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El. knyga: Spatio-Temporal Methods in Environmental Epidemiology

(University of Bath, UK), (University of British Columbia, Vancouver, Canada)
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Spatio-temporal modeling has been used for many exciting applications but this is the first book to address the interface between this type of modeling and environmental epidemiology. Relying heavily on real-life problems, the authors of this book introduce readers to spatio-temporal methodology with epidemiological applications. The authors use a Bayesian approach as their unifying frame work as they introduce topics such as visualization, mapping, high-dimensional data analysis, monitoring networks and preferential sampling. The text also include embedded R code with information about other software computational methods. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological Studies

Spatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and environmental epidemiologists, the book links recent developments in spatio-temporal methodology with epidemiological applications. Drawing on real-life problems, it provides the necessary tools to exploit advances in methodology when assessing the health risks associated with environmental hazards. The book’s clear guidelines enable the implementation of the methodology and estimation of risks in practice.

Designed for graduate students in both epidemiology and statistics, the text covers a wide range of topics, from an introduction to epidemiological principles and the foundations of spatio-temporal modeling to new research directions. It describes traditional and Bayesian approaches and presents the theory of spatial, temporal, and spatio-temporal modeling in the context of its application to environmental epidemiology. The text includes practical examples together with embedded R code, details of specific R packages, and the use of other software, such as WinBUGS/OpenBUGS and integrated nested Laplace approximations (INLA). A supplementary website provides additional code, data, examples, exercises, lab projects, and more.

Representing a major new direction in environmental epidemiology, this book—in full color throughout—underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Students will learn how to identify and model patterns in spatio-temporal data as well as exploit dependencies over space and time to reduce bias and inefficiency.

Recenzijos

"The authors of this text, both accomplished researchers in the area, provide a much-needed consolidation of spatio-temporal modelling methodsThe textbook condenses many complex topics into accessible and manageable chapters addressing key elements of modern spatio-temporal analyses of environmental epidemiologic dataThe authors provide helpful R examples throughoutAnalytic challenges such as missing data, measurement error, and preferential sampling often arise in environmental epidemiology and are each described in detail along with focused data examples and accompanying codeThe text covers a remarkable number of topics in its 318 pages (including many full color graphics and examples of code and output). The structure outlined above provides excellent coverage of many areas of recent development, held together with compelling examples and illustrationsOverall, I found the book a comprehensive overview placing many different topics into a logical perspective with focused, helpful examples. I enjoyed reading the book, am already recommending it to colleagues, and anticipate referring to it often in my future work." Lance A.Waller, Emory University, The American Statistician, November 2016 "The authors of this text, both accomplished researchers in the area, provide a much-needed consolidation of spatio-temporal modelling methodsThe textbook condenses many complex topics into accessible and manageable chapters addressing key elements of modern spatio-temporal analyses of environmental epidemiologic dataThe authors provide helpful R examples throughoutAnalytic challenges such as missing data, measurement error, and preferential sampling often arise in environmental epidemiology and are each described in detail along with focused data examples and accompanying codeThe text covers a remarkable number of topics in its 318 pages (including many full color graphics and examples of code and output). The structure outlined above provides excellent coverage of many areas of recent development, held together with compelling examples and illustrationsOverall, I found the book a comprehensive overview placing many different topics into a logical perspective with focused, helpful examples. I enjoyed reading the book, am already recommending it to colleagues, and anticipate referring to it often in my future work." Lance A.Waller, Emory University, The American Statistician, November 2016

