Statistics for Spatial Data.

The scan statistic is commonly used to test if a one dimensional point process is purely random, or if any clusters can be detected. Here it is simultaneously extended in three directions:(i) a spatial scan statistic for the detection of clusters in a multi-dimensional point process is proposed, (ii) the area of the scanning window is allowed to vary, and (iii) the baseline process may be any inhomogeneous Poisson process or Bernoulli process with intensity pro-portional to some known function. The main interest is in detecting clusters not explained by the baseline process. These methods are illustrated on an epidemiological data set, but there are other potential areas of application as well.

A spatial scan statistic

Preface.Acknowledgments.1 Introduction.1.1 Why Spatial Data in Public Health?1.2 Why Statistical Methods for Spatial Data?1.3 Intersection of Three Fields of Study.1.4 Organization of the Book.2 Analyzing Public Health Data.2.1 Observational vs. Experimental Data.2.2 Risk and Rates.2.2.1 Incidence and Prevalence.2.2.2 Risk.2.2.3 Estimating Risk: Rates and Proportions.2.2.4 Relative and Attributable Risks.2.3 Making Rates Comparable: Standardized Rates.2.3.1 Direct Standardization.2.3.2 Indirect Standardization.2.3.3 Direct or Indirect?2.3.4 Standardizing to What Standard?2.3.5 Cautions with Standardized Rates.2.4 Basic Epidemiological Study Designs.2.4.1 Prospective Cohort Studies.2.4.2 Retrospective Case-Control Studies.2.4.3 Other Types of Epidemiological Studies.2.5 Basic Analytic Tool: The Odds Ratio.2.6 Modeling Counts and Rates.2.6.1 Generalized Linear Models.2.6.2 Logistic Regression.2.6.3 Poisson Regression.2.7 Challenges in the Analysis of Observational Data.2.7.1 Bias.2.7.2 Confounding.2.7.3 Effect Modification.2.7.4 Ecological Inference and the Ecological Fallacy.2.8 Additional Topics and Further Reading.2.9 Exercises.3 Spatial Data.3.1 Components of Spatial Data.3.2 An Odyssey into Geodesy.3.2.1 Measuring Location: Geographical Coordinates.3.2.2 Flattening the Globe: Map Projections and Coordinate Systems.3.2.3 Mathematics of Location: Vector and Polygon Geometry.3.3 Sources of Spatial Data.3.3.1 Health Data.3.3.2 Census-Related Data.3.3.3 Geocoding.3.3.4 Digital Cartographic Data.3.3.5 Environmental and Natural Resource Data.3.3.6 Remotely Sensed Data.3.3.7 Digitizing.3.3.8 Collect Your Own!3.4 Geographic Information Systems.3.4.1 Vector and Raster GISs.3.4.2 Basic GIS Operations.3.4.3 Spatial Analysis within GIS.3.5 Problems with Spatial Data and GIS.3.5.1 Inaccurate and Incomplete Databases.3.5.2 Confidentiality.3.5.3 Use of ZIP Codes.3.5.4 Geocoding Issues.3.5.5 Location Uncertainty.4 Visualizing Spatial Data.4.1 Cartography: The Art and Science of Mapmaking.4.2 Types of Statistical Maps.MAP STUDY: Very Low Birth Weights in Georgia Health Care District 9.4.2.1 Maps for Point Features.4.2.2 Maps for Areal Features.4.3 Symbolization.4.3.1 Map Generalization.4.3.2 Visual Variables.4.3.3 Color.4.4 Mapping Smoothed Rates and Probabilities.4.4.1 Locally Weighted Averages.4.4.2 Nonparametric Regression.4.4.3 Empirical Bayes Smoothing.4.4.4 Probability Mapping.4.4.5 Practical Notes and Recommendations.CASE STUDY: Smoothing New York Leukemia Data.4.5 Modifiable Areal Unit Problem.4.6 Additional Topics and Further Reading.4.6.1 Visualization.4.6.2 Additional Types of Maps.4.6.3 Exploratory Spatial Data Analysis.4.6.4 Other Smoothing Approaches.4.6.5 Edge Effects.4.7 Exercises.5 Analysis of Spatial Point Patterns.5.1 Types of Patterns.5.2 Spatial Point Processes.5.2.1 Stationarity and Isotropy.5.2.2 Spatial Poisson Processes and CSR.5.2.3 Hypothesis Tests of CSR via Monte Carlo Methods.5.2.4 Heterogeneous Poisson Processes.5.2.5 Estimating Intensity Functions.DATA BREAK: Early Medieval Grave Sites.5.3 K Function.5.3.1 Estimating the K Function.5.3.2 Diagnostic Plots Based on the K Function.5.3.3 Monte Carlo Assessments of CSR Based on the K Function.DATA BREAK: Early Medieval Grave Sites.5.3.4 Roles of First- and Second-Order Properties.5.4 Other Spatial Point Processes.5.4.1 Poisson Cluster Processes.5.4.2 Contagion/Inhibition Processes.5.4.3 Cox Processes.5.4.4 Distinguishing Processes.5.5 Additional Topics and Further Reading.5.6 Exercises.6 Spatial Clusters of Health Events: Point Data for Cases and Controls.6.1 What Do We Have? Data Types and Related Issues.6.2 What Do We Want? Null and Alternative Hypotheses.6.3 Categorization of Methods.6.4 Comparing Point Process Summaries.6.4.1 Goals.6.4.2 