1st Edition
Model-based Geostatistics for Global Public Health Methods and Applications
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.
1 Introduction
Motivating example: mapping river-blindness in Africa
Empirical or mechanistic models
What is in this book?
2 Regression modelling for spatially referenced data
Linear regression models
Malnutrition in Ghana
Generalized linear models
Logistic Binomial regression: river-blindness in Liberia
Log-linear Poisson regression: abundance of Anopheles
Gambia mosquitoes in Southern Cameroon
Questioning the assumption of independence
Testing for residual spatial correlation: the empirical variogram
3 Theory
Gaussian processes
Families of spatial correlation functions
The exponential family
The Matter family
The spherical family
The theoretical variogram and the nugget variance
Statistical inference
Likelihood-based inference
Bayesian Inference
Predictive inference
Approximations to Gaussian processes
Low-rank approximations
Gaussian Markov random held approximations via stochastic partial differential equations
Contents
4 The linear geostatistical model
Model formulation
Inference
Likelihood-based inference
Maximum likelihood estimation
Bayesian inference
Trans-Gaussian models
Model validation
Scenario 1: omission of the nugget effect
Scenario 2: miss-specification of the smoothness parameter
Scenario 3: non-Gaussian data
Spatial prediction
Applications
Heavy metal monitoring in Galicia
Malnutrition in Ghana (continued)
Spatial predictions for the target population
5 Generalized linear geostatistical models 85
Model formulation
Binomial sampling
Poisson sampling
Negative binomial sampling?
Inference
Likelihood-based inference
Laplace approximation
Monte Carlo maximum likelihood
Bayesian inference
Model validation
Spatial prediction
Applications
River-blindness in Liberia (continued)
Abundance of Anopheles Gambia mosquitoes in Southern
Cameroon (continued)
A link between geostatistical models and point processes
A link between geostatistical models and spatially discrete processes
6 Geostatistical design
Introduction
Definitions
Non-adaptive designs
Two extremes: completely random and completely regular designs
Inhibitory designs
Contents
Inhibitory-plus-close-pairs designs
Comparing designs: a simple example
Modified regular lattice designs
Application: rolling malaria indicator survey sampling in the Manjeet perimeter, southern Malawi
Adaptive designs
An adaptive design algorithm
Application: sampling for malaria prevalence in the Manjeet perimeter (continued)
Discussion
7 Preferential sampling
Definitions
Preferential sampling methodology
Non-uniform designs need not be preferential
Adaptive designs need not be strongly preferential
The Diggle, Menezes and Su model
The Patti, Reich and Dunson model
Monte Carlo maximum likelihood using stochastic partial differential equations
Lead pollution in Galicia
Mapping ozone concentration in Eastern United States
Discussion
8 Zero-inaction
Models with zero-inaction
Inference
Spatial prediction
Applications
River blindness mapping in Sudan and South Sudan
Loa loa: mapping prevalence and intensity of infection
9 Spatio-temporal geostatistical analysis
Setting the context
Is the sampling design preferential?
Geostatistical methods for spatio-temporal analysis
Exploratory analysis: the spatio-temporal variogram
Diagnostics and novel extensions
Example: a model for disease prevalence with
temporally varying variance
Defining targets for prediction
Accounting for parameter uncertainty using classical
methods of inference
Visualization
Contents
Historical mapping of malaria prevalence in Senegal from 1905 to 2014
Discussion
10 Further topics in model-based geostatistics
Combining data from multiple surveys
Using school and community surveys to estimate
malaria prevalence in Nyanza province, Kenya
Combining multiple instruments
Case I: Predicting prevalence for a gold-standard diagnostic
Case II: Joint prediction of prevalence from two complementary
diagnostics
Incomplete data
Positional error
Missing locations
Modelling of the sampling design
Appendices
A Background statistical theory
Probability distributions
The Binomial distribution
The Poisson distribution
The Normal distribution
Independent and dependent random variables
Statistical models: responses, covariates, parameters and random
effects
Statistical inference
The likelihood and log-likelihood functions
Estimation, testing and prediction
Classical inference
Bayesian inference
Prediction
Monte Carlo methods
Direct simulation
Markov chain Monte Carlo
Monte Carlo maximum likelihood
B Spatial data handling 225
Handling shape-_les in R
Handling raster-_les in R
Creating spatial covariates
Maps and animations
References
Biography
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.
"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 book’s 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
