Statistical Detection and Surveillance of Geographic Clusters

by Rogerson; Peter

• ISBN13: 9781584889359
• ISBN10: 1584889357
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-12-24
• Publisher: Chapman & Hall/

Summary

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.

Table of Contents

List of Figures	p. xv
List of Tables	p. xix
Acknowledgments	p. xxiii
Introduction and Overview	p. 1
Setting the Stage	p. 1
The Roles of Spatial Statistics in Public Health and Other Fields	p. 2
Limitations Associated with the Visualization of Spatial Data	p. 3
Visual Assessment of Clustering Tendency	p. 3
What to Map: Mapping Rates versus Mapping p-Values	p. 5
Example 1: Sudden Infant Death Syndrome in North Carolina	p. 6
Example 2: Breast Cancer in the Northeastern United States	p. 7
Some Fundamental Concepts and Distinctions	p. 9
Descriptive versus Inferential, and Exploratory versus Confirmatory, Spatial Statistics	p. 9
Types of Health Data	p. 10
Point Data	p. 10
Case-Control Data	p. 10
Areal Data	p. 10
Time-Subscripted Data	p. 11
Types of Tests for Clustering	p. 11
Structure of the Book	p. 12
Software Resources and Sample Data	p. 13
Software Resources	p. 13
GeoSurveillance	p. 13
GeoDa	p. 13
R	p. 13
SaTScan	p. 13
Cancer Atlas Viewer	p. 14
CrimeStat	p. 14
Sample Datasets	p. 14
Breast Cancer Mortality in the Northeastern United States	p. 14
Prostate Cancer Mortality in the United States	p. 15
Sudden Infant Death Syndrome in North Carolina	p. 16
Leukemia in Central New York State	p. 16
Leukemia and Lymphoma Case-Control Data in England	p. 16
Low Birthweight in California	p. 18
Introductory Spatial Statistics: Description and Inference	p. 21
Introduction	p. 21
Mean Center	p. 22
Median Center	p. 23
Standard Distance	p. 23
Relative Standard Distance	p. 25
Inferential Statistical Tests of Central Tendency and Dispersion	p. 25
Illustration	p. 27
Angular Data	p. 29
Characteristics of Spatial Processes: First-Order and Second-Order Variation	p. 31
Kernel Density Estimation	p. 32
K-Functions	p. 35
Differences and Ratios of Kernel Density Estimators	p. 37
Differences in K-Functions	p. 40
Global Statistics	p. 43
Introduction	p. 43
Nearest Neighbor Statistic	p. 44
Illustration	p. 45
Quadrat Methods	p. 46
Unconditional Approach	p. 47
Conditional Approach	p. 48
Example 1: Leukemia in Central New York State	p. 49
Example 2: Sudden Infant Death Syndrome in North Carolina	p. 49
Example 3: Lung Cancer in Cambridgeshire	p. 50
Minimum Expected Frequencies	p. 51
Issues Associated with Scale	p. 51
Testing with Multiple Quadrat Sizes	p. 52
Optimal Quadrat Size: Appropriate Spatial Scales for Cluster Detection	p. 53
A Comparison of Alternative Quadrat-Based Global Statistics	p. 54
Spatial Dependence: Moran's I	p. 56
Illustration	p. 57
Example: Low Birthweight Cases in California	p. 59
Geary's C	p. 59
Illustration	p. 60
Example: Low Birthweight Cases in California	p. 60
A Comparison of Moran's I and Geary's C	p. 61
Example: Spatial Variation in Handedness in the United States	p. 62
Statistical Power of I and C	p. 64
Oden's I[subscript pop] Statistic	p. 67
Illustration	p. 68
Tango's Statistic and a Spatial Chi-Square Statistic	p. 69
Illustration	p. 71
Example: Sudden Infant Death Syndrome in North Carolina	p. 71
Getis and Ord's Global Statistic	p. 73
Example: Low Birthweight Cases in California	p. 74
Case-Control Data: The Cuzick-Edwards Test	p. 75
Illustration	p. 76
A Global Quadrat Test of Clustering for Case-Control Data	p. 76
Example	p. 78
Spatial Scale	p. 80
A Modified Cuzick-Edwards Test	p. 80
Example: Leukemia and Lymphoma Case-Control Data in England	p. 82
Local Statistics	p. 85
Introduction	p. 85
Local Moran Statistic	p. 86
Illustration	p. 87
Example: Low Birthweight Cases in California	p. 87
Score Statistic	p. 89
Illustration	p. 90
Tango's C[subscript F] Statistic	p. 91
Illustration	p. 92
Getis' G[subscript i] Statistic	p. 93
