Disease Prevalence Estimates for
Neighbourhoods: Combining
Spatial Interpolation and Spatial
Factor Models
Peter Congdon, Queen Mary University of London
p.congdon@qmul.ac.uk
http://www.geog.qmul.ac.uk/staff/congdonp.html
http://webspace.qmul.ac.uk/pcongdon/
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Data on disease prevalence
 Health
data may be collected across one
spatial framework (e.g. health providers), but
policy interest may be contrasts in health
over another spatial framework (e.g.
neighbourhoods).
 Seek to use data for one framework to
provide spatially interpolated estimates of
disease prevalence for the other.
 But also incorporate neighbourhood
morbidity indicators that may also provide
information on prevalence
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Data Framework



Focusing on England, prevalence totals for
chronic diseases maintained by 8200 general
practices for their populations (subject to
measurement error, excess or deficits in “casefinding”). See Prevalence data tables at http://www.ic.nhs.uk/qof
These data not provided for any small area
populations, e.g. 32000 neighbourhoods across
England (Lower Super Output Areas or LSOAs)
Study focus: GP populations and LSOAs in Outer
NE London (970K population) and on estimating
neighbourhood psychosis prevalence
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London Borough Map
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Discrete Process Convolution




Use principles of discrete process convolution to
estimate neighbourhood prevalence.
Geostatistical techniques (multivariate Gaussian
process) computationally demanding for large
number of units involved
Base Framework: Prevalence for GP Populations
Target Framework: Prevalence for
Neighbourhoods
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Discrete Process Model
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Model for Base Framework, Study Data
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Model for Target Framework
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INCORPORATING OBSERVED INDICATORS of
NEIGHBOURHOOD PREVALENCE
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SCHEMATIC REPRESENTATION
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LIKELIHOOD: REFLEXIVE INDICATORS
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PARAMETER IDENTIFICATION
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POTENTIAL SENSITIVITY IN INFERENCES & FIT
 Sensitivity
to kernel density choice
 Sensitivity to constraint adopted (kernel
scale set or known; process variance set or
unknown)
 Sensitivity to form of process effects: e.g. wj
normal vs Student t
 Sensitivity to density of discrete grid
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SPATIAL SENSITIVITY IN INTERPOLATED
NEIGHBOURHOOD PREVALENCE

Can compare models in terms of localised hot spot
probabilities of high psychosis risk


Pr(k>1|y,h)>0.9
Or compare clustering of excess psychosis risk. Define
binary indicators

Jk=I(k>1)

Over MCMC iterations monitor excess risk in both
neighbourhood k and its adjacent neighbourhoods
l=1,..,Lk.

Ck is probability indicator of high risk cluster centred on
neighbourhood k.
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Study Specifications

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Locations: population centroids for GP populations and
LSOAs
Grid set at 2km spacing, no grid point more than 2km
from any neighbourhood centroid
Kernel form as in seed dispersal literature (e.g. Austerlitz
et al, 2004; Clark et al, 1999), e.g. bivariate exponential
with scale a and with distance d (from GP population
or neighbourhood to discrete grid point) as argument is


P(d|a)=
𝟏
𝟐𝝅𝒂
𝒅
𝟐
𝒆𝒙𝒑(− )
𝒂
Compare four models out of wide possible range of
options
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Fit Comparisons
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Comparing Neighbourhood Spatial Risk
Patterns
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OVERLAP AT NEIGHBOURHOOD LEVEL (K=562)
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Density plot (M4), prevalence rate
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Map of Interpolated Neighbourhood
Prevalence under M4
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Map of Clustering Probabilities under M4
(posterior means of Ck)
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Future Research
 Modify
interpolation to include “formative”
influences on prevalence (e.g. area
deprivation)
 How does model work with other chronic
diseases, or with jointly dependent disease
outcomes (e.g. diabetes, obesity)
 Space-time prevalence models, etc
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References
 Austerlitz
C et al (2004) Using genetic
markers to estimate the pollen dispersal
curve Molecular Ecology, 13, 937–954
 Clark J et al (1999) Seed dispersal near and
far: patterns across temperate and tropical
forests. Ecology, 80, 1475–1494.