Introduction

Model-based Geostatistics for Global Public Health

Emanuele Giorgi

Lancaster University

Overview

• Defining geostatistical problems
• Spatial exploratory analysis based on the variogram

Epidemiological Data

• Incidence: Number of new cases per unit time per unit population
  
• Prevalence: Number of existing cases per unit population
  
• Risk: Probability that a person will contract the disease (per unit time or lifetime)

Objective: Understand spatial variation in disease incidence, prevalence, and risk

Relevant books:
Elliott et al. (2000), Gelfand et al. (2010), Rothman (1986), Waller & Gotway (2004), Woodward (1999)

Cholera in Victorian London, 1854

• John Snow removed the handle of the Broad Street water pump
  
• Identified contaminated water as the disease source
  
• Contradicted conventional wisdom at the time

1854 Broad Street cholera outbreak

Study Designs

1. Registry
   • Case counts in sub-regions
     
   • Population size as denominator
     
   • Covariates from census data
2. Case-Control
   • Cases: All known cases in the study region
     
   • Controls: Probability sample of non-cases
3. Survey
   • Sampled locations within study region
     
   • Data collected per location
     
   • Common in low-resource settings

Registry Example: Plague in Madagascar

Research Question:
Does plague infection risk increase above 800m elevation?

Giorgi et al., 2016, Spatial and Spatio-temporal Epidemiology

Case-Control Example: Childhood Leukaemia in Humberside

• Locations of all known cases (1974–82)
  
• Residential locations of a random sample of births

References:
Cuzick & Edwards (1990), Diggle & Chetwynd (1991)

Survey Example: Loa loa in Cameroon

• Data: Empirical prevalences in surveyed villages
  
• Map: Predictive probabilities of exceeding 20% prevalence threshold

Diggle et al., 2007

Research Questions

Plague in Madagascar

• Is elevation an important risk factor?
  
• If so, why?

Childhood Leukaemia in Humberside

• Do cases show unexpected clustering?

Loa loa in Cameroon

• What environmental factors influence risk?
  
• Can we predict areas exceeding an intervention threshold?

Epidemic vs Endemic Patterns

• Epidemic: Foot-and-mouth in Cumbria (2001)
  
• Endemic: Gastroenteric disease in Hampshire (AEGISS)

Animations:
- Foot-and-mouth
- AEGISS

How are these patterns different?

Empirical Modelling: AEGISS Project

• Objective: Early detection of incidence anomalies
  
• 3,374 reports of gastro-intestinal illness
  
• Log-Gaussian Cox process for space-time correlation

Geostatistics

• Data: \((y_i, x_i)\), where \(x_i \in A \subset \mathbb{R}^2\)
  

• Model: \(Y_i = S(x_i) + Z_i\)
  

• Objective: Estimate \(\int_{A} S(x) dx\) (e.g., mining yield)

Model-Based Geostatistics for Public Health

Animation: Malaria in Chikwawa district

Science and Statistics

Key Concepts:
- \(S\): “Process of nature”
- \(Y\): “Observed data”
- Bayesian Framework: \([Y, S] = [S][Y | S]\)

Adapted from: Statistics and Scientific Method (Diggle & Chatwynd, 2011)

Workflow of a statistical analysis

How do we apply the workflow of a statistical analysis in model-based geostatistics?