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Part 09
Application of Multi-level Models
to Spatial Epidemiology
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DATA STRUCTURE & GOALS
• We have geographically indexed dependent
variable and covariates
– Outcome, exposures, demographics, ...
• Want to study the relation between spatiotemporal variation in the dependent variable
and covariates
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CRUDE, COUNTY-SPECIFIC RELATIVE RISKS
Rates appear to cluster, with a noticeable
grouping of counties with SMR> 200 in the North
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SHRINKAGE
When the population in a region is large
• The statistical uncertainty is relatively small
• High credibility (weight) is given to the direct (MLE)
estimate
• The smoothed rate is close to observed rate
When the population in a region is small
• The statistical uncertainty is relatively large
• Little credibility (weight) is given to the direct (MLE)
estimate
• The smoothed rate is shrunken toward a local
(computed by other nearby regions) or a global target
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THE CAR MODEL
Local Smoothing
Crude SMR
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Smoothed SMR
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Posterior distribution of Relative Risk
for maximum exposure
(Maximum AFF)
Global smoothing
(posterior mean = 3.25)
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Local smoothing
(posterior mean = 2.18)
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Posterior distribution of Relative Risk
for average exposure
Global smoothing
(posterior mean = 1.08)
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Local smoothing
(posterior mean=1.09)
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Best
Histogram
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Comparison of Ranks
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Percentiles and Moments
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Highest estimated relative risk regions
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Lowest estimated
relative risk regions
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DISCUSSION
• It is important to explore sensitivity of the
results to modeling assumptions
– Priors, data models, .....
• For spatially correlated data use of global
smoothing may not be effective
• In the lip cancer study, the sensitivity of
results to choice of prior (global and local
smoothing) suggest presence of spatially
correlated latent factors
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Socio-economic and dietary factors of
pellagra deaths in southern US
Shum, Dominici & Marks
•
•
•
1930 data from approximately 800 counties in 9
states in Southern US
Outcome is county-specific observed and expected
number of pellagra deaths
Data set includes county-specific socio-economic
characteristics and dietary factors
• % acres in cotton
• % farms under 20 acres
• dairy cows per capita
• Access to a mental hospital
• % afro-american
• % single women
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PELLAGRA
• Disease caused by a deficient diet or failure of the body
to absorb B complex vitamins or an amino acid
• Prevalent in locations where people consume large
quantities of corn
• Characterized by scaly skin sores, diarrhea, mucosal
changes and mental symptoms such as schizophrenialike dementia
• May develop after gastrointestinal diseases or
alcoholism
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THE SMR
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Computing Expected Deaths
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Crude SMR (Observed/Expected) of
Pellagra Deaths in Southern USA in 1930
(Courtesy of Harry Marks)
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Analysis Questions & Framework
Use a Conditional Autoregressive (CAR) Model
• To assess which social, economic, behavioral or
dietary factors best explain the spatial distribution of
pellagra in southern US
• Which of the above factors are most important in
explaining the history of pellagra incidence in the US
• To what extent have state laws affected pellagra
incidence
• To adjust and smooth estimated rates 
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Crude and smoothed SMRs:
Pellagra Deaths in Southern USA in 1930
Crude SMR
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Smoothed SMR
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Complex Spatial Relations
and Data Structures
Requiring a hierarchical model
to sort things out
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Need a rosetta stone!
Mugglin, A.S., and Carlin, B.P. (1998)
Hierarchical Modeling in Geographic
Information Systems, Population interpolation
over incompatible zones
J. Agricultural, Biolological and Environmental
Statistics, 3: 111-130
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