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E-raamat: Model-based Geostatistics for Global Public Health: Methods and Applications

(Lancaster University, UK), (Lancaster University)
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Model-based Geostatistics for Global Public Health: Methods and Applications provides an introductory account of model-based geostatistics, its implementation in open-source software and its application in public health research. In the public health problems that are the focus of this book, the authors describe and explain the pattern of spatial variation in a health outcome or exposure measurement of interest. Model-based geostatistics uses explicit probability models and established principles of statistical inference to address questions of this kind.

Features:











Presents state-of-the-art methods in model-based geostatistics.





Discusses the application these methods some of the most challenging global public health problems including disease mapping, exposure mapping and environmental epidemiology.





Describes exploratory methods for analysing geostatistical data, including: diagnostic checking of residuals standard linear and generalized linear models; variogram analysis; Gaussian process models and geostatistical design issues.





Includes a range of more complex geostatistical problems where research is ongoing.





All of the results in the book are reproducible using publicly available R code and data-sets, as well as a dedicated R package.

This book has been written to be accessible not only to statisticians but also to students and researchers in the public health sciences.

The Authors

Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences.

Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.

Arvustused

"This is an excellent source for public health professionals so far as the needed state-of-the-art concepts and methods that are needed to analyse and interpret geostatistical data. Basic knowledge of mathematical statistics is necessary to read through this well-written book... Focus has been made on disease mapping, environmental epidemiology, generalized linear models, variogram, and R-codes. The references are thorough and up-to-date. The examples are real-life oriented and interesting... Some unique features of this well-written book are the illustrations and they include river blindness in Liberia, heavy metal monitoring in Galicia, malnutrition in Ghana, rolling malaria in Malawi, ozone concentration in Eastern United States, prevalence and intensity of infection among others.This book is quite suitable to be a textbook for a graduate level course in global public health or geo-statistics. Researchers and doctoral graduate students seeking thesis topic ought to read this book. I enjoyed reading this book. I recommend this book to statistics and computing professionals." - Ramalingam Shanmugam, in the Journal of Statistical Computation and Simulation, April 2020

"This book was written primarily to introduce geostatistics to public health researchers...The text goes beyond introductory descriptions and provides a fairly comprehensive guide to geostatistics, ranging from the design of geostatistical experiments to the analysis of complicated datasets. While the books target audience is mainly public health researchers, the material is also helpful to PhD students and even statistics faculty that want an introduction to geostatistics. Each chapter can be read as an independent guide or read jointly to gain a more complete understanding of geostatistical research from data collection to analysis... The text is well-written and genuinely enjoyable to read. One of the main attractions of the book is that the authors offer tidbits of advice from their own expert experience analyzing geostatistical data...While other texts can lose the readers in the seemingly endless modeling choices, Diggle and Giorgi guide their audience to make informed decisions from the first design stages to the final visualizations." - Ian Laga and Xiaoyue Niu, JASA 2020

"The book provides an integrated mix of statistical theory and applications, working up from linear regression through to generalised geostatistical models and on to specialised topics, such as zero-inflation in geostatistical models, spatiotemporal models and approaches to combining data from multiple sources...The relevant case studies developed throughout the course of the book provide an excellent demonstration of the methods and potential insight available from using geostatistical approaches. Furthermore, the emphasis on the communication of model results is a beneficial addition for any statistician working in a collaborative environment. Model-based Geostatistics for Global Public Health provides a good grounding in geostatistical modelling with excellent worked case studies in the global public health domain. It offers particular value to applied statisticians with its technical detail and thorough case studies. The book is supported by an open-source R package, PrevMap." - Kirsty L. Hassall, Rothamsted Research, Harpenden, UK "This is an excellent source for public health professionals so far as the needed state-of-the-art concepts and methods that are needed to analyse and interpret geostatistical data. Basic knowledge of mathematical statistics is necessary to read through this well-written book... Focus has been made on disease mapping, environmental epidemiology, generalized linear models, variogram, and R-codes. The references are thorough and up-to-date. The examples are real-life oriented and interesting... Some unique features of this well-written book are the illustrations and they include river blindness in Liberia, heavy metal monitoring in Galicia, malnutrition in Ghana, rolling malaria in Malawi, ozone concentration in Eastern United States, prevalence and intensity of infection among others.This book is quite suitable to be a textbook for a graduate level course in global public health or geo-statistics. Researchers and doctoral graduate students seeking thesis topic ought to read this book. I enjoyed reading this book. I recommend this book to statistics and computing professionals." - Ramalingam Shanmugam, in the Journal of Statistical Computation and Simulation, April 2020

