Disease Prevalence Estimates for Neighbourhoods: Combining Spatial Interpolation and Spatial Factor Models Peter Congdon, Queen Mary University of London 1

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 2

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 “case- finding”). See Prevalence data tables at See Prevalence data tables at  These data not provided for any small area populations, e.g 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 3

London Borough Map 4

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 5

Discrete Process Model 6

Model for Base Framework, Study Data 7

Model for Target Framework 8

INCORPORATING OBSERVED INDICATORS of NEIGHBOURHOOD PREVALENCE 9

SCHEMATIC REPRESENTATION 10

LIKELIHOOD: REFLEXIVE INDICATORS 11

PARAMETER IDENTIFICATION 12

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. w j normal vs Student t  Sensitivity to density of discrete grid 13

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  J k =I(  k >1)  Over MCMC iterations monitor excess risk in both neighbourhood k and its adjacent neighbourhoods l =1,..,L k.  C k is probability indicator of high risk cluster centred on neighbourhood k. 14

Study Specifications 15

Fit Comparisons 16

Comparing Neighbourhood Spatial Risk Patterns 17

OVERLAP AT NEIGHBOURHOOD LEVEL (K=562) 18

Density plot (M4), prevalence rate 19

Map of Interpolated Neighbourhood Prevalenceunder M4 20

Map of Clustering Probabilities under M4 (posterior means of C k ) 21

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 22

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–