Assumptions and Typical Output.6.4.3 Method: Ratio of Kernel Intensity Estimates.DATA BREAK: Early Medieval Grave Sites.6.4.4 Method: Difference between K Functions.DATA BREAK: Early Medieval Grave Sites.6.5 Scanning Local Rates.6.5.1 Goals.6.5.2 Assumptions and Typical Output.6.5.3 Method: Geographical Analysis Machine.6.5.4 Method: Overlapping Local Case Proportions.DATA BREAK: Early Medieval Grave Sites.6.5.5 Method: Spatial Scan Statistics.DATA BREAK: Early Medieval Grave Sites.6.6 Nearest-Neighbor Statistics.6.6.1 Goals.6.6.2 Assumptions and Typical Output.6.6.3 Method: q Nearest Neighbors of Cases.CASE STUDY: San Diego Asthma.6.7 Further Reading.6.8 Exercises.7 Spatial Clustering of Health Events: Regional Count Data.7.1 What Do We Have and What Do We Want?7.1.1 Data Structure.7.1.2 Null Hypotheses.7.1.3 Alternative Hypotheses.7.2 Categorization of Methods.7.3 Scanning Local Rates.7.3.1 Goals.7.3.2 Assumptions.7.3.3 Method: Overlapping Local Rates.DATA BREAK: New York Leukemia Data.7.3.4 Method: Turnbull et al.'s CEPP.7.3.5 Method: Besag and Newell Approach.7.3.6 Method: Spatial Scan Statistics.7.4 Global Indexes of Spatial Autocorrelation.7.4.1 Goals.7.4.2 Assumptions and Typical Output.7.4.3 Method: Moran's I .7.4.4 Method: Geary's c.7.5 Local Indicators of Spatial Association.7.5.1 Goals.7.5.2 Assumptions and Typical Output.7.5.3 Method: Local Moran's I.7.6 Goodness-of-Fit Statistics.7.6.1 Goals.7.6.2 Assumptions and Typical Output.7.6.3 Method: Pearson's chi2.7.6.4 Method: Tango's Index.7.6.5 Method: Focused Score Tests of Trend.7.7 Statistical Power and Related Considerations.7.7.1 Power Depends on the Alternative Hypothesis.7.7.2 Power Depends on the Data Structure.7.7.3 Theoretical Assessment of Power.7.7.4 Monte Carlo Assessment of Power.7.7.5 Benchmark Data and Conditional Power Assessments.7.8 Additional Topics and Further Reading.7.8.1 Related Research Regarding Indexes of Spatial Association.7.8.2 Additional Approaches for Detecting Clusters and/or Clustering.7.8.3 Space-Time Clustering and Disease Surveillance.7.9 Exercises.8 Spatial Exposure Data.8.1 Random Fields and Stationarity.8.2 Semivariograms.8.2.1 Relationship to Covariance Function and Correlogram.8.2.2 Parametric Isotropic Semivariogram Models.8.2.3 Estimating the Semivariogram.DATA BREAK: Smoky Mountain pH Data.8.2.4 Fitting Semivariogram Models.8.2.5 Anisotropic Semivariogram Modeling.8.3 Interpolation and Spatial Prediction.8.3.1 Inverse-Distance Interpolation.8.3.2 Kriging.CASE STUDY: Hazardous Waste Site Remediation.8.4 Additional Topics and Further Reading.8.4.1 Erratic Experimental Semivariograms.8.4.2 Sampling Distribution of the Classical Semivariogram Estimator.8.4.3 Nonparametric Semivariogram Models.8.4.4 Kriging Non-Gaussian Data.8.4.5 Geostatistical Simulation.8.4.6 Use of Non-Euclidean Distances in Geostatistics.8.4.7 Spatial Sampling and Network Design.8.5 Exercises.9 Linking Spatial Exposure Data to Health Events.9.1 Linear Regression Models for Independent Data.9.1.1 Estimation and Inference.9.1.2 Interpretation and Use with Spatial Data.DATA BREAK: Raccoon Rabies in Connecticut.9.2 Linear Regression Models for Spatially Autocorrelated Data.9.2.1 Estimation and Inference.9.2.2 Interpretation and Use with Spatial Data.9.2.3 Predicting New Observations: Universal Kriging.DATA BREAK: New York Leukemia Data.9.3 Spatial Autoregressive Models.9.3.1 Simultaneous Autoregressive Models.9.3.2 Conditional Autoregressive Models.9.3.3 Concluding Remarks on Conditional Autoregressions.9.3.4 Concluding Remarks on Spatial Autoregressions.9.4 Generalized Linear Models.9.4.1 Fixed Effects and the Marginal Specification.9.4.2 Mixed Models and Conditional Specification.9.4.3 Estimation in Spatial GLMs and GLMMs.DATA BREAK: Modeling Lip Cancer Morbidity in Scotland.9.4.4 Additional Considerations in Spatial GLMs.CASE STUDY: Very Low Birth Weights in Georgia Health Care District 9.9.5 Bayesian Models for Disease Mapping.9.5.1 Hierarchical Structure.9.5.2 Estimation and Inference.9.5.3 Interpretation and Use with Spatial Data.9.6 Parting Thoughts.9.7 Additional Topics and Further Reading.9.7.1 General References.9.7.2 Restricted Maximum Likelihood Estimation.9.7.3 Residual Analysis with Spatially Correlated Error Terms.9.7.4 Two-Parameter Autoregressive Models.9.7.5 Non-Gaussian Spatial Autoregressive Models.9.7.6 Classical/Bayesian GLMMs.9.7.7 Prediction with GLMs.9.7.8 Bayesian Hierarchical Models for Spatial Data.9.8 Exercises.References.Author Index.Subject Index.

