Geographical Disease Surveillance

1
Geographical Disease Surveillance

• Martin Kulldorff
• Harvard Medical School and
• Harvard Pilgrim Health Care

2
Two Applications of Spatial Statistics in
Epidemiology

• Studies of Specific Hypotheses Evaluate the
  relationship between cancer and geographical
  variables of interest such as radon, pesticide
  use or income levels, adjusting for geographical
  variation.
• Surveillance Evaluate the geographical variation
  of cancer, adjusting for known or suspected
  variables such as age, gender or income.

3
Reasons for Geographical Disease Surveillance

• Disease Etiology
• Known Etiology but Unknown Presence
• Health Services

• Public Education
• Outbreak Detection
• New Diseases

4
Example Questions

• Are people in some geographical area at higher
  risk of brain cancer? This could be due to
  environmental, socio-economical, behavioral or
  genetic risk factors.
• Are there geographical differences in the access
  to and/or use of early detection programs, such
  as mammography screening?
• Are there geographical differences in the access
  to and/or use of prostate cancer treatment?

5
Different Types of Disease Data

• Count Data Incidence, Mortality, Prevalence
• Categorical Data Stage, Histology, Treatment
• Continuous Data Survival, Lead levels, BMI

6
For Incidence and Mortality
Poisson Data Numerator Number of
Cases Denominator Person-years at risk
7
For Prevalence
Bernoulli Data (0/1 Data) Numerator People with
Thyroid Cancer Denominator Those without Thyroid
Cancer
Note When prevalence is low, a Poisson model is
a very good approximation for Bernoulli data.
8
For Stage, Histology and Treatment
Bernoulli Data (0/1 Data) Numerator Cases of a
specific type, e.g. late stage. Denominator All
cases.
Ordinal Data For example Stage 1, 2, 3, 4
9
For Survival
Survival Data Length of Survival (Censored Data
is Common)
10
For Weight, Lead Levels, etc
Normal Data May sometime want to use a log
transformation to normalize the data
11
Data Aggregation (spatial resolution)

• Exact Location
• Census Block Group
• Zip Code
• Census Tract
• County
• State

12
Data Aggregation

• Same level of aggregation usually needed due to
  data availability.
• Less aggregation is typically better as more
  information is retained.
• Many statistical methods can be used
  irrespectively of aggregation level.

13
Exploratory/DescriptiveMapping Techniques

• Maps of rates or relative risks
• Probability maps
• Smoothed rates or relative risks
• Smoothed probability maps

14
Iowa Breast Cancer Incidence, 1993-1996 Age-Adjust
ed Relative Risks
15
Uncertainty of Rate Estimates
In a regular map, a relative risk of 2 could mean
that there are 2000 cases with 1000 expected in
an urban county, or 2 cases with 1 expected in a
rural county. For the urban county, the
relative risk of 2 is a good estimate of the true
relative risk, but not for the rural county.
16
Probability Map
For a particular county, one can test whether the
observed cases are significantly more than
expected, providing a p-value for that county. A
map of these p-values is called a probability
map. Reference Chownowski M. Maps Based on
Probabilities. Journal of the American
Statistical Association, 54385-388, 1959.
17
County p-values
County Obs Exp RR p
Dubuque 275 235 1.17 0.004 Polk 892 817 1.09 0.
004 Clayton 77 57 1.34 0.006 Mills 51
36 1.43 0.006 Scott 411 368 1.12 0.012 Linn 467
429 1.09 0.033 Marion 97 82 1.18 0.048
18
Regular vs. Probability Map
plt0.05
0.05ltplt0.10
19
Warning
By chance, 5 of the counties will by chance have
a statistically significant p-value at the 0.05
level. Need to adjust for multiple testing.
20
Maps of rates and probability maps are very
useful for descriptive purposes
Problem Maps of Rates No statistical
testing Probability Maps Multiple
testing Solution Tests for Spatial Randomness
One test
21
Statistical SignificanceTests for Spatial
Randomness
22
Whether or not there are true geographical
differences in risk, there will always be some
geographical patterns apparent to the naked eye.
As in all medical research, it is important to
evaluate whether observed patterns/results are
likely to be due to chance or not.
23
Breast Cancer Incidence, Relative
Risks Age-Adjusted, Indirect Standardization
24
Brain Cancer Mortality, Children 1986-1995
25
Brain Cancer Mortality, Adults 1986-1995
26
Tests for Spatial Randomness
Null Hypothesis The risk of disease is the same
in all parts of the map.
27
Covariate Adjustments
For incidence and mortality analyses, it is
important to adjust for age, and sometimes for
other variables as well. This is done using
indirect standardization, so that
a covariate-adjusted expected number of cases are
obtained for each census area. Can be used
with any test for spatial randomness.
28
Tests for Spatial Randomness
Three Different Types

