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.

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

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

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

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

Introduction

Definitions

Non-adaptive designs

Two extremes: completely random and completely regular designs

Inhibitory designs

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

An adaptive design algorithm

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

Models with zero-inaction

Inference

Spatial prediction