The Spatial Scan Statistic

1
The Spatial Scan Statistic
2
Null Hypothesis
The risk of disease is the same in all parts of
the map.
3
One-Dimensional Scan Statistic
4
The Spatial Scan Statistic

• Create a regular or irregular grid of centroids
  covering the whole study region.
• Create an infinite number of circles around each
  centroid, with the radius anywhere from zero up
  to a maximum so that at most 50 percent of the
  population is included.

5
Collection of overlapping circles of different
sizes.
6

• For each circle
• Obtain actual and expected number of cases
  inside and outside the circle.
• Calculate Likelihood Function.

• Compare Circles
• Pick circle with highest likelihood function as
  Most Likely Cluster.

• Inference
• Generate random replicas of the data set under
  the null-hypothesis of no clusters (Monte Carlo
  sampling).
• Compare most likely clusters in real and random
  data sets (Likelihood ratio test).

7
Spatial Scan Statistic Properties

• Adjusts for inhomogeneous population density.
• Simultaneously tests for clusters of any size and
  any location, by using circular windows with
  continuously variable radius.
• Accounts for multiple testing.
• Possibility to include confounding variables,
  such as age, sex or socio-economic variables.
• Aggregated or non-aggregated data (states,
  counties, census tracts, block groups,
  households, individuals).

8
Breast Cancer Incidence, Relative
Risks Age-Adjusted, Indirect Standardization
9
A small sample of the circles used
10
Four Most Likely Clusters
p0.99
p0.11
p0.37
p0.88
11
Four Most Likely Clusters
Cluster Obs Exp RR p
East 1853 1722 1.08 0.11 Central 986
899 1.10 0.37 Southwest 51
36 1.43 0.89 Northwest 199 172 1.16 0.99
12
Geographical Aggregation

• In traditional mapping of rates or relative risks
  for disjoint geographical areas, there is a
  trade-off between the stability of the estimates
  and the geographical resolution.
• With tests for spatial randomness, less
  geographical data aggregation is always better
• Ability to detect clusters not conforming to
  political boundaries.
• More accurate data / less loss of information.

13
Breast Cancer IncidenceCensus Tract Analysis
732 census tracts
14
Eight Most Likely Clusters for Breast Cancer
Incidence
(approximate locations)
15
Iowa Breast Cancer Incidence
Census Tract Aggregation
Cluster Obs Exp RR LLR p
1 341 240 1.4 19.4 0.001 2 28
11 2.6 9.8 0.03 3 1843 1708 1.1 6.7 0.39 4
29 15 2.0 5.3 0.80 5 21
10 2.1 4.4 0.98 6 30 17 1.8 4.4 0.98 7 208 1
71 1.2 3.8 0.99 8 41 26 1.6 3.8 0.99
16
Iowa Breast Cancer Staging
Census Tract Aggregation
Late Stage Cases 758 Total Cases 7415
17
Six Most Likely Clusters of Late Stage Breast
Cancer
B
C
A
F
E
D
18
Late Stage Breast Cancer
Census Tract Aggregation
Cluster Obs Exp RR LLR p
A 15 4.5 3.3 9.2 0.049
B 13 4.7 2.8 5.9 0.62 C
6 1.3 4.5 5.5 0.75 D 44
27.1 1.6 5.3 0.81 E 9 3.1 2.9 4.5 0.97
F 4 0.9 3.5 4.3 0.99
19
Summary Breast Cancer in Iowa

• A cluster of high breast cancer incidence was
  found west of Des Moines.
• The geographical distribution of late stage
  breast cancer is rather even, with only one
  marginally significant cluster

20
Summary Spatial Scan Statistic

• Cluster detection irrespectively of political
  boundaries, and without assumptions about cluster
  size or location.
• Adjusts for multiple testing.
• It is only possible to pinpoint the general
  location of a cluster. The borders are
  approximate.
• It is a surveillance tool. The cause of a
  cluster must be investigated through other means.

21
Two Complimentary Maps
A map with smoothed disease rates provides a rate
estimate for all parts of the map, but it does
not tell us whether the pattern is random or
not. A map based on the spatial scan statistic
tells us if and where there are areas with a
significantly higher disease rate, but it does
not provide a rate estimate for all parts of the
map.
22
Breast Cancer MortalityNortheastern United States
States Maine, N.H., Vermont, Mass., R.I.,
Connecticut, N.Y., N.J., Pennsylvania, Delaware,
Maryland, D.C. Years 1988-1992 Deaths
58,943 Population 29,535,210 Geographical
Aggregation 245 counties Joint work with E
Feuer, B Miller, L Freedman, NCI
23
Breast cancer mortality
24
(No Transcript)
25
Breast cancer mortality Most likely cluster
p0.001
26
Most Likely Clusters
Location Obs Exp RR LLR
p NY/Philadelphia 24,044 23,040 1.074 35.7 0.001
Buffalo 1,416 1,280 1.109 7.1
0.12 Washington DC 712 618 1.154
6.9 0.15 Boston 5,966 5,726 1.047 5.5
0.40 Eastern Maine 267 229 1.166
3.0 0.99
27
References
General Theory Kulldorff M. A Spatial Scan
Statistic, Communications in Statistics, Theory
and Methods, 261481-1496, 1997. Application Kull
dorff M. Feuer E, Miller B, Freedman L. Breast
Cancer in Northeast United States A Geographic
Analysis. American Journal of Epidemiology,
146161-170, 1997.