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E-raamat: Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Third Edition

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Since the publication of the second edition, many new Bayesian tools and methods have been developed for space-time data analysis, the predictive modeling of health outcomes, and other spatial biostatistical areas. Exploring these new developments, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Third Edition provides an up-to-date, cohesive account of the full range of Bayesian disease mapping methods and applications.

In addition to the new material, the book also covers more conventional areas such as relative risk estimation, clustering, spatial survival analysis, and longitudinal analysis. After an introduction to Bayesian inference, computation, and model assessment, the text focuses on important themes, including disease map reconstruction, cluster detection, regression and ecological analysis, putative hazard modeling, analysis of multiple scales and multiple diseases, spatial survival and longitudinal studies, spatiotemporal methods, and map surveillance. It shows how Bayesian disease mapping can yield significant insights into georeferenced health data.

The target audience for this text is public health specialists, epidemiologists, and biostatisticians who need to work with geo-referenced health data.

Arvustused

Praise for the Previous Edition

This book provides a technical grounding in spatial models while maintaining a strong grasp on applied epidemiological problems. A welcome effort is made to clarify concepts which might, in other texts, have been skimmed over in a rush to fit models. From the start, the concepts are illustrated with disease mapping examples, including R and WinBUGS code. The book has relatively few errors I recommend the book. It taught me new ideas and clarified existing ones. I shall continue to use it and I expect it to be useful for other statisticians with an interest in spatial analysis. Journal of the Royal Statistical Society, Series A, April 2011

The readers who would like to get a big picture of hierarchical modeling in spatial epidemiology in a quick fashion will find this book very useful. This book covers a range of topics in hierarchical modeling for spatial epidemiological data and provides a practical, comprehensive, and up-to-date overview of the use of spatial statistics in epidemiology. useful for readers to track down the topics of interests and see the varieties of up-to-date modeling techniques in spatial epidemiology or, more generally, spatial binary or count data. The author also lists the reference following each method for further information. Hongfei Li, Technometrics, November 2010

Lawson begins by building a solid Bayesian background The remaining seven chapters provide a thorough review of modeling relative risk Lawson provides well-written reviews of many topics and many aspects of those topics are covered in his reviews. The literature cited is huge and diverse, showing the current importance of the subjects covered. One can also gain hands-on training in analysis and visual presentations by following carefully the detailed introduction to R and WinBUGS given in the book. Many important data sets used in the book are available online International Statistical Review (2009), 77, 2

This book is an excellent reference for intermediate learners of Bayesian disease mapping many of the methodologies discussed in this book are applicable not only to spatial epidemiology but also to many other fields that utilize spatial data. J. Law, Biometrics, June 2009

