The Spatial Scan Statistic

Null Hypothesis

The risk of disease is the same in all parts of the map.

One-Dimensional Scan Statistic

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.

Collection of overlapping circles of different sizes.

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).

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).

Age a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25

Breast Cancer Incidence, Relative RisksAge-Adjusted, Indirect Standardization

A small sample of the circles used

Four Most Likely Clusters

p=0.11

p=0.88

p=0.99

p=0.37

Four Most Likely Clusters

Cluster Obs Exp RR p= East 1853 1722 1.08 0.11Central 986 899 1.10 0.37Southwest 51 36 1.43 0.89Northwest 199 172 1.16 0.99

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.

Breast Cancer IncidenceCensus Tract Analysis

732 census tracts

Eight Most Likely Clusters for Breast Cancer Incidence

(approximate locations)

Iowa Breast Cancer IncidenceCensus Tract Aggregation

Cluster Obs Exp RR LLR p= 1 341 240 1.4 19.4 0.0012 28 11 2.6 9.8 0.033 1843 1708 1.1 6.7 0.394 29 15 2.0 5.3 0.805 21 10 2.1 4.4 0.986 30 17 1.8 4.4 0.987 208 171 1.2 3.8 0.998 41 26 1.6 3.8 0.99

Iowa Breast Cancer StagingCensus Tract Aggregation

Late Stage Cases: 758Total Cases: 7415

A

B

C

DE

F

Six Most Likely Clustersof Late Stage Breast Cancer

Late Stage Breast CancerCensus 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

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

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.

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.

Breast Cancer MortalityNortheastern United States

States: Maine, N.H., Vermont, Mass., R.I., Connecticut, N.Y., N.J., Pennsylvania, Delaware, Maryland, D.C.Years: 1988-1992Deaths: 58,943Population: 29,535,210Geographical Aggregation: 245 counties

Joint work with: E Feuer, B Miller, L Freedman, NCI

Breast cancer mortality

p=0.001

Breast cancer mortalityMost likely cluster

Most Likely Clusters

Location Obs Exp RR LLR p

NY/Philadelphia 24,044 23,040 1.074 35.7 0.001Buffalo 1,416 1,280 1.109 7.1 0.12Washington DC 712 618 1.154 6.9 0.15Boston 5,966 5,726 1.047 5.5 0.40Eastern Maine 267 229 1.166 3.0 0.99

References

General TheoryKulldorff M. A Spatial Scan Statistic, Communications in Statistics, Theory and Methods, 26:1481-1496, 1997.

ApplicationKulldorff M. Feuer E, Miller B, Freedman L. Breast Cancer in Northeast United States: A Geographic Analysis. American Journal of Epidemiology, 146:161-170, 1997.