This document discusses different methods for mapping disease data, including scatter mapping, choropleth mapping, and disease mapping. It describes using rates to map disease data by dividing case counts by population at risk. Examples are provided of mapping lung cancer rates in the US to show higher rates in Appalachian regions and lower rates in parts of the West. The document discusses evaluating spatial clusters using techniques like Moran's I and issues with using crude rates for small, sparse populations. It introduces empirical Bayesian estimation methods that "borrow strength" from neighboring areas to produce more stable risk estimates for mapping.

1. DISEASE MAPPING
Eric Delmelle
Geography & Earth Sciences, University of North Carolina at Charlotte,N.C.,U.S.A.
University of Eastern Finland (UEF) October 22 2018
Presentation of IMPRO project funded by Strategic Research Council

2. Introduction
• Different ways to map health related data
• Scattermap
• Areal data (choropleth mapping)
• Cases aggregated to geographic units
• Generally mapped as rates, using
population at risk as a denominator
• In the case of breast cancer deaths,
count of cancer deaths divided by
females (can be more restrictive for
the age segment).
Disease mapping Introduction

3. Rationale
• GIScientists and epidemiologists are interested to map the
variation of these rates across a specific region.
Disease mapping
• The map indicates that individuals
dying from tracheal, bronchus and lung
cancer are mostly concentrated in the
Appalachian regions (very rural, with
deprived access to care).
• Very low rates Southern Idaho, and
Utah, but also parts of Arizona, New
Mexico and Colorado. Note that
Southern Idaho and Utah are mostly
Mormon, where smoking is certainly
not encouraged.
Introduction

4. Rationale
Another example for the
Eastern USA, just focusing on
average annual rates for lung
and tracheal cancer rates
among males from 2011 to
2015, and using the 65+ male
census population as the
denominator
Disease mapping Introduction

5. Rationale
Disease mapping
• Clearly we saw some patterns, very
high in the Appalachian, but lower
along the coast.
• We also see thatVirginia has lower
rates.
• There could be some reasons for
this, such as prevention measures
that can vary by state.
• Although smoking is the main factor
contributing to lung cancer, living in
a heavy coal-mining area such as
Kentucky is found to be an
additional risk factor as residents in
these areas are exposed to
pollution from mining activities.
Introduction

6. Estimating spatial patterns/clusters
Disease mapping
• Evaluate whether regions of high rate have a tendency to cluster, using
techniques such as Moran’s I.
• Moran’s I will evaluate whether neighboring census units (in our case, counties)
tend to exhibit similar (high, or low) values.
• Adjacency matrix W; that is for each geographic unit, determine its neighbors, for
instance through an adjacency matrix (0 or 1 – resulting in wij), or the number
of closest neighbors (Rook versus Queen).This can easily be done within a
commercial GIS or Geoda.
Patterns and clustering

7. Estimating spatial patterns/clusters
Disease mapping
• Once this is complete, we can evaluate the Moran’s I.
𝐼 =
𝑁
𝑊
𝑤𝑖𝑗(𝑂𝑖 − 𝑂)(𝑂𝑗 − 𝑂𝑗𝑖
𝑂𝑗 − 𝑂
2
𝑖
With N the number of geographic units and O the rate.The term wij
denotes the adjacency value between i and j and W the sum.
Patterns and clustering

8. Estimating local spatial patterns/clusters
Disease mapping
• Unfortunately, the Moran’s I statistic does not tell us where clusters may be
located. Anselin developed a local version of the test, taking on the same values.
• The results can be particularly useful for health purposes.
Patterns and clustering

9. Estimating local spatial patterns/clusters
Disease mapping
• The local Moran’s I also returns a map of its significance
Patterns and clustering

10. Issues with rates
Disease mapping
• Oftentimes, assumption of normality. But not so evident when you use
proportion or count. – rather use Poisson or binomial distribution…the
variance may be related to the mean value.
Rates
Crude rate
𝑟𝑖 =
𝑂𝑖
𝑃𝑖
with 𝑂𝑖 observed count at i and 𝑃𝑖 the population at risk at i.
 The use of crude rates and ratios to estimate rare disease risks in small
areas is often problematic since these measures are typically subject to
large chance variation.
 Disease maps that are based directly on these crude estimates are difficult
to interpret and often misleading  unreliable rates that occur for sparsely
populated areas and/or rare cancers

