EllipticScan: Kulldorff's elliptic scan (as
smerc::elliptic.test); zones are nearest-neighbour prefixes in the
elliptic distance for each shape and angle, the Poisson likelihood ratio is
multiplied by the penalty \((4s/(s+1)^2)^a\), clusters are chosen
greedily without overlap and p-values come from multinomial
redistributions of the cases (Philox). FlexScan: Tango and
Takahashi's flexibly shaped scan (as smerc::flex.test) over the
connected subsets of each region's k nearest neighbours;
FlexZones lists those zones (1-based). NormalScan: the
normal-model scan for continuous outcomes, \(N\ln(s_0/s_z)\) over
circular zones, with a permutation p-value. CuzickEdwards: the
\(T_k\) count of case-case k-nearest-neighbour pairs, its expectation
\(k n_1(n_1-1)/(n-1)\) and a permutation p-value. LawsonWaller:
the focused score statistic \(U = \sum c_i(O_i - E_i)\) with
multinomial (conditional) or Poisson variance. FixedCircleScan:
Openshaw's GAM (Poisson tail) or the Rushton-Lolonis Monte Carlo test on
circles of fixed radii centred on a grid of spacing overlap * r.
Regions are 1-based. Identical to the Python arm
morie.fn.clusterdetect.
Usage
EllipticScan(
coords,
cases,
pop,
ex = NULL,
ubpop = 0.5,
shape = c(1, 1.5, 2, 3, 4, 5),
nangle = c(1, 4, 6, 9, 12, 15),
a = 0.5,
nsim = 499L,
alpha = 0.1,
min_cases = 2,
seed = 1L
)
FlexZones(coords, w, k = 10)
FlexScan(
coords,
cases,
pop,
w,
k = 10,
ex = NULL,
kind = "poisson",
nsim = 499L,
alpha = 0.1,
seed = 1L
)
NormalScan(
coords,
values,
pop = NULL,
ubpop = 0.5,
direction = "high",
nsim = 499L,
seed = 1L
)
CuzickEdwards(coords, case, k = 1, nsim = 999L, seed = 1L)
LawsonWaller(cases, expected, exposure, conditional = TRUE)
FixedCircleScan(
coords,
cases,
pop,
radii,
overlap = 0.2,
method = "gam",
alpha = 0.002,
nsim = 99L,
seed = 1L
)Arguments
- coords
Two-column coordinates.
- cases
Case counts (or indicators for
CuzickEdwards).- pop
Populations.
- ex
Expected counts (default proportional to
pop).- ubpop
Maximum population share of a zone.
- shape
Ellipse shapes (ratio of axes).
- nangle
Number of angles per shape.
- a
Eccentricity penalty exponent.
- nsim
Monte Carlo replicates.
- alpha
Significance level.
- min_cases
Minimum cases in a zone.
- seed
Philox seed.
- w
Adjacency matrix.
- k
Number of nearest neighbours.
- kind
"poisson"or"binomial".- values
Continuous outcome, one per location.
- direction
"high","low"or"both".- case
Case indicator (1 case, 0 control).
- expected
Expected counts.
- exposure
Exposure covariate \(c_i\).
- conditional
Condition on the total number of cases.
- radii
Circle radii.
- overlap
Grid spacing as a fraction of the radius.
- method
"gam"or"rushton_lolonis".
References
Kulldorff, M., Huang, L., Pickle, L. and Duczmal, L. (2006). An elliptic spatial scan statistic. Statistics in Medicine 25, 3929-3943.
Tango, T. and Takahashi, K. (2005). A flexibly shaped spatial scan statistic for detecting clusters. International Journal of Health Geographics 4, 11.
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.
Cuzick, J. and Edwards, R. (1990). Spatial clustering for inhomogeneous populations. Journal of the Royal Statistical Society B 52, 73-104.
Waller, L. A., Turnbull, B. W., Clark, L. C. and Nasca, P. (1992). Chronic disease surveillance and testing of clustering of disease and exposure. Environmetrics 3, 281-300.
Openshaw, S., Charlton, M., Wymer, C. and Craft, A. (1987). A Mark 1 Geographical Analysis Machine for the automated analysis of point data sets. International Journal of Geographical Information Systems 1, 335-358.
Rushton, G. and Lolonis, P. (1996). Exploratory spatial analysis of birth defect rates in an urban population. Statistics in Medicine 15, 717-726.