• Global Clustering Tests
• Cluster Detection Tests
• Focused Tests

Complementary. Used for different purposes.
29
Global Clustering Tests
Evaluates whether clustering exist as a global
phenomena throughout the map, without
pinpointing the location of specific clusters.
30
Global Clustering Tests

• Chi-square, Pearson, 1900
• Forbes' Coefficient of Association, 1907
• Troup-Maynard, 1912
• Poisson Dispersion Index, Fisher 1922
• Renkonens Test, 1938
• Dice' Association Index, 1945
• Dice' Coincidence Index, 1945

31
Global Clustering Tests

• Jahn et al.'s Index 1, 1947
• Jahn et al.'s Index 2, 1947
• Jahn et al.'s Index 4, 1947
• Moran's BB Join Count, 1948
• Moran's BW Join Count, 1948
• Moran's I, 1950
• Jahn's Reproducibility Index, 1950

32
Global Clustering Tests

• Geary's c for binary data, 1954
• Duncan-Duncan's C0, 1955
• Morisita's Cd, 1959
• Pielou's S, 1961
• Martínez-Picó et al., 1965
• Horn's Ro, 1966
• Horn's Adjustment of Morisita's Cd, 1966

33
Global Clustering Tests

• Potthoff-Whittinghill's V, 1966
• Potthoff-Wittinghill's z, 1966
• Lloyd's Mean Crowding, 1967
• Levin's a, 1968
• Mantel-Bailar, 1970
• Pianka-Stewart's Ojk, Pianka 1973
• Lloyd-Robert's Close Pairs Test, 1973

34
Global Clustering Tests

• Walter, 1974
• Smith-Pike's T, 1976
• Ohno-Aoki-Aokis Test, 1979
• Weighted Moran's I, Cliff-Ord 1981
• Grimson-Wang-Johnson, 1981
• Lotwick-Silverman's Empty Space Test 1982
• Fraser's Clustering Index, 1983

35
Global Clustering Tests

• Esseen's Test, 1983
• Symons-Grimson-Yuan, 1983
• White 1983
• Jansson's Count, 1983
• Fraser's Clustering Index, 1983
• Barnes et al, 1987
• Whittemore et al. 1987

36
Global Clustering Tests

• Cuzick-Edwards k-NN, 1990
• Cuzick-Edwards Tinv, 1990
• Grimson-Rose's Method, 1991
• Besag-Newell's R, 1991
• Diggle-Chetwynd's D(s), 1991
• Diggle-Chetwynd's Dmax, 1991
• Diggle-Chetwynd's Dsum, 1991

37
Global Clustering Tests

• Alexander's NNA, 1991
• Grimson's U, 1993
• Palmer, 1993
• Dixon's Zs, 1994
• Dixon's ZAA, 1994
• Tango's Excess Events Test, 1995
• Britton 1997

38
Global Clustering Tests

• Anderson-Titterington's Thh, 1997
• Swartz' Entropy Test, 1998
• Conradt's Segregation Coefficient, 1998
• Perrys T, 1998
• Rogersons R, 1999
• Bithell's D, 1999
• Bithell's Tvar, 1999

39
Global Clustering Tests

• Assuncao-Reis Empirical Bayes Index, 1999
• Tangos Max Excess Events Test, 2000
• Bonettis Polytope Tests, 2000
• Gangnon-Claytons Test, 2001
• Bonetti-Paganos M, 2004
• Bonetti-Paganos M(1), 2004
• Bonetti-Paganos M(KL), 2004 etc,etc,etc

40
Cluster Detection Tests
Determine the location and statistical
significance of clusters without prior
assumptions about their locations.
41
Cluster Detection Tests

