smerc (version 1.3)

mst.seq: Minimum spanning tree sequence

Description

mst.seq finds the sequence of connected regions that maximize the spatial scan statistic (the likelihood ratio test statistic) from a starting region. The set of connected regions at each step is a candidate zone. The zone continues to grow until no region should be added to the zone due to relevant constraints (size, connectivity, or other stopping criteria). This function is not intended to be used by users directly, but it can be quite educational for seeing the spread of the cluster. Consequently, it prioritizes efficiency over user friendliness.

Usage

mst.seq(
  start,
  neighbors,
  cases,
  pop,
  w,
  ex,
  ty,
  max_pop,
  type = "maxonly",
  nlinks = "one",
  early = FALSE
)

Arguments

start

The initial region to start the candidate zone.

neighbors

A vector containing the neighbors for the starting region (in ascending order of distance from the region). The staring region itself is included among the neighbors.

cases

The number of cases observed in each region.

pop

The population size associated with each region.

w

A binary spatial adjacency matrix for the regions.

ex

The expected number of cases for each region. The default is calculated under the constant risk hypothesis.

ty

The total number of cases in the study area.

max_pop

The population upperbound (in total population) for a candidate zone.

type

One of "maxonly", "pruned", or "all". The default is "maxonly". See Details.

nlinks

A character vector. The options are "one", "two", or "max". See Details.

early

A logical value indicating whether the "early" stopping criterion should be used. If TRUE, the sequence is stopped when the next potential zone doesn't produce a test statistic larger than the current zone. The default is FALSE.

Value

Returns a list of relevant information. See Details.

Details

The function can be used to construct candidate zones for the dynamic minimum spanning tree (dmst), early stopping dynamic minimum spanning tree (edmst), double connection spatial scan test (dc), and maximum linkage spatial scan test (mlink).

type is a character vector indicating what should be returned by the function. If type = "maxonly", then only the maximum of the log likelihood ratio test statistic across all candidate zones is returned. If type = "pruned",, the function returns a list that includes the location ids, test statistic, total cases, expected cases, and total population for the zone with the maximum test statistic. It type = "all", the same information the same information is returned for the entire sequence of zones.

If nlinks = "one", then a region only needs to be connected to one other region in the current zone to be considered for inclusion in the next zone. If nlinks = "two", then the region must be connected to at least two other regions in the current zone. If nlinks = "max", then only regions with the maximum number of connections to the current zone are considered for inclusion in the next zone.

Examples

# NOT RUN {
# load data
data(nydf)
data(nyw)

# create relevant data
coords = nydf[,c("longitude", "latitude")]
cases = floor(nydf$cases)
pop = nydf$population
w = nyw
ex = sum(cases)/sum(pop)*pop
ubpop = 0.5
ubd = 0.5
ty = sum(cases)   # total number of cases
# intercentroid distances
d = sp::spDists(as.matrix(coords), longlat = TRUE)
# upperbound for population in zone
max_pop = ubpop * sum(pop)
# upperbound for distance between centroids in zone
max_dist = ubd * max(d)
# create list of neighbors for each region (inclusive of region itself)
all_neighbors = nndist(d, ubd)
# find the dmst max zone
mst.seq(start = 1, all_neighbors[[1]], cases, pop, w, ex,
        ty, max_pop)
mst.seq(start = 1, all_neighbors[[1]], cases, pop, w, ex,
        ty, max_pop, "pruned")
bigout = mst.seq(start = 1, all_neighbors[[1]], cases, pop,
                 w, ex, ty, max_pop, "all")
head(bigout)
# }