Preface xi
List of Figures
xv
List of Tables
xxv
1 Introduction
1(10)
1.1 Motivating example: mapping river-blindness in Africa
1(4)
1.2 Empirical or mechanistic models
5(2)
1.3 What is in this book?
7(4)
2 Regression modelling for spatially referenced data
11(18)
2.1 Linear regression models
11(5)
2.1.1 Malnutrition in Ghana
13(3)
2.2 Generalised linear models
16(5)
2.2.1 Logistic Binomial regression: river-blindness in Liberia
16(4)
2.2.2 Log-linear Poisson regression: abundance of Anopheles Gambiae mosquitoes in Southern Cameroon
20(1)
2.3 Questioning the assumption of independence
21(8)
2.3.1 Testing for residual spatial correlation: the empirical variogram
24(5)
3 Theory
29(26)
3.1 Gaussian processes
29(2)
3.2 Families of spatial correlation functions
31(6)
3.2.1 The exponential family
31(1)
3.2.2 The Matern family
32(2)
3.2.3 The spherical family
34(1)
3.2.4 The theoretical variogram and the nugget variance
35(2)
3.3 Statistical inference
37(5)
3.3.1 Likelihood-based inference
38(4)
3.4 Bayesian Inference
42(1)
3.5 Predictive inference
43(1)
3.6 Approximations to Gaussian processes
44(11)
3.6.1 Low-rank approximations
45(3)
3.6.2 Gaussian Markov random field approximations via stochastic partial differential equations
48(7)
4 The linear geostatistical model
55(28)
4.1 Model formulation
55(2)
4.2 Inference
57(5)
4.2.1 Likelihood-based inference
57(1)
4.2.1.1 Maximum likelihood estimation
58(1)
4.2.2 Bayesian inference
59(2)
4.2.3 Trans-Gaussian models
61(1)
4.3 Model validation
62(4)
4.3.1 Scenario 1: omission of the nugget effect
63(1)
4.3.2 Scenario 2: miss-specification of the smoothness parameter
64(1)
4.3.3 Scenario 3: non-Gaussian data
64(2)
4.4 Spatial prediction
66(4)
4.5 Applications
70(13)
4.5.1 Heavy metal monitoring in Galicia
70(5)
4.5.2 Malnutrition in Ghana (continued)
75(3)
4.5.2.1 Spatial predictions for the target population
78(5)
5 Generalised linear geostatistical models
83(22)
5.1 Model formulation
84(5)
5.1.1 Binomial sampling
85(2)
5.1.2 Poisson sampling
87(1)
5.1.3 Negative binomial sampling?
88(1)
5.2 Inference
89(4)
5.2.1 Likelihood-based inference
89(1)
5.2.1.1 Laplace approximation
89(1)
5.2.1.2 Monte Carlo maximum likelihood
90(1)
5.2.2 Bayesian inference
91(2)
5.3 Model validation
93(1)
5.4 Spatial prediction
94(1)
5.5 Applications
95(4)
5.5.1 River-blindness in Liberia (continued)
95(3)
5.5.2 Abundance of Anopheles Gambiae mosquitoes in Southern Cameroon (continued)
98(1)
5.6 A link between geostatistical models and point processes
99(3)
5.7 A link between geostatistical models and spatially discrete processes
102(3)
6 Geostatistical design
105(18)
6.1 Introduction
105(2)
6.2 Definitions
107(1)
6.3 Non-adaptive designs
107(10)
6.3.1 Two extremes: completely random and completely regular designs
108(1)
6.3.2 Inhibitory designs
109(1)
6.3.3 Inhibitory-plus-close-pairs designs
109(3)
6.3.3.1 Comparing designs: a simple example
112(2)
6.3.4 Modified regular lattice designs
114(1)
6.3.5 Application: rolling malaria indicator survey sampling in the Majete perimeter, southern Malawi
115(2)
6.4 Adaptive designs
117(3)
