Statistical detection and surveillance of geographic clusters

The widespread popularity of geographic information systems (GIS) has led to new insights in countless areas of application. It has facilitated not only the collection and storage of geographic data, but also the display of such data. Building on this progress by using an integrated approach, Statistical Detection and Monitoring of Geographic Clusters provides the statistical tools to identify whether data on a given map deviates significantly from expectations and to determine quickly whether new point patterns are emerging over time.

The book begins with a review of statistical methods for cluster detection, organized according to the different types of hypotheses and questions about clustering that can be investigated. It then delineates methods that allow for the quick detection of emergent geographic clusters.

The book delivers a cohesive presentation unlike that of most edited volumes. Drawing on the authors' extensive work in the field, the book delineates methods in such a way that they can be applied, almost instantly, to an array of disciplines. The readily applicable methods the book describes are useful for a multitude of problems in a variety of fields, particularly disease surveillance in the public health industry. Statistical Detection and Monitoring of Geographic Clusters is an essential volume for your reference shelf.

Author Notes

Peter Rogerson, Ikuho Yamada

List of Figures	p. xv
List of Tables	p. xix
Acknowledgments	p. xxiii
1 Introduction and Overview	p. 1
1.1 Setting the Stage	p. 1
1.2 The Roles of Spatial Statistics in Public Health and Other Fields	p. 2
1.3 Limitations Associated with the Visualization of Spatial Data	p. 3
1.3.1 Visual Assessment of Clustering Tendency	p. 3
1.3.2 What to Map: Mapping Rates versus Mapping p-Values	p. 5
1.3.2.1 Example 1: Sudden Infant Death Syndrome in North Carolina	p. 6
1.3.2.2 Example 2: Breast Cancer in the Northeastern United States	p. 7
1.4 Some Fundamental Concepts and Distinctions	p. 9
1.4.1 Descriptive versus Inferential, and Exploratory versus Confirmatory, Spatial Statistics	p. 9
1.4.2 Types of Health Data	p. 10
1.4.2.1 Point Data	p. 10
1.4.2.2 Case-Control Data	p. 10
1.4.2.3 Areal Data	p. 10
1.4.2.4 Time-Subscripted Data	p. 11
1.5 Types of Tests for Clustering	p. 11
1.6 Structure of the Book	p. 12
1.7 Software Resources and Sample Data	p. 13
1.7.1 Software Resources	p. 13
1.7.1.1 GeoSurveillance	p. 13
1.7.1.2 GeoDa	p. 13
1.7.1.3 R	p. 13
1.7.1.4 SaTScan	p. 13
1.7.1.5 Cancer Atlas Viewer	p. 14
1.7.1.6 CrimeStat	p. 14
1.7.2 Sample Datasets	p. 14
1.7.2.1 Breast Cancer Mortality in the Northeastern United States	p. 14
1.7.2.2 Prostate Cancer Mortality in the United States	p. 15
1.7.2.3 Sudden Infant Death Syndrome in North Carolina	p. 16
1.7.2.4 Leukemia in Central New York State	p. 16
1.7.2.5 Leukemia and Lymphoma Case-Control Data in England	p. 16
1.7.2.6 Low Birthweight in California	p. 18
2 Introductory Spatial Statistics: Description and Inference	p. 21
2.1 Introduction	p. 21
2.2 Mean Center	p. 22
2.3 Median Center	p. 23
2.4 Standard Distance	p. 23
2.5 Relative Standard Distance	p. 25
2.6 Inferential Statistical Tests of Central Tendency and Dispersion	p. 25
2.7 Illustration	p. 27
2.8 Angular Data	p. 29
2.9 Characteristics of Spatial Processes: First-Order and Second-Order Variation	p. 31
2.10 Kernel Density Estimation	p. 32
2.11 K-Functions	p. 35
2.12 Differences and Ratios of Kernel Density Estimators	p. 37
2.13 Differences in K-Functions	p. 40