List of Tables
xv
Preface to Third Edition xvii
Preface to Second Edition xix
Preface to First Edition xxi
I Background
1(78)
1 Introduction
3(16)
1.1 Data Sets
6(13)
2 Bayesian Inference and Modeling
19(18)
2.1 Likelihood Models
19(3)
2.1.1 Spatial Correlation
20(1)
2.1.1.1 Conditional Independence
20(1)
2.1.1.2 Joint Densities with Correlations
20(1)
2.1.1.3 Pseudolikelihood Approximation
21(1)
2.2 Prior Distributions
22(2)
2.2.1 Propriety
22(1)
2.2.2 Non-Informative Priors
22(2)
2.3 Posterior Distributions
24(3)
2.3.1 Conjugacy
25(1)
2.3.2 Prior Choice
25(1)
2.3.2.1 Regression Parameters
26(1)
2.3.2.2 Variance or Precision Parameters
26(1)
2.3.2.3 Correlation Parameters
26(1)
2.3.2.4 Probabilities
26(1)
2.3.2.5 Correlated Parameters
27(1)
2.4 Predictive Distributions
27(1)
2.4.1 Poisson-Gamma Example
27(1)
2.5 Bayesian Hierarchical Modeling
28(1)
2.6 Hierarchical Models
28(2)
2.7 Posterior Inference
30(5)
2.7.1 Bernoulli and Binomial Examples
31(4)
2.8 Exercises
35(2)
3 Computational Issues
37(24)
3.1 Posterior Sampling
37(1)
3.2 Markov Chain Monte Carlo (MCMC) Methods
38(1)
3.3 Metropolis and Metropolis-Hastings Algorithms
39(10)
3.3.1 Metropolis Updates
40(1)
3.3.2 Metropolis-Hastings Updates
40(1)
3.3.3 Gibbs Updates
40(1)
3.3.4 Metropolis-Hastings (M-H) versus Gibbs Algorithms
41(1)
3.3.5 Special Methods
42(1)
3.3.6 Convergence
42(1)
3.3.6.1 Single-Chain Methods
43(3)
3.3.6.2 Multi-Chain Methods
46(2)
3.3.7 Subsampling and Thinning
48(1)
3.3.7.1 Monitoring Metropolis-Like Samplers
48(1)
3.4 Perfect Sampling
49(1)
3.5 Posterior and Likelihood Approximations
50(7)
3.5.1 Pseudolikelihood and Other Forms
50(2)
3.5.2 Asymptotic Approximations
52(1)
3.5.2.1 Asymptotic Quadratic Form
52(3)
3.5.2.2 Laplace Integral Approximation
55(1)
3.5.2.3 INLA and R-INLA
55(2)
3.6 Alternative Computational Aproaches
57(1)
3.6.1 Maximum A Posteriori Estimation (MAP)
57(1)
3.6.2 Iterated Conditional Modes (ICMs)
57(1)
3.6.3 MC3 and Parallel Tempering
57(1)
3.6.4 Variational Bayes
58(1)
3.6.5 Sequential Monte Carlo
58(1)
3.7 Approximate Bayesian Computation (ABC)
58(1)
3.8 Exercises
59(2)
4 Residuals and Goodness-of-Fit
61(18)
4.1 Model GOF Measures
61(4)
4.1.1 Deviance Information Criterion
62(2)
4.1.2 Posterior Predictive Loss
64(1)
4.2 General Residuals
65(3)
4.3 Bayesian Residuals
68(1)
4.4 Predictive Residuals and Bootstrap
68(2)
4.4.1 Conditional Predictive Ordinates (CPOs.)
69(1)
4.5 Interpretation of Residuals in a Bayesian Setting
70(2)
4.6 Pseudo-Bayes Factors and Marginal Predictive Likelihood
72(1)
4.7 Other Diagnostics
73(1)
4.8 Exceedance Probabilities
74(1)
4.9 Exercises
75(4)
II Themes
79(304)
5 Disease Map Reconstruction and Relative Risk Estimation
81(50)
5.1 Introduction to Case Event and Count Likelihoods
81(5)
5.1.1 Poisson Process Model
81(2)
5.1.2 Conditional Logistic Model
83(1)
5.1.3 Binomial Model for Count Data
84(1)
5.1.4 Poisson Model for Count Data
84(1)
5.1.4.1 Standardisation
85(1)
5.1.4.2 Relative Risk
86(1)
5.2 Specification of Predictor in Case Event and Count Models
86(4)
5.2.1 Bayesian Linear Model
88(2)
5.3 Simple Case and Count Data Models with Uncorrelated Random Effects
90(4)
5.3.1 Gamma and Beta Models
90(1)
5.3.1.1 Gamma Models
90(1)
5.3.1.1.1 Hyperprior Distributions
91(1)
5.3.1.1.2 Linear Parameterization
91(1)
5.3.1.2 Beta Models
92(1)
5.3.1.2.1 Hyperprior Distributions
92(1)
5.3.1.2.2 Linear Parameterization
92(1)
5.3.2 Log-Normal and Logistic-Normal Models
93(1)
5.4 Correlated Heterogeneity Models
94(7)
