS.clusters <- echenor(SIDS.echelon, val = V, weight = W, K = 20,
  n.sim = 0, cluster.info = TRUE, main = "Hgih value clusters", ens = FALSE)

#Significance assessment of clusters using Monte Carlo simulation
SIDS.clusters <- echenor(SIDS.echelon, val = V, weight = W, K = 20,
  n.sim = 199, cluster.info = TRUE, main = "Hgih value clusters", ens = FALSE)

text(SIDS.echelon$coord, labels = SIDS.echelon$regions.name,
  adj = -0.1, cex = 0.7)

#Load geospatial information for North Carolina
nc <- sf::st_read(system.file("shape/nc.shp", package = "sf"))

#Extract detected clusters
MLC <- SIDS.clusters$clusters[[1]]
Secondary <- SIDS.clusters$clusters[[2]]

#Assign colors to clusters for plotting
cluster.col <- rep(0, length(V))
cluster.col[MLC$regionsID] <- 2
cluster.col[Secondary$regionsID] <- 3

#Plot detected high-value clusters on a simple map
plot(nc$geom, col = cluster.col, 
  main = "Detected high value clusters")
legend("bottomleft",
  legend = c(
    paste("1- p-value:", MLC$p),
    paste("2- p-value:", Secondary$p)
  ),
  text.col = c(2, 3)
)

#Interactive map visualization with mapview
library(mapview)
nc$cluster.col <- cluster.col
mapview(nc, zcol = "cluster.col", 
  col.regions=c("white", "red", "green"), 
  label = "NAME", legend=FALSE)

Echelon spatial scan statistic based on Poisson model

Description

The echepoi function detects spatial clusters using the echelon spatial scan statistic with a Poisson model.

Usage

echepoi(echelon.obj, cas, pop = NULL, ex = NULL, K = length(cas)/2, Kmin = 1, n.sim = 99,
        cluster.type = "high", cluster.legend.pos = "bottomleft",
        dendrogram = TRUE, cluster.info = FALSE, coo = NULL, ...)

Arguments

Value

Note

The function 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.

echenor for cluster detection based on echelons using Normal model.

Examples

##Hotspot detection for SIDS cases in North Carolina using echelon scan

#Load required packages and data
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
#Echelon analysis
SIDS.echelon <- echelon(x = SIDS.rate, nb = ncCR85.nb, name = row.names(nc.sids))

#Basic cluster detection (significance not evaluated)
SIDS.clusters <- echepoi(SIDS.echelon, cas = SIDS.cas, pop = SIDS.pop, K = 20,
  n.sim = 0, cluster.info = TRUE, main = "Hgih rate clusters", ens = FALSE)

#Significance assessment of clusters using Monte Carlo simulation
SIDS.clusters <- echepoi(SIDS.echelon, cas = SIDS.cas, pop = SIDS.pop, K = 20,
  n.sim = 199, cluster.info = TRUE, 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,
  n.sim = 0, coo = NC.coo, dendrogram = FALSE)

#Load geospatial information for North Carolina
nc <- sf::st_read(system.file("shape/nc.shp", package = "sf"))

#Extract detected clusters
MLC <- SIDS.clusters$clusters[[1]]
Secondary <- SIDS.clusters$clusters[[2]]

#Assign colors to clusters for plotting
cluster.col <- rep(0, length(SIDS.rate))
cluster.col[MLC$regionsID] <- 2
cluster.col[Secondary$regionsID] <- 3

#Plot detected high-rate clusters on a simple map
plot(nc$geom, col = cluster.col, 
  main = "Detected high rate clusters")
legend("bottomleft",
  legend = c(
    paste("1- p-value:", MLC$p),
    paste("2- p-value:", Secondary$p)
  ),
  text.col = c(2, 3)
)

#Interactive map visualization with mapview
library(mapview)
nc$cluster.col <- cluster.col
mapview(nc, zcol = "cluster.col", 
  col.regions=c("white", "red", "green"), 
  label = "NAME", legend=FALSE)