Illustration	p. 94
Example: Low Birthweight Cases in California	p. 95
Stone's Test	p. 95
Illustration	p. 96
Modeling around Point Sources with Case-Control Data	p. 96
Cumulative and Maximum Chi-Square Tests as Focused Tests	p. 97
Illustration	p. 99
Example: Leukemia and Lymphoma Case-Control Data in England	p. 100
Discreteness of the Maximum Chi-Square Statistic	p. 101
Relative Power of the Two Tests	p. 101
The Local Quadrat Test and an Introduction to Multiple Testing via the M-Test	p. 102
Fuchs and Kenett's M Test	p. 103
Example 1: Sudden Infant Death Syndrome in North Carolina	p. 105
Example 2: Lung Cancer in Cambridgeshire	p. 105
Tests for the Detection of Clustering, Including Scan Statistics	p. 107
Introduction	p. 107
Openshaw et al.'s Geographical Analysis Machine (GAM)	p. 108
Besag and Newell's Test for the Detection of Clusters	p. 109
Fotheringham and Zhan's Method	p. 110
Cluster Evaluation Permutation Procedure	p. 111
Exploratory Spatial Analysis Approach of Rushton and Lolonis	p. 112
Kulldorff's Spatial Scan Statistic with Variable Window Size	p. 113
Example 1: Low Birthweight Cases in California (Areal Data)	p. 113
Example 2: LBW Cases in California (Point Data)	p. 117
Bonferroni and Sidak Adjustments	p. 119
Power Loss with the Bonferroni Adjustment	p. 121
Improvements on the Bonferroni Adjustment	p. 122
Rogerson's Statistical Method for the Detection of Geographic Clustering	p. 123
The Geometry of Random Fields	p. 125
Illustration	p. 125
Approximation for Discreteness of Observations	p. 126
Approximations for the Exceedance Probability	p. 127
An Approach Based on the Effective Number of Independent Resels	p. 128
Example	p. 130
Discussion	p. 133
Retrospective Detection of Changing Spatial Patterns	p. 135
Introduction	p. 135
The Knox Statistic for Space-Time Interaction	p. 135
Illustration	p. 137
Test for a Change in Mean for a Series of Normally Distributed Observations	p. 137
Example	p. 138
Retrospective Detection of Change in Multinomial Probabilities	p. 140
Illustration	p. 141
Example 1: Breast Cancer Mortality in the Northeastern United States	p. 143
Example 2: Recent Changes in the Spatial Pattern of Prostate Cancer Mortality in the United States	p. 145
Introduction	p. 145
Geographic Variation in Incidence and Mortality Rates	p. 146
Data	p. 146
Descriptive Measures of Change	p. 147
Retrospective Detection of Change	p. 148
Discussion	p. 153
Example 3: Crime	p. 156
Introduction to Statistical Process Control and Nonspatial Cumulative Sum Methods of Surveillance	p. 157
Introduction	p. 157
Shewhart Charts	p. 158
Illustration	p. 159
Cumulative Sum (Cusum) Methods	p. 160
Illustration	p. 163
Monitoring Small Counts	p. 165
Transformations to Normality	p. 166
Cumulative Sums for Poisson Variables	p. 167
Cusum Charts for Poisson Data	p. 167
Example: Kidney Failure in Cats	p. 168
Poisson Cusums with Time-Varying Expectations	p. 169
Example: Lower Respiratory Infection Episodes	p. 170
Cusum Methods for Exponential Data	p. 171
Illustration	p. 173
Other Useful Modifications for Cusum Charts	p. 174
Fast Initial Response	p. 174
Unknown Process Parameters	p. 175
More on the Choice of Cusum Parameters	p. 176
Approximations for the Critical Threshold h for Given Choices of k and the In-Control ARL[subscript 0]	p. 177
Approximations for the Critical Threshold h for Given Choices of k and the Out-of-Control ARL[subscript 1]	p. 179
The Choice of k and h for Desired Values of ARL[subscript 0] and ARL[subscript 1]	p. 181
Other Methods for Temporal Surveillance	p. 183
Spatial Surveillance and the Monitoring of Global Statistics	p. 185
Brief Overview of the Development of Methods for Spatial Surveillance	p. 185
Introduction to Monitoring Global Spatial Statistics	p. 188
Cumulative Sum Methods and Global Spatial Statistics That Are Observed Periodically	p. 190
Moran's I and Getis' G	p. 190