• Jansons Largest Cluster Test, 1983
• Turnbulls CEPP, 1990
• Grimson's MAX, 1993
• Kulldorffs Spatial Scan Statistic, 1995,97
• Bithell's M, 1999
• Tango-Takahashis Flex Scan, 2005
• etc

42
Focused Tests
Determine whether there is a cluster around a
pre-specified point or linear feature.
43
Focused Tests

• Fixed Cut-Off, Lyon et al. 1981
• Isotonic Regression, Stone 1988
• Diggles D, 1990
• Lawson-Wallers Score Test, 1992,93
• Bithells Linear Rank Score Test, 1995
• Rogersons Ri, 1999
• etc.

44
The Spatial Scan Statistic
45
One-Dimensional Scan Statistic
46
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.

47
Collection of overlapping circles of different
sizes.
48

• 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).

49
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).

50
Breast Cancer Incidence, Relative
Risks Age-Adjusted, Indirect Standardization
51
A small sample of the circles used
52
Four Most Likely Clusters
p0.99
p0.11
p0.37
p0.88
53
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
54
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.

55
Breast Cancer IncidenceCensus Tract Analysis
732 census tracts
56
Eight Most Likely Clusters for Breast Cancer
Incidence
(approximate locations)
57
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
58
Iowa Breast Cancer Staging
Census Tract Aggregation
Late Stage Cases 758 Total Cases 7415
59
Six Most Likely Clusters of Late Stage Breast
Cancer
B
C
A
F
E
D
60
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
61
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

62
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.

63
Global Clustering Tests
64
Notation
Census areas i1, 2, ... , L Observed cases
in area i ci Total cases CSci Population in
area i ni Total population NSni Distance
between areas i and j dij
65
Moran's I

• Let , where ri ci / ni.
• Morans I is defined as
• where a(i,j) is 1 if county i and j are neighbors
  and 0 otherwise.

66
Whittemore's Test

• Whittemore et al. proposed the statistic

67
Cuzick-Edwards k-NN Test
åi åj ci cj I(dijltdik(i)) where k(i) the county
with the k-nearest neighbor to an individual in
county i. Note This test is a special case of
the Weighted Morans I Test, proposed by Cliff
and Ord, 1981
68
Besag- Newells R

• For each case, find the collection of nearest
  counties so that there are a total of at least k
  cases in the area of the original and neighboring
  counties.
• Using the Poisson distribution, check if this
  area is statistically significant (not adjusting
  for multiple testing)
• R is the the number of cases for which this
  procedure creates a significant area

69
Swartzs Entropy Test

• The test statistic is defined as

70
Tango's Maximized Excess Events Test

• For a given constant ?, the Excess Events Test
  statistic is defined as
• To be able to detect clustering irrespectively of
  its geographical scale, Tango proposed the
  Maximized Excess Events Test

71
Global Clustering TestsPower Evaluation
Joint work with Toshiro Tango, Peter Park and
Changhong Song
72
Power Evaluation

• 245 counties and county equivalents in
  Northeastern United States
• 600 randomly distributed cases, according to
  population size and different clustering models
• Different parameters used for Besag-Newells R
  and Cuzick-Edwards k-NN tests

Kulldorff M, Tango T, Park PJ. Power comparisons
for disease clustering tests. Computational
Statistics and Data Analysis, 2003,42665-684.
73
Global Chain Clustering

• Each county has the same expected number of cases
  under the null and alternative hypotheses
• 300 cases are distributed according to complete
  spatial randomness
• Each of these have a twin case, located nearby,
  at some distance from the original case (distance
  zero, 1 and 5 of population along a chain,
  respectively).