List of Figures xvii
List of Tables xxiii
Preface xxv
Abbreviations xxix
The Authors xxxi
1 Why spatio-temporal epidemiology? 1(16)
1.1 Overview
1(1)
1.2 Health-exposure models
2(1)
1.2.1 Estimating risks
2(1)
1.2.2 A new world of uncertainty
3(1)
1.3 Dependencies over space and time
3(3)
1.3.1 Contrasts
4(2)
1.4 Examples of spatio-temporal epidemiological analyses
6(3)
1.5 Bayesian hierarchical models
9(3)
1.5.1 A hierarchical approach to modelling spatio-temporal data
10(1)
1.5.2 Dealing with high-dimensional data
10(2)
1.6 Spatial data
12(2)
1.7 Good spatio-temporal modelling approaches
14(1)
1.8 Summary
15(2)
2 Modelling health risks 17(30)
2.1 Overview
17(1)
2.2 Types of epidemiological study
17(1)
2.3 Measures of risk
18(4)
2.3.1 Relative risk
19(1)
2.3.2 Population attributable risk
20(1)
2.3.3 Odds ratios
21(1)
2.3.4 Relationship between odds ratios and relative risk
21(1)
2.3.5 Odds ratios in case-control studies
22(1)
2.4 Standardised mortality ratio (SMR)
22(2)
2.4.1 Rates and expected numbers
23(1)
2.5 Generalised linear models
24(3)
2.5.1 Likelihood
25(1)
2.5.2 Quasi-likelihood
25(1)
2.5.3 Likelihood ratio tests
25(1)
2.5.4 Link functions and error distributions
26(1)
2.5.5 Comparing models
27(1)
2.6 Generalised additive models
27(4)
2.6.1 Smoothers
28(1)
2.6.2 Splines
29(1)
2.6.3 Penalised splines
30(1)
2.7 Generalised estimating equations
31(2)
2.8 Poisson models for count data
33(4)
2.8.1 Estimating SMRs
33(2)
2.8.2 Over-dispersion
35(2)
2.9 Estimating relative risks in relation to exposures
37(3)
2.10 Modelling the cumulative effects of exposure
40(2)
2.11 Logistic models for case-control studies
42(2)
2.12 Summary
44(1)
Exercises
44(3)
3 The importance of uncertainty 47(14)
3.1 Overview
47(1)
3.2 The wider world of uncertainty
48(1)
3.3 Quantitative uncertainty
49(2)
3.3.1 Data uncertainty
50(1)
3.3.2 Model uncertainty
51(1)
3.4 Methods for assessing uncertainty
51(2)
3.4.1 Sensitivity analysis
51(1)
3.4.2 Taylor series expansion
52(1)
3.4.3 Monte Carlo sampling
52(1)
3.4.4 Bayesian modelling
53(1)
3.5 Quantifying uncertainty
53(6)
3.5.1 Variance
54(2)
3.5.2 Entropyt
56(1)
3.5.3 Information and uncertainty
57(2)
3.5.4 Decomposing uncertainty with entropy
59(1)
3.6 Summary
59(1)
Exercises
60(1)
4 Embracing uncertainty: the Bayesian approach 61(14)
4.1 Overview
61(1)
4.2 Introduction to Bayesian inference
62(1)
4.3 Exchangeability
63(3)
4.4 Using the posterior for inference
66(1)
4.5 Predictions
66(1)
4.6 Transformations of parameters
67(1)
4.6.1 Prior distributions
67(1)
4.6.2 Likelihood
67(1)
4.6.3 Posterior distributions
67(1)
4.7 Prior formulation
68(3)
4.7.1 Conjugate priors
68(1)
4.7.2 Reference priors
69(1)
4.7.3 Transformations
69(1)
4.7.4 Jeffreys' prior
69(1)
4.7.5 Improper priors
69(1)
4.7.6 Joint priors
70(1)
4.7.7 Nuisance parameters
70(1)
4.8 Summary
71(1)
Exercises
71(4)
5 The Bayesian approach in practice 75(16)
5.1 Overview
75(1)
5.2 Analytical approximations
75(1)
5.3 Markov Chain Monte Carlo (MCMC)
76(4)
5.3.1 Metropolis-Hastings algorithm
77(1)
5.3.2 Gibbs sampling
78(1)
5.3.3 Block updating
79(1)
5.4 Using samples for inference
80(1)
5.5 WinBUGS
80(3)
5.6 INLA
83(4)
5.6.1 R-INLA
84(3)
5.7 Summary
87(1)
Exercises
87(4)
6 Strategies for modelling 91(30)
6.1 Overview
91(1)
6.2 Contrasts
92(1)
6.3 Hierarchical models
93(2)
6.3.1 Cluster effects
94(1)
6.4 Generalised linear mixed models
95(2)
6.5 Linking exposure and health models
97(5)
6.5.1 Two-stage approaches
99(1)
6.5.2 Multiple imputation
100(2)
6.6 Model selection and comparison
102(7)
6.6.1 Effect of selection on properties of estimators
102(4)
6.6.2 Selection procedures
106(3)
6.7 What about the p-value?
109(2)
6.8 Comparison of models - Bayes factors
111(2)
6.9 Bayesian model averaging
113(5)
6.9.1 Interpretation
116(2)
6.10 Summary
118(1)
Exercises
119(2)
7 Is 'real' data always quite so real? 121(18)
7.1 Overview
121(1)
7.2 Missing values
122(3)
7.2.1 Imputation
123(1)
7.2.2 Regression method
124(1)
7.2.3 MCMC method
124(1)
7.3 Measurement error
125(4)
7.3.1 Classical measurement error
126(1)
7.3.2 Berkson measurement error
126(1)
7.3.3 Attenuation and bias
127(1)
7.3.4 Estimation
128(1)
7.4 Preferential sampling
129(6)
7.4.1 A method for mitigating the effects of preferential sampling
132(3)
7.5 Summary
135(1)
Exercises
136(3)
8 Spatial patterns in disease 139(18)
8.1 Overview
139(4)
8.1.1 Smoothing models
140(1)
8.1.2 Empirical Bayes smoothing
140(3)
8.2 The Markov random field (MRF)t
143(4)
8.3 The conditional autoregressive (CAR) model
147(2)
8.3.1 The intrinsic conditional autoregressive (ICAR) model
148(1)
8.3.2 The simultaneous autoregressive (SAR) model
149(1)
8.4 Spatial models for disease mapping
149(5)