Example: Breast Cancer Mortality in the Northeastern United States	p. 191
Monitoring Chi-Square Statistics	p. 196
Illustration	p. 197
CUSUM Methods and Global Spatial Statistics That Are Updated Periodically	p. 198
Spatial Surveillance Using Tango's Test for General Clustering	p. 199
Illustration	p. 200
Example: Burkitt's Lymphoma in Uganda	p. 203
Discussion	p. 206
A Cusum Method Based upon the Knox Statistic: Monitoring Point Patterns for the Development of Space-Time Clusters	p. 207
A Local Knox Statistic	p. 207
A Method for Monitoring Changes in Space-Time Interaction	p. 210
Example: Burkitt's Lymphoma in Uganda	p. 211
Summary and Discussion	p. 212
Cusum Method Combined with Nearest-Neighbor Statistic	p. 214
Monitoring Changes in Point Patterns	p. 214
A Cusum Approach for the Nearest-Neighbor Statistic	p. 215
Simulations of Clustering in the Unit Square	p. 217
Example: Application to Crime Analysis and Data from the Buffalo Police Department	p. 218
Cusum Approach for Arson Data	p. 218
Surveillance Using a Moving Window of Observations	p. 222
Summary and Discussion	p. 228
Cusum Charts for Local Statistics and for the Simultaneous Monitoring of Many Regions	p. 231
Monitoring around a Predefined Location	p. 231
Introduction	p. 231
Raubertas' Approach to Monitoring Local Statistics	p. 231
Monitoring a Single Local Statistic: Autocorrelated Regional Variables	p. 232
An Approach Based on Score Statistics	p. 233
Spatial Surveillance around Foci: A Generalized Score Statistic, Tango's C[subscript F]	p. 233
A Distance-Based Method	p. 235
Application to Data on Burkitt's Lymphoma	p. 236
Surveillance around Prespecified Locations Using Case-Control Data	p. 238
Introduction	p. 238
Prospective Monitoring around a Source, Using Case-Control Data	p. 238
Illustration	p. 239
Spatial Surveillance: Separate Charts for Each Region	p. 243
Illustration	p. 245
Example: Kidney Failure in Cats	p. 249
Example: Breast Cancer Mortality in the Northeastern United States	p. 250
Monitoring Many Local Statistics Simultaneously	p. 252
Example: Breast Cancer Mortality in the Northeastern United States	p. 255
Poisson Variables	p. 256
Summary	p. 257
Appendix	p. 257
More Approaches to the Statistical Surveillance of Geographic Clustering	p. 259
Introduction	p. 259
Monitoring Spatial Maxima	p. 260
Monitoring Spatial Maxima	p. 261
Type I Extreme Value (Gumbel) Distribution	p. 262
Cusum Surveillance of Gumbel Variates	p. 263
Example: Female Breast Cancer Mortality Rates in the Northeastern United States	p. 264
Example: Prostate Cancer Data in the United States	p. 266
Determination of Threshold Parameter	p. 268
Summary	p. 268
Multivariate Cusum Approaches	p. 269
Introduction	p. 269
Alternative Approaches to Monitoring Regional Change for More Than One Region	p. 270
Methods and Illustrations	p. 271
Multivariate Monitoring	p. 271
Hypothetical, Simulated Scenarios	p. 272
Spatial Autocorrelation	p. 276
Example: Breast Cancer Mortality in the Northeastern United States	p. 278
Multiple Univariate Results	p. 280
Multivariate Results	p. 283
Interpretation of Multivariate Results	p. 283
Estimation of Covariance and a Nonparametric Approach	p. 285
Discussion	p. 287
Summary: Associated Tests for Cluster Detection and Surveillance	p. 289
Introduction	p. 289
Associated Retrospective Statistical Tests	p. 290
Associated Retrospective Statistical Tests: Aspatial Case	p. 291
Associated Retrospective Statistical Tests: Spatial Case	p. 292
Maximum Local Statistic	p. 296
Illustration	p. 297
Example: Application to Leukemia Data for Central New York State	p. 297
Associated Prospective Statistical Tests: Regional Surveillance for Quick Detection of Change	p. 300
Prospective Methods: Aspatial Case	p. 300
Prospective Methods: Spatial Case	p. 301
References	p. 303
Author Index	p. 313
Subject Index	p. 317
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