74
PowerZero Distance

• Morans I 0.05
• Whittemores Test 0.13
• Cuzick-Edwards 1.00 0.92 0.73
• Besag-Newell 0.48 0.49 0.42
• Swartz Entropy 1.00
• Tangos MEET 0.99
• Spatial Scan 0.79

75
PowerRandom Distance, 1

• Morans I 0.12
• Whittemores Test 0.12
• Cuzick-Edwards 0.53 0.52 0.47
• Besag-Newell 0.14 0.21 0.27
• Swartz Entropy 0.39
• Tangos MEET 0.56
• Spatial Scan 0.35

76
PowerRandom Distance, 4

• Morans I 0.07
• Whittemores Test 0.10
• Cuzick-Edwards 0.14 0.17 0.18
• Besag-Newell 0.08 0.10 0.12
• Swartz Entropy 0.13
• Tangos MEET 0.25
• Spatial Scan 0.18

77
Hot Spot Clusters

• One or more neighboring counties have higher risk
  that outside.
• Constant risks among counties in the cluster, as
  well as among those outside the cluster

78
PowerGrand Isle, Vermont (RR193)

• Morans I 0.00
• Whittemores Test 0.01
• Cuzick-Edwards 0.75 0.17 0.04
• Besag-Newell 0.71 0.39 0.09
• Swartz Entropy 0.94
• Tangos MEET 0.20
• Spatial Scan 1.00

79
PowerGrand Isle 15 neigbors (RR3.9)

• Morans I 0.71
• Whittemores Test 0.01
• Cuzick-Edwards 0.76 0.62 0.25
• Besag-Newell 0.82 0.88 0.50
• Swartz Entropy 0.71
• Tangos MEET 0.23
• Spatial Scan 0.97

80
PowerPittsburgh, PA (RR2.85)

• Morans I 0.05
• Whittemores Test 0.00
• Cuzick-Edwards 0.65 0.92 0.90
• Besag-Newell 0.04 0.02 0.98
• Swartz Entropy 0.27
• Tangos MEET 0.92
• Spatial Scan 0.94

81
PowerPittsburgh 15 neighbors (RR2.1)

• Morans I 0.19
• Whittemores Test 0.00
• Cuzick-Edwards 0.60 0.72 0.84
• Besag-Newell 0.29 0.28 0.91
• Swartz Entropy 0.35
• Tangos MEET 0.83
• Spatial Scan 0.95

82
PowerManhattan (RR2.73)

• Morans I 0.05
• Whittemores Test 0.27
• Cuzick-Edwards 0.63 0.86 0.89
• Besag-Newell 0.04 0.03 0.95
• Swartz Entropy 0.26
• Tangos MEET 0.94
• Spatial Scan 0.92

83
PowerManhattan 15 neighbors (RR1.53)

• Morans I 0.07
• Whittemores Test 0.87
• Cuzick-Edwards 0.26 0.65 0.80
• Besag-Newell 0.01 0.06 0.37
• Swartz Entropy 0.05
• Tangos MEET 0.99
• Spatial Scan 0.93

84
Conclusions

• Besag-Newells R and Cuzick-Edwards k-NN often
  perform well, but are highly dependent on the
  chosen parameter
• Morans I and Whittemores Test have problems
  with many types of clustering
• Tangos MEET perform very well for global
  clustering
• The spatial scan statistic perform well for
  hot-spot clusters

85
Brain Cancer Mortalityin the United States

• Joint work with
• Zixing Fang, Cancer Prevention Institute
• David Gregorio, Univ Connecticut

86
U.S. Brain Cancer Mortality1986-1995
deaths rate (95 CI) Children (age lt20)
5,062 0.75 (0.66-0.83) Adults (age 20)
106,710 6.0 (5.8-6.2) Adult Women
48,650 4.9 (4.7-5.0) Adult Men
58,060 7.2 (7.0-7.5) annual deaths / 100,000
87
Brain Cancer

• Known risk factors
• High dose ionizing radiation
• Selected congenital and genetic disorders
• Explains only a small percent of cases.
• Potential risk factors
• N-nitroso compounds?, phenols?, pesticides?,
  polycyclic aromatic hydrocarbons?, organic
  solvents?