8.4.1 Poisson-lognormal models
149(5)
8.5 Summary
154(1)
Exercises
154(3)
9 From points to fields: modelling environmental hazards over space 157(42)
9.1 Overview
157(1)
9.2 A brief history of spatial modelling
157(1)
9.3 Exploring spatial data
158(3)
9.3.1 Transformations and units of measurement
159(2)
9.4 Modelling spatial data
161(1)
9.5 Spatial trend
162(1)
9.6 Spatial prediction
163(2)
9.7 Stationary and isotropic spatial processes
165(1)
9.8 Variograms
166(4)
9.8.1 The nugget
168(1)
9.8.2 Variogram models
168(2)
9.9 Fitting variogram models
170(2)
9.10 Kriging
172(2)
9.11 Extensions of simple kriging
174(4)
9.11.1 Co-kriging
175(1)
9.11.2 Trans-Gaussian kriging
175(1)
9.11.3 Non-linear kriging
176(1)
9.11.4 Model-based kriging
176(1)
9.11.5 Bayesian kriging
177(1)
9.12 A hierarchical model for spatially varying exposures
178(6)
9.12.1 Implementation
179(1)
9.12.2 Prediction at unmeasured locations
180(4)
9.13 INLA and spatial modelling in a continuous domain
184(6)
9.13.1 Implementing the SPDE approach
185(5)
9.14 Non-stationary random fields
190(5)
9.14.1 Geometric and zonal anisotropy
190(2)
9.14.2 Moving window kriging
192(1)
9.14.3 Convolution approach
193(2)
9.15 Summary
195(1)
Exercises
195(4)
10 Why time also matters 199(28)
10.1 Overview
199(1)
10.2 Time series epidemiology
199(2)
10.2.1 Confounders
200(1)
10.2.2 Known risk factors
200(1)
10.2.3 Unknown risk factors
201(1)
10.3 Time series modelling
201(5)
10.3.1 Low-pass filtering
204(2)
10.4 Modelling the irregular components
206(4)
10.4.1 Stationary processes
207(1)
10.4.2 Models for irregular components
207(3)
10.5 The spectral representation theorem and Bochner's lemmas
210(3)
10.5.1 The link between covariance and spectral analysis
212(1)
10.6 Forecasting
213(5)
10.6.1 Exponential smoothing
213(1)
10.6.2 ARIMA models
214(1)
10.6.3 Forecasting using ARMA models
215(3)
10.7 State space models
218(2)
10.7.1 Normal Dynamic Linear Models (DLMs)
218(2)
10.8 A hierarchical model for temporally varying exposures
220(4)
10.9 Summary
224(1)
Exercises
225(2)
11 The interplay between space and time in exposure assessment 227(24)
11.1 Overview
227(1)
11.2 Strategies
227(2)
11.3 Spatio-temporal models
229(7)
11.3.1 Separable models
231(4)
11.3.2 Non-separable processest
235(1)
11.4 Dynamic linear models for space and time
236(2)
11.5 An empirical Bayes approach
238(6)
11.6 A hierarchical model for spatio-temporal exposure data
244(2)
11.7 Approaches to modelling non-separable processes
246(2)
11.8 Summary
248(1)
Exercises
248(3)
12 Roadblocks on the way to causality: exposure pathways, aggregation and other sources of bias 251(18)
12.1 Overview
251(1)
12.2 Causality
252(2)
12.3 Ecological bias
254(4)
12.3.1 Individual level model
254(1)
12.3.2 Aggregation if individual exposures are known
255(1)
12.3.3 Aggregation if the individual exposures are not known
256(2)
12.4 Acknowledging ecological bias
258(1)
12.4.1 Aggregate approach
258(1)
12.4.2 Parametric approach
258(1)
12.5 Exposure pathways
259(2)
12.5.1 Concentration and exposure response functions
259(2)
12.6 Personal exposure models
261(5)
12.6.1 Micro-environments
262(4)
12.7 Summary
266(1)
Exercises
266(3)
13 Better exposure measurements through better design 269(30)
13.1 Overview
269(1)
13.2 Design objectives?
270(3)
13.3 Design paradigms
273(2)
13.4 Geometry-based designs
275(1)
13.5 Probability-based designs
276(3)
13.6 Model-based designs
279(1)
13.6.1 Regression parameter estimation
280(1)
13.7 An entropy-based approach
280(13)
13.7.1 The design of a network
283(5)
13.7.2 Redesigning networks
288(5)
13.8 Implementation challenges
293(2)
13.9 Summary
295(1)
Exercises
295(4)
14 New frontiers 299(20)
14.1 Overview
299(1)
14.2 Non-stationary fields
300(8)
14.2.1 Spatial deformations
300(4)
14.2.2 Dimension expansiont
304(4)
14.3 Physical-statistical modelling
308(3)
14.3.1 Dynamic processes
309(2)
14.4 The problem of extreme values
311(7)
14.5 Summary
318(1)
Exercises
318(1)
Appendix 1: Distribution theory 319(6)
A.1 Overview
319(1)
A.2 The multivariate and matric normal distributions
319(6)
A.2.1 Multivariate and matric t-distribution
320(1)
A.2.2 The Wishart distribution
321(1)
A.2.3 Inverted Wishart distribution
321(1)
A.2.4 Properties
322(1)
A.2.5 Bartlett decomposition
322(1)
A.2.6 Generalized Inverted Wishart
322(3)
Appendix 2: Entropy decomposition 325(2)
A.3 Overview
325(2)
References 327(22)
Index 349(8)
Author index 357
Gavin Shaddick is a reader in statistics in the Department of Mathematical Sciences at the University of Bath. He received his masters in applied stochastic systems from University College London and his PhD in statistics and epidemiology from Imperial College London.