5.4.1 Conditional Autoregressive (CAR) Models
95(1)
5.4.1.1 Improper CAR (ICAR) Models
95(2)
5.4.1.2 Proper CAR (PCAR) Models
97(1)
5.4.1.3 Gaussian Process Convolution (PC) and GCM Models
97(1)
5.4.1.4 Case Event Models
98(2)
5.4.2 Fully Specified Covariance Models
100(1)
5.5 Convolution Models
101(3)
5.5.1 Leroux Prior Specification
103(1)
5.6 Model Comparison and Goodness-of-Fit Diagnostics
104(3)
5.6.1 Residual Spatial Autocorrelation
105(2)
5.7 Alternative Risk Models
107(15)
5.7.1 Autologistic Models
107(4)
5.7.1.1 Other Auto Models
111(1)
5.7.2 Spline-Based Models
112(1)
5.7.3 Zip Regression Models
113(5)
5.7.4 Ordered and Unordered Multi-Category Data
118(1)
5.7.5 Latent Structure Models
118(1)
5.7.5.1 Mixture Models
119(3)
5.7.6 Quantile Regression
122(1)
5.8 Edge Effects
122(5)
5.8.1 Edge Weighting Schemes and MCMC Methods
124(1)
5.8.1.0.1 Weighting Systems
124(2)
5.8.1.1 MCMC and Other Computational Methods
126(1)
5.8.2 Discussion and Extension to Space-Time
126(1)
5.9 Exercises
127(4)
5.9.1 Maximum Likelihood
127(1)
5.9.2 Poisson-Gamma Model: Posterior and Predictive Inference
128(1)
5.9.3 Poisson-Gamma Model: Empirical Bayes
129(2)
6 Disease Cluster Detection
131(32)
6.1 Cluster Definitions
131(3)
6.1.1 Hot Spot Clustering
133(1)
6.1.2 Clusters as Objects or Groupings
133(1)
6.1.3 Clusters Defined as Residuals
133(1)
6.2 Cluster Detection Using Residuals
134(7)
6.2.1 Case Event Data
134(1)
6.2.1.1 Unconditional Analysis
134(2)
6.2.1.2 Conditional Logistic Analysis
136(3)
6.2.2 Count Data
139(1)
6.2.2.1 Poisson Likelihood
139(1)
6.2.2.2 Binomial Likelihood
140(1)
6.3 Cluster Detection Using Posterior Measures
141(3)
6.4 Cluster Models
144(16)
6.4.1 Case Event Data
144(1)
6.4.1.1 Object Models
145(2)
6.4.1.2 Estimation Issues
147(3)
6.4.1.3 Data-Dependent Models
150(1)
6.4.1.3.1 Partition Models and Regression Trees
150(2)
6.4.1.3.2 Local Likelihood
152(1)
6.4.2 Count Data
153(1)
6.4.2.1 Hidden Process and Object Models
153(2)
6.4.2.2 Data-Dependent models
155(1)
6.4.2.2.1 Partition Models and Regression Trees
155(2)
6.4.2.2.2 Local Likelihood
157(1)
6.4.3 Markov-Connected Component Field (MCCF) Models
158(2)
6.5 Edge Detection and Wombling
160(3)
7 Regression and Ecological Analysis
163(36)
7.1 Basic Regression Modeling
163(5)
7.1.1 Linear Predictor Choice
163(1)
7.1.2 Covariate Centering
164(1)
7.1.3 Initial Model Fitting
165(2)
7.1.4 Contextual Effects
167(1)
7.2 Missing Data
168(4)
7.2.1 Missing Outcomes
169(3)
7.2.2 Missing Covariates
172(1)
7.3 Non-Linear Predictors
172(2)
7.4 Confounding and Multi-Colinearity
174(3)
7.5 Geographically Dependent Regression
177(3)
7.6 Variable Selection
180(2)
7.7 Ecological Analysis: General Case of Regression
182(6)
7.8 Biases and Misclassification Errors
188(8)
7.8.1 Ecological Biases
189(1)
7.8.1.1 Within-Area Exposure Distribution
190(2)
7.8.1.2 Measurement Error (ME)
192(2)
7.8.1.3 Unobserved Confounding and Contextual Effects in Ecological Analysis
194(2)
7.9 Sample Surveys and Small Area Estimation
196(3)
7.9.1 Estimation of Aggregate Quantities
197(2)
8 Putative Hazard Modeling
199(20)
8.1 Case Event Data
201(5)
8.2 Aggregated Count Data
206(3)
8.3 Spatio-Temporal Effects
209(10)
8.3.1 Case Event Data
210(3)
8.3.2 Count Data
213(6)
9 Multiple Scale Analysis
219(18)
9.1 Modifiable Areal Unit Problem (MAUP)
219(6)
9.1.1 Scaling Up
219(2)
9.1.2 Scaling Down
221(1)
9.1.3 Multiscale Analysis
221(2)
9.1.3.1 Georgia Oral Cancer 2004 Example
223(2)
9.2 Misaligned Data Problem (MIDP)
225(12)
9.2.1 Predictor Misalignment
226(4)
