Model-based Geostatistics for Global Public Health

Methods and Applications

Peter J. Diggle, Emanuele Giorgi

• Publisher: Chapman and Hall/CRC
• Year: 2019
• eBook ISBN:
  9781351743266
• Topic: Medicine
• Subtopic: Probability & Statistics

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

CONTENTS

1.1 Motivating example: mapping river-blindness in Africa

1.2 Empirical or mechanistic models

1.3 What is in this book?

1.1 Motivating example: mapping river-blindness in Africa

FIGURE 1.1
Map of estimated pre-control prevalence of onchocericasis infection Africa-wide.

The African Programme for Onchocerciasis Control (APOC) was a WHO-coordinated programme to control onchocerciasis, more commonly known as river-blindness; see www.who.int/blindness/partnerships/APOC/en/. The programme was launched in 1995 and covered 20 participating African countries (Coffeng et al., 2013). In 2015, APOC was absorbed into the more wide-ranging Expanded Special Project for the Elimination of Neglected Tropical Diseases (ESPEN), see www.afro.who.int/en/espen.html.

River-blindness is a parasitic infection transmitted by the bite of an infected blackfly. APOC’s principal control strategy is annual mass prophylactic treatment of affected communities with an antifilarial medication, ivermectin, that kills the parasites before they can cause clinical disease. A useful tool to help prioritise mass distribution of the drug to the worst affected areas would be a map showing the geographical variation in prevalence throughout the APOC target region. Figure 1.1 shows such a map.

River-blindness

• The disease. River-blindness, also known as Onchocerciasis, is an infectious disease caused by the parasitic worm Onchocerca volvulus. It is currently endemic in 30 African countries, Yemen, and isolated regions of South America.

• The vector. It is transmitted from human to human through repeated bites of blackflies of the genus Simulium which breed along fast-owing rivers.

• The symptoms. The subcutaneous dying larvae can cause longterm damage to the skin. The larvae residing in the eye can also lead to visual impairment and, in severe cases, to blindness.

• The treatment. The standard medication used to kill the larvae of an infected person is ivermectin.

• Source. www.cdc.gov/parasites/onchocerciasis

How was this map constructed? Field-epidemiologists visited a number of rural communities in each of the 20 countries, selected a sample of between 30 and 50 adult members of each community, and tested each sampled individual for presence/absence of infection using a rapid diagnostic test (REMO, http://www.who.int/apoc/cdti/remo/en/). The resulting data can be characterised as a set of triplets, $\left(m_i,y_i,x_i\right):i=1,...,n$ in which m_i is the number of individuals tested and y_i the number who tested positive for infection in each of n sampled communities at locations x_i.

At any sampled location x_i, the observed proportion, $p_i=y_i∕m_i$, of sampled individuals who test positive is an estimate of the local prevalence, $P\left(x_i\right)$. To extend these estimates to unsampled locations x we need to interpolate spatially between the estimates at the sampled locations. There are many ways in which this can be done. One of the simplest objective methods is inverse-distance-weighting (Shepard, 1968). To interpolate the prevalence, p(x), at a location x, Shepard’s method first calculates the distances d_i between each x_i and x, then defines a set of weights, $w_i\left(x\right)=1∕d_i^p$ where, typically, p = 1 or 2, and defines the interpolated prevalence as

$p\left(x\right)=\left(\sum _{i=1}^n{w}_i{p}_i\right)∕\left(\sum _{i=1}^n{w}_i\right).$

Note that, by definition, any interpolation method will reproduce the observed prevalences p_i at the corresponding sampled locations x_i. From a statistical perspective, this is not obviously a good idea. We might prefer also to smooth the p_i themselves, to acknowledge that part of the variation amongst the p_i reflects binomial sampling error rather than genuine geographical variation in prevalence.

FIGURE 1.2
Prevalence map for onchocerciasis in Liberia produced by WHO (methodology unspecified).

In this book, our guiding principle is that problems of this kind are best solved by formulating, and empirically validating, a statistical model for the data and applying general principles of statistical inference to provide an answer to the scientific question, with the following features: it is as precise as possible; and it carries with it a quantitative indication of exactly how precise or imprecise the answer is. The details of how we do this will be developed in the remainder of the book. Here, we simply illustrate the result of applying our methods to data from one of the APOC countries, Liberia, and compare the result with a map published by the WHO that used an unspecified method of interpolation (http://www.who.int/apoc/cdti/remo/en/). The two maps use the same data, and are shown in Figures 1.3 and 1.2. On the model-based map, the data are plotted at their sampling locations with circles whose radius is proportional to the corresponding prevalence, and colour-coded to identify quintiles of the observed prevalences from blue (lowest) through green, yellow and brown to red (highest). The model-based estimates of prevalence are mapped using a continuous colour gradation from approximately 0.05 (5%, white) to 0.3 (30%, dark green).

FIGURE 1.3
Prevalence map for onchocerciasis in Liberia produced by the application of model-based geostatistics.

On the WHO map, the data are shown as circles at sampled locations with filled black wedges indicating the corresponding observed prevalence. Areas on the map are coloured red where “onchocerciasis is highly endemic and constitutes a significant public health problem” and green where “the prevalence of skin nodules is ≤20%.” Areas coloured yellow indicate “where results are not clear and additional rapid epidemiological assessment surveys are needed.”

The two maps tell a qualitatively similar story. However, an advantage of the model-based map is that it comes with estimates of its precision. Note in particular that the WHO defines areas with prevalence greater than 20% to be “treatment priority areas.” Accordingly, Figure 1.4 shows model-based predictive probabilities that local prevalence is greater than 20%. The maps in Figures 1.2 and 1.4 identify similar priority areas (red on the WHO map, green on the model-based map indicating ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• List of Figures
• List of Tables
• 1 Introduction
• 2 Regression modelling for spatially referenced data
• 3 Theory
• 4 The linear geostatistical model
• 5 Generalised linear geostatistical models
• 6 Geostatistical design
• 7 Preferential sampling
• 8 Zero-inflation
• 9 Spatio-temporal geostatistical analysis
• 10 Further topics in model-based geostatistics
• Appendices
• References
• Index