His research interests include the theory and application of Bayesian statistics to the areas of spatial epidemiology, environmental health risk, and the modeling of spatio-temporal fields of environmental hazards. Of particular interest are computational techniques that allow the implementation of complex statistical models to real-life applications where the scope over both space and time may be very large.

Dr. Shaddick is actively involved in a number of substantive epidemiological projects related to the effects of air pollution to health. He has worked on many large-scale funded projects, including the high-resolution mapping of environmental pollutants, the utilization of information from multiple sources in estimating exposures to environmental hazards, and the characterization of uncertainty in scenario assessment and policy support.

He is a co-author of the Oxford Handbook of Epidemiology for Clinicians, which was Highly Commended in the Basis of Medicine Category, BMA Book Awards 2013.

James V. Zidek is a professor emeritus in the Department of Statistics at the University of British Columbia. Professor Zidek received his MSc and PhD in statistics from the University of Alberta and Stanford University, respectively.

He began his research career working on Walds statistical decision theory. That interest shifted into Bayesian decision analysis. His interest in applications also emerged early in his career and as a consultant, published with engineering collaborators, the first design code for long-span bridges, such as the famous Golden Gate Bridge in San Francisco. The combination of theory and practice led him to an EPA project on acid rain where he, with a few of his collaborators, started to lay the foundations of environmetrics as it is now called, notably on the design of environmental monitoring networks and spatio-temporal modeling of environmental processes. That work led naturally into spatio-temporal epidemiology, which remains an area of interest. He has published about 100 refereed articles and a book on modeling environmental processes.

His contributions to statistics have been recognized by a number of honors. He is a fellow of the ASA, IMS, and Royal Society of Canada; member of the ISI; and a recipient of the Gold Medal of the Statistical Society of Canada (its highest honor).
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