3 Global Statistics	p. 43
3.1 Introduction	p. 43
3.2 Nearest Neighbor Statistic	p. 44
3.2.1 Illustration	p. 45
3.3 Quadrat Methods	p. 46
3.3.1 Unconditional Approach	p. 47
3.3.2 Conditional Approach	p. 48
3.3.2.1 Example 1: Leukemia in Central New York State	p. 49
3.3.2.2 Example 2: Sudden Infant Death Syndrome in North Carolina	p. 49
3.3.2.3 Example 3: Lung Cancer in Cambridgeshire	p. 50
3.3.3 Minimum Expected Frequencies	p. 51
3.3.4 Issues Associated with Scale	p. 51
3.3.5 Testing with Multiple Quadrat Sizes	p. 52
3.3.6 Optimal Quadrat Size: Appropriate Spatial Scales for Cluster Detection	p. 53
3.3.7 A Comparison of Alternative Quadrat-Based Global Statistics	p. 54
3.4 Spatial Dependence: Moran's I	p. 56
3.4.1 Illustration	p. 57
3.4.2 Example: Low Birthweight Cases in California	p. 59
3.5 Geary's C	p. 59
3.5.1 Illustration	p. 60
3.5.2 Example: Low Birthweight Cases in California	p. 60
3.6 A Comparison of Moran's I and Geary's C	p. 61
3.6.1 Example: Spatial Variation in Handedness in the United States	p. 62
3.6.2 Statistical Power of I and C	p. 64
3.7 Oden's I[subscript pop] Statistic	p. 67
3.7.1 Illustration	p. 68
3.8 Tango's Statistic and a Spatial Chi-Square Statistic	p. 69
3.8.1 Illustration	p. 71
3.8.2 Example: Sudden Infant Death Syndrome in North Carolina	p. 71
3.9 Getis and Ord's Global Statistic	p. 73
3.9.1 Example: Low Birthweight Cases in California	p. 74
3.10 Case-Control Data: The Cuzick-Edwards Test	p. 75
3.10.1 Illustration	p. 76
3.11 A Global Quadrat Test of Clustering for Case-Control Data	p. 76
3.11.1 Example	p. 78
3.11.2 Spatial Scale	p. 80
3.12 A Modified Cuzick-Edwards Test	p. 80
3.12.1 Example: Leukemia and Lymphoma Case-Control Data in England	p. 82
4 Local Statistics	p. 85
4.1 Introduction	p. 85
4.2 Local Moran Statistic	p. 86
4.2.1 Illustration	p. 87
4.2.2 Example: Low Birthweight Cases in California	p. 87
4.3 Score Statistic	p. 89
4.3.1 Illustration	p. 90
4.4 Tango's C[subscript F] Statistic	p. 91
4.4.1 Illustration	p. 92
4.5 Getis' G[subscript i] Statistic	p. 93
4.5.1 Illustration	p. 94
4.5.2 Example: Low Birthweight Cases in California	p. 95
4.6 Stone's Test	p. 95
4.6.1 Illustration	p. 96
4.7 Modeling around Point Sources with Case-Control Data	p. 96
4.8 Cumulative and Maximum Chi-Square Tests as Focused Tests	p. 97
4.8.1 Illustration	p. 99
4.8.2 Example: Leukemia and Lymphoma Case-Control Data in England	p. 100
4.8.3 Discreteness of the Maximum Chi-Square Statistic	p. 101
4.8.4 Relative Power of the Two Tests	p. 101
4.9 The Local Quadrat Test and an Introduction to Multiple Testing via the M-Test	p. 102
4.9.1 Fuchs and Kenett's M Test	p. 103
4.9.2 Example 1: Sudden Infant Death Syndrome in North Carolina	p. 105
4.9.3 Example 2: Lung Cancer in Cambridgeshire	p. 105
5 Tests for the Detection of Clustering, Including Scan Statistics	p. 107
5.1 Introduction	p. 107
5.2 Openshaw et al.'s Geographical Analysis Machine (GAM)	p. 108
5.3 Besag and Newell's Test for the Detection of Clusters	p. 109
5.4 Fotheringham and Zhan's Method	p. 110
5.5 Cluster Evaluation Permutation Procedure	p. 111
5.6 Exploratory Spatial Analysis Approach of Rushton and Lolonis	p. 112
5.7 Kulldorff's Spatial Scan Statistic with Variable Window Size	p. 113
5.7.1 Example 1: Low Birthweight Cases in California (Areal Data)	p. 113
5.7.2 Example 2: LBW Cases in California (Point Data)	p. 117
5.8 Bonferroni and Sidak Adjustments	p. 119
5.8.1 Power Loss with the Bonferroni Adjustment	p. 121
5.9 Improvements on the Bonferroni Adjustment	p. 122
5.10 Rogerson's Statistical Method for the Detection of Geographic Clustering	p. 123