9.2.1.1 Binary Logistic Spatial Example
230(3)
9.2.2 Outcome Misalignment
233(1)
9.2.3 Misalignment and Edge Effects
234(3)
10 Multivariate Disease Analysis
237(26)
10.1 Notation for Multivariate Analysis
237(1)
10.1.1 Case Event Data
237(1)
10.1.2 Count Data
238(1)
10.2 Two Diseases
238(8)
10.2.1 Case Event Data
238(1)
10.2.1.1 Specification of λl1
239(1)
10.2.2 Count Data
240(2)
10.2.3 Georgia County Level Example Involving Three diseases
242(4)
10.3 Multiple Diseases
246(17)
10.3.1 Case Event Data
246(5)
10.3.2 Count Data
251(2)
10.3.3 Multivariate Spatial Correlation and MCAR Models
253(1)
10.3.3.1 Multivariate Gaussian Models
253(3)
10.3.3.2 MVCAR Models
256(1)
10.3.3.3 Linear Model of Coregionalization
257(1)
10.3.3.4 Model Fitting on WinBUGS
258(1)
10.3.4 Georgia Chronic Ambulatory Care-Sensitive Example
258(5)
11 Spatial Survival and Longitudinal Analysis
263(26)
11.1 General Issues
263(1)
11.2 Spatial Survival Analysis
264(6)
11.2.1 Endpoint Distributions
264(2)
11.2.2 Censoring
266(1)
11.2.3 Random Effect Specification
266(2)
11.2.4 General Hazard Model
268(1)
11.2.5 Cox Model
268(1)
11.2.6 Extensions
269(1)
11.3 Spatial Longitudinal Analysis
270(9)
11.3.1 General Model
273(1)
11.3.2 Seizure Data Example
273(4)
11.3.3 Missing Data
277(2)
11.4 Extensions to Repeated Events
279(10)
11.4.1 Simple Repeated Events
279(1)
11.4.2 More Complex Repeated Events
280(1)
11.4.2.1 Known Times
281(1)
11.4.2.1.1 Single Events
281(1)
11.4.2.1.2 Multiple Event Types
282(1)
11.4.3 Fixed Time Periods
283(1)
11.4.3.1 Single Events
284(1)
11.4.3.2 Multiple Event Types
284(1)
11.4.3.2.1 Asthma-Comorbidity Medicaid Example
285(4)
12 Spatio-Temporal Disease Mapping
289(18)
12.1 Case Event Data
289(2)
12.2 Count Data
291(8)
12.2.1 Georgia Low Birth Weight Example
296(3)
12.3 Alternative Models
299(8)
12.3.1 Autologistic Models
300(2)
12.3.2 Spatio-Temporal Leroux Model
302(1)
12.3.3 Latent Structure Spatial-Temporal (ST) Models
302(5)
13 Disease Map Surveillance
307(18)
13.1 Surveillance Concepts
307(3)
13.1.1 Syndromic Surveillance
308(1)
13.1.2 Process Control Ideas
309(1)
13.2 Temporal Surveillance
310(4)
13.2.1 Single Disease Sequence
312(1)
13.2.2 Multiple Disease Sequences
313(1)
13.2.3 Infectious Disease Surveillance
313(1)
13.3 Spatial and Spatio-Temporal Surveillance
314(11)
13.3.1 Components of Pij
315(1)
13.3.1.1 Component Identification and Estimation Issues
315(1)
13.3.1.1.1 Refitting?
315(1)
13.3.1.1.2 Background and Endemicity
316(1)
13.3.2 Prospective Space-Time Analysis
317(1)
13.3.2.1 An EWMA Approach
318(1)
13.3.3 Sequential Conditional Predictive Ordinate Approach
318(4)
13.3.4 Surveillance Kullback Leibler (SKL) Measure
322(1)
13.3.4.1 Residual-Based Approach
323(1)
13.3.4.2 Sequential MCMC
324(1)
14 Infectious Disease Modeling
325(26)
14.0.1 Spatial Scale and Ascertainment
325(1)
14.0.1.1 Asymptomatic Cases
326(1)
14.0.2 Individual Level Modeling
327(1)
14.0.3 Aggregate Level Modeling
328(1)
14.0.4 Poisson or Binomial Approximation
328(1)
14.1 Descriptive Methods
329(2)
14.1.1 Case Event Data
329(1)
14.1.1.1 Partial Likelihood Formulation in Space-Time
329(1)
14.1.2 Count Data
330(1)
14.2 Mechanistic Count Models
331(2)
14.2.0.1 South Carolina Influenza Data
332(1)
14.3 Veterinary Disease Mapping
333(8)
14.3.0.1 Foot and Mouth Descriptive Data Example
336(2)
14.3.0.2 Mechanistic Infection Modeling
338(1)
14.3.0.3 Some Complicating Factors
338(1)
14.3.1 FMD Mechanistic Count Modeling
339(1)
14.3.1.1 Susceptible-Infected-Removed (SIR) Models
339(1)