6.4.1 An adaptive design algorithm
118(2)
6.5 Application: sampling for malaria prevalence in the Majete perimeter (continued)
120(2)
6.6 Discussion
122(1)
7 Preferential sampling
123(18)
7.1 Definitions
123(2)
7.2 Preferential sampling methodology
125(5)
7.2.1 Non-uniform designs need not be preferential
126(1)
7.2.2 Adaptive designs need not be strongly preferential
126(1)
7.2.3 The Diggle, Menezes and Su model
127(1)
7.2.4 The Pati, Reich and Dunson model
127(1)
7.2.4.1 Monte Carlo maximum likelihood using stochastic partial differential equations
128(2)
7.3 Lead pollution in Galicia
130(4)
7.4 Mapping ozone concentration in Eastern United States
134(4)
7.5 Discussion
138(3)
8 Zero-inflation
141(16)
8.1 Models with zero-inflation
141(3)
8.2 Inference
144(1)
8.3 Spatial prediction
145(1)
8.4 Applications
146(11)
8.4.1 River blindness mapping in Sudan and South Sudan
146(4)
8.4.2 Loa loa: mapping prevalence and intensity of infection
150(7)
9 Spatio-temporal geostatistical analysis
157(26)
9.1 Setting the context
158(2)
9.2 Is the sampling design preferential?
160(3)
9.3 Geostatistical methods for spatio-temporal analysis
163(8)
9.3.1 Exploratory analysis: the spatio-temporal variogram
164(2)
9.3.2 Diagnostics and novel extensions
166(1)
9.3.2.1 Example: a model for disease prevalence with temporally varying variance
167(1)
9.3.3 Defining targets for prediction
168(1)
9.3.4 Accounting for parameter uncertainty using classical methods of inference
168(2)
9.3.5 Visualization
170(1)
9.4 Historical mapping of malaria prevalence in Senegal from 1905 to 2014
171(9)
9.5 Discussion
180(3)
10 Further topics in model-based geostatistics
183(16)
10.1 Combining data from multiple surveys
183(5)
10.1.1 Using school and community surveys to estimate malaria prevalence in Nyanza province, Kenya
184(4)
10.2 Combining multiple instruments
188(3)
10.2.1 Case I: Predicting prevalence for a gold-standard diagnostic
189(1)
10.2.2 Case II: Joint prediction of prevalence from two complementary diagnostics
190(1)
10.3 Incomplete data
191(8)
10.3.1 Positional error
191(4)
10.3.2 Missing locations
195(1)
10.3.2.1 Modelling of the sampling design
196(3)
Appendices
199(32)
A Background statistical theory
201(1)
A.1 Probability distributions
201(22)
A.1.1 The Binomial distribution
202(1)
A.1.2 The Poisson distribution
202(1)
A.1.3 The Normal distribution
203(1)
A.1.4 Independent and dependent random variables
204(2)
A.2 Statistical models: responses, covariates, parameters and random effects
206(2)
A.3 Statistical inference
208(1)
A.3.1 The likelihood and log-likelihood functions
208(2)
A.3.2 Estimation, testing and prediction
210(1)
A.3.3 Classical inference
211(4)
A.3.4 Bayesian inference
215(1)
A.3.5 Prediction
216(1)
A.4 Monte Carlo methods
217(1)
A.4.1 Direct simulation
218(1)
A.4.2 Markov chain Monte Carlo
218(2)
A.4.3 Monte Carlo maximum likelihood
220(3)
B Spatial data handling
223(8)
B.1 Handling vector data in R
223(4)
B.2 Handling raster data in R
227(4)
References 231(12)
Index 243
Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences.

Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.