/pdf/applied-spatial-statistics-for-public-health-data-5e3go3weys.pdf

Applied Spatial Statistics for Public Health Data

Preface Readership Acknowledgements Introduction Part I. The Context for Spatial Data Analysis: 1. Spatial data analysis: scientific and policy context 2. The nature of spatial data Part II. Spatial Data: Obtaining Data And Quality Issues: 3. Obtaining spatial data through sampling 4. Data quality: implications for spatial data analysis Part III. The Exploratory Analysis of Spatial Data: 5. Exploratory analysis of spatial data 6. Exploratory spatial data analysis: visualisation methods 7. Exploratory spatial data analysis: numerical methods Part IV. Hypothesis Testing in the Presence of Spatial Autocorrelation: 8. Hypothesis testing in the presence of spatial dependence Part V. Modeling Spatial Data: 9. Models for the statistical analysis of spatial data 10. Statistical modeling of spatial variation: descriptive modeling 11. Statistical modeling of spatial variation: explanatory modeling Appendices References Index.

/pdf/spatial-data-analysis-theory-and-practice-94s5yre4u5.pdf

Spatial Data Analysis: Theory and Practice

OBJECTIVE: We aimed to develop consensus-based recommendations for streamlining medical communication among various health care professionals, to improve accuracy of diagnosis and treatment, and to facilitate future investigations for mucous membrane pemphigoid. PARTICIPANTS: Because of the highly specific nature of this group of diseases, the 26 invited participants included either international scholars in the field of mucous membrane pemphigoid or experts in cutaneous pharmacology representing the 3 medical disciplines ophthalmology, oral medicine, and dermatology. EVIDENCE: The first author (L.S.C.) conducted a literature search. Based on the information obtained, international experts who had contributed to the literature in the clinical care, diagnosis, and laboratory investigation for mucous membrane pemphigoid were invited to participate in a consensus meeting aimed at developing a consensus statement. CONSENSUS PROCESS: A consensus meeting was convened and conducted on May 10, 1999, in Chicago, Ill, to discuss the relevant issues. The first author drafted the statement based on the consensus developed at the meeting and the participants' written comments. The draft was submitted to all participants for 3 separate rounds of review, and disagreements were reconciled based on literature evidence. The third and final statement incorporated all relevant evidence obtained in the literature search and the consensus developed by the participants. The final statement was approved and endorsed by all 26 participants. CONCLUSIONS: Specific consensus-based recommendations were made regarding the definition, diagnostic criteria, pathogenic factors, medical treatment, and prognostic indicators for mucous membrane pemphigoid. A system of standard reporting for these patients was proposed to facilitate a uniform data collection.