11. Issues with rates
Disease mapping Rates
Standard Mortality Rate (SMR) – also called excess or relative risk
Then, the expected number
of events in i 𝐸𝑖 (also noted 𝜇𝑖)
is given as:
Idea is to compare observed mortality rate to a national (or regional) standard.
We will compare the number of events to the expected count of events.
𝜋 =
𝑂𝑖𝑖∈𝐼
𝑃𝑖𝑖∈𝐼
Reference rate
𝐸𝑖 = 𝜋 ∗ 𝑃𝑖
𝑆𝑀𝑅𝑖 =
𝑂𝑖
𝐸𝑖
SMR

12. Issues with rates
Disease mapping Rates
Population….

13. Issues with rates
Disease mapping Rates
• A very high relative risk (or SMR) could also happen if you have one case, and
expect 0.1 (near 1,000). Interestingly enough, this would lead to the same SMR:
(𝑂𝑖=100, 𝐸𝑖=50) and (𝑂𝑖=3, 𝐸𝑖=1.5) – same SMR.
• But if I add just one case to the second scenario, I would end up with wild SMR.
This suggests that the reliability of the estimates can vary widely and we need to
take the reliability into account.
• Probability mapping maps the probability of getting a count more ‘extreme’ than
the one we actually observed – assumption is that the count in each area is
Poisson distribution with mean value 𝜇𝑖

14. Issues with rates
Disease mapping Rates
• Extreme ratios associated with areas with the smallest populations.
• Solutions. Disease mapping methods, usually using Bayesian inference, seek to
borrow strength across areas to produce stable risk estimates. Essentially, we try
to improve the reliability of observed rates by using (or “borrowing”) information
from neighboring entities (Waller and Gotway 2004).
• The model is fit using data, and estimates of relative risks based on posterior
distributions for the random effects are derived.
• The resulting estimates for disease risks in small areas are based on pooling
information from related areas.
• Maps based on these estimates are often more interpretable and informative
(Lawson et al., 1999; Elliott et al., 2 000).

15. Empirical Bayesian Estimates
Disease mapping EBS
• Let’s suppose that we are trying to estimate the observed rate, say 𝜃𝑖 Then, we
can re-write this as:
• With 𝛾𝑖 and 𝜑𝑖 the mean and the variance of the prior probability distribution,
respectively.The first part of Equation puts emphasis on the observed rate, while
the second emphasizes prior belief.
𝜃𝑖 = 𝑤𝑖 ∗ 𝑟𝑖 + (1 − 𝑤𝑖) ∗ 𝛾𝑖

16. Empirical Bayesian Estimates
Disease mapping EBS
• The term 𝑤𝑖 is defined as follows:
• So then how to get 𝛾𝑖 and 𝜑𝑖? A first estimate would be that 𝛾𝑖 = 𝛾 and 𝜑𝑖 = 𝜑
for all areas.This means that the prior is gamma distributed with two parameters
𝑣 (scale) and 𝛼 (shape).We can deduct that 𝛾 =
𝑣
𝛼
and 𝜑 =
𝑣
𝛼2.
𝑤𝑖 =
𝜑𝑖
𝜑𝑖 +
𝛾𝑖
𝑛𝑖

17. Empirical Bayesian Estimates
Disease mapping EBS

18. Local Empirical Bayesian Estimates
Disease mapping EBS
Strength is borrowed from to correct for variance instability is localized as
opposed to global (i.e., based on all observations)

19. Local Empirical Bayesian Estimates
Disease mapping EBS
Strength is borrowed from to correct for variance instability is localized as
opposed to global (i.e., based on all observations)

20. Local Empirical Bayesian Estimates
Disease mapping EBS
Strength is borrowed from to correct for variance instability is localized as
opposed to global (i.e., based on all observations)

21. Questions
Department of Geography and Earth Sciences
University of North Carolina at Charlotte
Charlotte, NC 28223
Tel: (704) 687-5991
Email: Eric.Delmelle@uncc.edu
Disease mapping