5.10.1 The Geometry of Random Fields	p. 125
5.10.2 Illustration	p. 125
5.10.3 Approximation for Discreteness of Observations	p. 126
5.10.4 Approximations for the Exceedance Probability	p. 127
5.10.5 An Approach Based on the Effective Number of Independent Resels	p. 128
5.10.6 Example	p. 130
5.10.7 Discussion	p. 133
6 Retrospective Detection of Changing Spatial Patterns	p. 135
6.1 Introduction	p. 135
6.2 The Knox Statistic for Space-Time Interaction	p. 135
6.2.1 Illustration	p. 137
6.3 Test for a Change in Mean for a Series of Normally Distributed Observations	p. 137
6.3.1 Example	p. 138
6.4 Retrospective Detection of Change in Multinomial Probabilities	p. 140
6.4.1 Illustration	p. 141
6.4.2 Example 1: Breast Cancer Mortality in the Northeastern United States	p. 143
6.4.3 Example 2: Recent Changes in the Spatial Pattern of Prostate Cancer Mortality in the United States	p. 145
6.4.3.1 Introduction	p. 145
6.4.3.2 Geographic Variation in Incidence and Mortality Rates	p. 146
6.4.3.3 Data	p. 146
6.4.3.4 Descriptive Measures of Change	p. 147
6.4.3.5 Retrospective Detection of Change	p. 148
6.4.3.6 Discussion	p. 153
6.4.4 Example 3: Crime	p. 156
7 Introduction to Statistical Process Control and Nonspatial Cumulative Sum Methods of Surveillance	p. 157
7.1 Introduction	p. 157
7.2 Shewhart Charts	p. 158
7.2.1 Illustration	p. 159
7.3 Cumulative Sum (Cusum) Methods	p. 160
7.3.1 Illustration	p. 163
7.4 Monitoring Small Counts	p. 165
7.4.1 Transformations to Normality	p. 166
7.5 Cumulative Sums for Poisson Variables	p. 167
7.5.1 Cusum Charts for Poisson Data	p. 167
7.5.1.1 Example: Kidney Failure in Cats	p. 168
7.5.2 Poisson Cusums with Time-Varying Expectations	p. 169
7.5.2.1 Example: Lower Respiratory Infection Episodes	p. 170
7.6 Cusum Methods for Exponential Data	p. 171
7.6.1 Illustration	p. 173
7.7 Other Useful Modifications for Cusum Charts	p. 174
7.7.1 Fast Initial Response	p. 174
7.7.2 Unknown Process Parameters	p. 175
7.8 More on the Choice of Cusum Parameters	p. 176
7.8.1 Approximations for the Critical Threshold h for Given Choices of k and the In-Control ARL[subscript 0]	p. 177
7.8.2 Approximations for the Critical Threshold h for Given Choices of k and the Out-of-Control ARL[subscript 1]	p. 179
7.8.3 The Choice of k and h for Desired Values of ARL[subscript 0] and ARL[subscript 1]	p. 181
7.9 Other Methods for Temporal Surveillance	p. 183
8 Spatial Surveillance and the Monitoring of Global Statistics	p. 185
8.1 Brief Overview of the Development of Methods for Spatial Surveillance	p. 185
8.2 Introduction to Monitoring Global Spatial Statistics	p. 188
8.3 Cumulative Sum Methods and Global Spatial Statistics That Are Observed Periodically	p. 190
8.3.1 Moran's I and Getis' G	p. 190
8.3.1.1 Example: Breast Cancer Mortality in the Northeastern United States	p. 191
8.3.2 Monitoring Chi-Square Statistics	p. 196
8.3.2.1 Illustration	p. 197
8.4 CUSUM Methods and Global Spatial Statistics That Are Updated Periodically	p. 198
8.4.1 Spatial Surveillance Using Tango's Test for General Clustering	p. 199
8.4.1.1 Illustration	p. 200
8.4.1.2 Example: Burkitt's Lymphoma in Uganda	p. 203
8.4.1.3 Discussion	p. 206
8.4.2 A Cusum Method Based upon the Knox Statistic: Monitoring Point Patterns for the Development of Space-Time Clusters	p. 207
8.4.2.1 A Local Knox Statistic	p. 207
8.4.2.2 A Method for Monitoring Changes in Space-Time Interaction	p. 210
8.4.2.3 Example: Burkitt's Lymphoma in Uganda	p. 211
8.4.2.4 Summary and Discussion	p. 212
8.4.3 Cusum Method Combined with Nearest-Neighbor Statistic	p. 214