The first international consensus on mucous membrane pemphigoid: definition, diagnostic criteria, pathogenic factors, medical treatment, and prognostic indicators.

We present a new method of detection and inference for spatial clusters of a disease. To avoid ad hoc procedures to test for clustering, we have a clearly defined alternative hypothesis and our test statistic is based on the likelihood ratio. The proposed test can detect clusters of any size, located anywhere in the study region. It is not restricted to clusters that conform to predefined administrative or political borders. The test can be used for spatially aggregated data as well as when exact geographic co-ordinates are known for each individual. We illustrate the method on a data set describing the occurrence of leukaemia in Upstate New York.

Spatial disease clusters: detection and inference.

The study of disease clustering is becoming increasingly common in the field of medical epidemiology. There is great public concern and numerous reports on perceived clusters of various diseases, with cancers, and especially leukaemia, being the most commonly studied. We present a population based study on acute childhood leukaemia in Sweden 1973–1993, illustrating the possibility of a system for full-scale spatial epidemiological study design. The aim of the study is to test a large set of childhood leukaemia cases for the presence of geographical clusters. Necessary prerequisites, in the form of extensive population and disease data, a tool for geographical spatial analysis and a proper statistical method were fulfilled. No significant clusters were found.

Childhood leukaemia in sweden: using gis and a spatial scan statistic for cluster detection

Farrington CP, Andrews NJ, Beale AD, Catchpole MA (1996) A statistical algorithm for the early detection of outbreaks of infectious disease. J R Stat Soc A Stat Soc 159: 547–563. Hutwagner LC, Maloney EK, Bean NH, Slutsker L, Martin SM (1997) Using laboratory-based surveillance data for prevention: An algorithm for detecting salmonella outbreaks. Emerg Infect Dis 3: 395–400. Nobre FF, Stroup DF (1994) A monitoring system to detect changes in public health surveillance data. Int J Epidemiol 23: 408–418. Reis B, Mandl K (2003) Time series modeling for syndromic surveillance. BMC Med Inform Decis Mak 3: 2.

A Space-Time Permutation Scan Statistic for the Early Detection of Disease Outbreaks

Given N points or events occurring according to some probability distribution in the unit interval (0,1), the simple scan statistic is defined to be the maximum number of points in any sub-interval of length d. In many areas, as in epidemiology, it is used to test the null hypothesis that the events are random, against the alternative that they cluster within some window of fixed width d. Since d must be chosen without snooping at the data, the test restricts the alternative to clusters of a fixed size. In this paper, we propose a scan statistic with a variable window, whose size does not need to be chosen a priori. This test is the generalized likelihood ratio test for a uniform null distribution against an alternative of non-random clustering which allows for clusters of variable width. A simple algorithm for the implementation of the method is given and applied to birth defects data previously analysed by a simple scan statistic.

A scan statistic with a variable window.

Objective. Cicatricial pemphigoid (CP) is an autoimmune blistering disease characterized by anti-basement membrane zone (BMZ) antibodies with a varied heterogeneous clinical spectrum. We sought to characterize a subset of patients with disease limited to the oral cavity. Study Design. Twenty-nine random patients with vesiculobullous disease limited to the oral cavity were studied. We identified patients by clinical criteria, the presence of subepidermal/subepithelial bullae on routine histopathologic study, and deposition of IgG, complement, or both on the BMZ of perilesional tissue by immunopathological studies. Treatment included local and systemic therapies. Patients were monitored for a mean period of 6.7 years (range, 3.5 to 11 years). Results. The female/male ratio was 4.8:1. Patients with limited or minimal disease received local therapy only. In patients with extensive or severe disease, the use of dapsone yielded significant clinical improvement. Long-term follow-up showed that patients with severe disease treated with dapsone followed a clinical course similar to that in patients with minimal disease. Conclusions. Oral pemphigoid is a distinct clinical subset of CP. Overall it has a relatively benign course compared with that in patients with CP involving the oral cavity and other mucosae and the skin. Patients with minimal disease respond satisfactorily to topical therapy. Patients with severe and extensive disease benefit from dapsone therapy. In most patients the clinical course is prolonged and treatment is required for several months; in our study the mean treatment period was 42 months (range, 24 to 78 months). All the patients in this study went into clinical remission and remained in remission on cessation of therapy. No other mucosae or the skin were involved during the follow-up period.

Neville Nagarwalla

Papers

Spatial disease clusters: detection and inference.

Childhood leukaemia in sweden: using gis and a spatial scan statistic for cluster detection

A Space-Time Permutation Scan Statistic for the Early Detection of Disease Outbreaks

A scan statistic with a variable window.

Oral pemphigoid: Subset of cicatricial pemphigoid?