88
Adjustments
All subsequent analyses where adjusted for

• Age
• Gender
• Ethnicity (African-American, White, Other)

89
Brain Cancer Mortality, Children 1986-1995
90
Cuzick-Edwards Test Children
k p-value 200 0.04 500 0.13
91
Tangos Excess Events TestChildren
l p-value 1000 0.005 2000 0.06
5000 0.21 10000 0.29
92
Spatial Scan Statistic, Children
93
Children Seven Most Likely Clusters
Cluster Obs Exp RR
p 1. Carolinas 86 51 1.7 0.24 2.
California 16 4.9 3.3 0.74 3. Michigan
318 250 1.3 0.74 4. S Carolina 24 10 2.5 0.79 5
. Kentucky-Tenn 127 88 1.4 0.79 6.
Wisconsin 10 2.4 4.1 0.98 7. Nebraska 12 3.6 3.3
0.99
94
Conclusions Children
Some evidence of global spatial clustering, but
rather weak. No statistically significant
clusters detected. Any part of the pattern seen
on the original map may be due to chance.
95
How About Adults?
96
Brain Cancer Mortality, Adults 1986-1995
97
Cuzick-Edwards k-NN All Adults
k p-value 4000 0.0001
10000 0.0001
98
Tangos EET All Adults
l p-value 1000 0.0001
2000 0.0001 5000 0.0001 10000 0.0001
99
Spatial Scan Statistic Adults
100
Brain Cancer Mortality, Adults 1986-1995
101
Cuzick-Edwards Women
k p-value 1500 0.0001
3000 0.0001
102
Tangos EET Women
l p-value 1000 0.0001
2000 0.0001 5000 0.0001 10000 0.0001
103
Spatial Scan Statistic, Women
104
Women Most Likely Clusters
Cluster Obs Exp RR
p 1. Arkansas et al. 2830 2328 1.22 0.0001
2. Carolinas 1783 1518 1.17 0.0001 3. Oklahoma
et al. 1709 1496 1.14 0.003 4. Minnesota et
al. 2616 2369 1.10 0.01 10. N.J. /
N.Y. 1809 2300 0.79 0.0001 11. S Texas 127
214 0.59 0.0001 12. New Mexico et al.
849 1049 0.81 0.0001
105
Cuzick-Edwards Men
k p-value 2000 0.0001
4000 0.0001
106
Tangos EET Men
l p-value 1000 0.0001
2000 0.0001 5000 0.0001 10000 0.0001
107
Spatial Scan Statistic Men
108
Men Most Likely Clusters
Cluster Obs Exp RR
p 1. Kentucky et al. 3295 2860 1.15 0.0001
2. Carolinas 1925 1658 1.16 0.0001 3. Arkansas
et al. 1143 964 1.19 0.001 4. Washington
et al. 1664 1455 1.14 0.003 5. Michigan 1251 1074
1.17 0.005 11. N.J. / N.Y. 2084 2615 0.80 0.00
01 12. S Texas 157 262 0.60 0.0001 13. New
Mexico et al. 1418 1680 0.84 0.0001 14. Upstate
N.Y. et al. 1642 1895 0.87 0.0001
109
Conclusions Adults
Strong evidence of global spatial clustering. It
is possible to pinpoint specific areas with
higher and lower rates that are statistically
significant, and unlikely to be due to
chance. The exact borders of detected clusters
are uncertain. Similar patterns for men and
women.
110
Conclusion General
Tests for spatial randomness are very useful
additions to cancer maps, in order to determine
if the observed patterns are likely due to chance
or not. Different tests provide complementary
information.
111
Reference

• Fang, Kulldorff, Gregorio Brain cancer in the
  United States 1986-1995, A Geographical Analysis.
  Neuro-Oncology, 2004, 6179-187.

112
Childhood Leukemia in Sweden

• Ulf Hjalmars, Martin Kulldorff
• Göran Gustafsson, Neville Nagarwalla

Statistics in Medicine, 1995
113
Leukemia Incidence Data

• Acute leukemia
• Children, age 0-15 years
• Years 1973-1993
• 1523 cases
• 2577 parishes
• Denominator 1,703,235 children, based on an
  average for years 1976,1982 and 1988.

114
Three Most Likely Clusters
115
Three Most Likely Clusters

• obs exp pop p
• Okome 3 0.1 133 0.70
• Ö Tunhem 5 0.6 695 0.91
• Stavnäs 20 9.9 10380 0.99

116
Conclusions

• No evidence of any childhood cancer clusters in
  Sweden
• A leukemia cluster in Åstorp that received
  media attention in 1981 was detected, but it was
  not among the top three clusters nor
  statistically significant.

117
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118
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
119
Breast cancer mortality
120
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121
Breast cancer mortality Most likely cluster
p0.001
122
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
123
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.