1. Application of Multi-level Models to Spatial Epidemiology
Part 09
Application of Multi-level Models to Spatial Epidemiology
BIO656--Multilevel Models

2. BIO656--Multilevel Models
DATA STRUCTURE & GOALS
We have geographically indexed dependent variable and covariates
Outcome, exposures, demographics, ...
Want to study the relation between spatio-temporal variation in the dependent variable and covariates
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6. 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
BIO656--Multilevel Models

20. THE CAR MODEL Local Smoothing
Crude SMR
Smoothed SMR
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21. BIO656--Multilevel Models
Posterior distribution of Relative Risk for maximum exposure (Maximum AFF)
Global smoothing
(posterior mean = 3.25)
Local smoothing
(posterior mean = 2.18)
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22. Posterior distribution of Relative Risk for average exposure
Global smoothing
(posterior mean = 1.08)
Local smoothing
(posterior mean=1.09)
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Best
Histogram
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Comparison of Ranks
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26. Percentiles and Moments
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27. Highest estimated relative risk regions
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28. 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
BIO656--Multilevel Models

34. BIO656--Multilevel Models
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 schizophrenia-like dementia
May develop after gastrointestinal diseases or alcoholism
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THE SMR
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36. Computing Expected Deaths
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Crude SMR (Observed/Expected) of Pellagra Deaths in Southern USA in (Courtesy of Harry Marks)
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38. 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 
BIO656--Multilevel Models

39. Crude and smoothed SMRs: Pellagra Deaths in Southern USA in 1930
Crude SMR
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40. 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:
BIO656--Multilevel Models