14.3.1.1.1 Transmission Models
339(1)
14.3.1.2 Estimation of Termination
340(1)
14.4 Zoonoses
341(10)
14.4.1 Leishmaniasis
343(1)
14.4.2 Tularemia
344(4)
14.4.3 Some Modeling Issues for Zoonoses and Infectious Diseases
348(3)
15 Computational Software Issues
351(32)
15.1 Graphics on GeoBUGS and R
351(7)
15.1.1 Mapping on R
351(1)
15.1.2 Handling Polygon Objects
352(1)
15.1.2.1 Thematic Maps
352(1)
15.1.2.1.1 tmap
353(2)
15.1.2.1.2 spplot
355(1)
15.1.2.1.3 ggplot2
355(2)
15.1.3 GeoBUGS and Quantum GIS (QGIS)
357(1)
15.2 Preparing Polygon Objects for WinBUGS, CARBayes or INLA
358(2)
15.2.1 Adjacencies and Weight Matrices
358(2)
15.3 Posterior Sampling Algorithms
360(3)
15.3.1 Software
360(1)
15.3.1.1 WinBUGS and OpenBUGS
361(1)
15.3.1.2 JAGS
362(1)
15.3.1.3 CARBayes
363(1)
15.4 Alternative Samplers
363(2)
15.4.1 Hamiltonian MC (HMC) and Langevin Sampling
363(1)
15.4.2 Software
364(1)
15.5 Approximate Bayesian Computation (ABC)
365(1)
15.6 Posterior Approximations
366(1)
15.6.1 Software
367(1)
15.7 Comparison of Software for Spatial and Spatio-Temporal Modeling
367(10)
15.7.1 Spatial Models
367(1)
15.7.1.1 Larynx Cancer Data set, Northwest England
367(2)
15.7.1.2 Georgia County Level Oral Cancer Incidence, 2004
369(5)
15.7.2 Spatio-Temporal Models
374(3)
15.8 Pros and Cons of Software Packages
377(6)
Appendices
383(1)
Appendix A Basic R, WinBUGS/OpenBUGS
383(24)
A.1 Basic R Usage
383(5)
A.1.1 Data
383(1)
A.1.2 Graphics
384(4)
A.2 Use of R in Bayesian Modeling
388(3)
A.3 WinBUGS and OpenBUGS
391(7)
A.3.1 Simulation
391(1)
A.3.2 Model Code
392(6)
A.4 R2WinBUGS and R20penBUGS Functions
398(6)
A.5 OpenBUGS and JAGS
404(1)
A.6 BRugs
404(3)
Appendix B Selected WinBUGS Code
407(12)
B.1 Code for Convolution Model (Chapter 5)
407(1)
B.2 Code for Spatial Spline Model (Chapter 5)
408(1)
B.3 Code for Spatial Autologistic Model (Chapter 6)
408(1)
B.4 Code for Logistic Spatial Case Control Model (Chapter 6)
409(1)
B.5 Code for PP Residual Model (Chapter 6)
409(1)
B.5.1 Same Model with Uncorrelated Random Effect
410(1)
B.6 Code for Logistic Spatial Case-Control Model (Chapter 6)
410(2)
B.6.0.1 R2WinBUGS Commands
411(1)
B.7 Code for Poisson Residual Clustering Example (Chapter 6)
412(1)
B.8 Code for Proper CAR Model (Chapter 5)
412(1)
B.9 Code for Multiscale Model for PH and County-Level Data (Chapter 9)
413(1)
B.10 Code for Shared Component Model for Georgia Asthma and COPD (Chapter 10)
414(1)
B.11 Code for Seizure Example with Spatial Effect (Chapter 11)
415(1)
B.12 Code for Knorr-Held Model for Space-Time Relative Risk Estimation (Chapter 12)
416(1)
B.13 Code for Space-Time Autologistic Model (Chapter 12)
416(3)
Appendix C R Code for Thematic Mapping
419(2)
Appendix D CAR Model Examples
421(2)
References 423(36)
Index 459
Andrew B. Lawson is a professor of biostatistics and eminent scholar in the Division of Biostatistics and Epidemiology in the College of Medicine at the Medical University of South Carolina. He is an ASA fellow and an advisor in disease mapping and risk assessment for the World Health Organization. Dr. Lawson has published over 100 journal papers and eight books and is the founding editor of Spatial and Spatio-temporal Epidemiology. He received a PhD in spatial statistics from the University of St. Andrews. His research interests include the analysis of clustered disease maps, spatial and spatio-temporal disease surveillance, nutritional measurement error, and Bayesian latent variable and SEM modeling.
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