8.4.3.1 Monitoring Changes in Point Patterns	p. 214
8.4.3.2 A Cusum Approach for the Nearest-Neighbor Statistic	p. 215
8.4.3.3 Simulations of Clustering in the Unit Square	p. 217
8.4.3.4 Example: Application to Crime Analysis and Data from the Buffalo Police Department	p. 218
8.4.3.5 Cusum Approach for Arson Data	p. 218
8.4.3.6 Surveillance Using a Moving Window of Observations	p. 222
8.5 Summary and Discussion	p. 228
9 Cusum Charts for Local Statistics and for the Simultaneous Monitoring of Many Regions	p. 231
9.1 Monitoring around a Predefined Location	p. 231
9.1.1 Introduction	p. 231
9.1.2 Raubertas' Approach to Monitoring Local Statistics	p. 231
9.1.3 Monitoring a Single Local Statistic: Autocorrelated Regional Variables	p. 232
9.1.4 An Approach Based on Score Statistics	p. 233
9.1.5 Spatial Surveillance around Foci: A Generalized Score Statistic, Tango's C[subscript F]	p. 233
9.1.6 A Distance-Based Method	p. 235
9.1.6.1 Application to Data on Burkitt's Lymphoma	p. 236
9.1.7 Surveillance around Prespecified Locations Using Case-Control Data	p. 238
9.1.7.1 Introduction	p. 238
9.1.7.2 Prospective Monitoring around a Source, Using Case-Control Data	p. 238
9.1.7.3 Illustration	p. 239
9.2 Spatial Surveillance: Separate Charts for Each Region	p. 243
9.2.1 Illustration	p. 245
9.2.2 Example: Kidney Failure in Cats	p. 249
9.2.3 Example: Breast Cancer Mortality in the Northeastern United States	p. 250
9.3 Monitoring Many Local Statistics Simultaneously	p. 252
9.3.1 Example: Breast Cancer Mortality in the Northeastern United States	p. 255
9.3.2 Poisson Variables	p. 256
9.4 Summary	p. 257
Appendix	p. 257
10 More Approaches to the Statistical Surveillance of Geographic Clustering	p. 259
10.1 Introduction	p. 259
10.2 Monitoring Spatial Maxima	p. 260
10.2.1 Monitoring Spatial Maxima	p. 261
10.2.1.1 Type I Extreme Value (Gumbel) Distribution	p. 262
10.2.1.2 Cusum Surveillance of Gumbel Variates	p. 263
10.2.1.3 Example: Female Breast Cancer Mortality Rates in the Northeastern United States	p. 264
10.2.1.4 Example: Prostate Cancer Data in the United States	p. 266
10.2.2 Determination of Threshold Parameter	p. 268
10.2.3 Summary	p. 268
10.3 Multivariate Cusum Approaches	p. 269
10.3.1 Introduction	p. 269
10.3.2 Alternative Approaches to Monitoring Regional Change for More Than One Region	p. 270
10.3.3 Methods and Illustrations	p. 271
10.3.3.1 Multivariate Monitoring	p. 271
10.3.3.2 Hypothetical, Simulated Scenarios	p. 272
10.3.3.3 Spatial Autocorrelation	p. 276
10.3.4 Example: Breast Cancer Mortality in the Northeastern United States	p. 278
10.3.4.1 Multiple Univariate Results	p. 280
10.3.4.2 Multivariate Results	p. 283
10.3.4.3 Interpretation of Multivariate Results	p. 283
10.3.4.4 Estimation of Covariance and a Nonparametric Approach	p. 285
10.3.5 Discussion	p. 287
11 Summary: Associated Tests for Cluster Detection and Surveillance	p. 289
11.1 Introduction	p. 289
11.2 Associated Retrospective Statistical Tests	p. 290
11.2.1 Associated Retrospective Statistical Tests: Aspatial Case	p. 291
11.2.2 Associated Retrospective Statistical Tests: Spatial Case	p. 292
11.2.3 Maximum Local Statistic	p. 296
11.2.4 Illustration	p. 297
11.2.5 Example: Application to Leukemia Data for Central New York State	p. 297
11.3 Associated Prospective Statistical Tests: Regional Surveillance for Quick Detection of Change	p. 300
11.3.1 Prospective Methods: Aspatial Case	p. 300
11.3.2 Prospective Methods: Spatial Case	p. 301
References	p. 303
Author Index	p. 313
Subject Index	p. 317

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents