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Smoothed Maps
This is a Smoothed Map
Age adjusted
<0.75
0.75-0.85
0.85-0.95
0.95-1.05
1.05-1.15
>1.25
Ideas Behind Smoothing
• To avoid arbitrary political boundaries
• To adjust unstable estimates towards a
global mean
• To borrow strength from neighboring areas
Spatial Smoothing Techniques
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Rates/RRs in disjoint areas such as counties
Empirical Bayes
Headbanging
Spatial Filters / Kernel Smoothers
All techniques may be used for rates,
proportions or relative risks. The latter also
for probabilities.
Empirical Bayes
Global smoothers adjust each area estimate
towards a global mean.
Local smoothers adjust each area estimate
up or down depending on the data in
neighboring areas.
Review: Devine OJ, Louis TA, Halloran ME. Empirical
Bayes methods for stabilizing incidence rates before
mapping. Epidemiology, 5:622-630, 1994.
Headbanging
Adjusts estimates in an area by borrowing
strength from neighbouring areas.
Hansen KM. Headbanging: Robust smoothing in the plane.
IEEE Transactions on Geoscience and Remote Sensing,
29:369-378, 1991.
Mungiole M, Pickle LW, Simonson KH. Application of a
weighted head-banging algorithm to mortality data maps.
Statistics in Medicine, 18:3201, 1999.
Pickle et al: United States Mortality Atlas
Spatial Filters / Kernel Smoothers
Calculates rates / RRs in multiple
overlapping circular areas.
The rate / RRs for each circle is depicted at
the center of that circle.
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Spatial Filters / Kernel Smoothers
Larger Circles =
More smoothing and more stable estimates
Smaller Circles =
Less smoothing but higher geographical resolution
Spatial Filters / Kernel Smoothers
Circles of fixed geographical size provides
equal geographical resolution across the map.
Circles of fixed population size provides
equally reliable estimates across the map.
Spatial Filters / Kernel Smoothers
Rather than a simple circle, one can use a
kernel with a higher weight in the center
and gradually lower weights further away
as one moves away from the center.
Smoothed Probability Maps
Provides contours of p-values
Low Birth Weight in
Des Moines, Iowa
Rushton & Lolonis
Statistics in Medicine
1996
Spatial Filters / Kernel Smoothers
References
Kafadar K. Smoothing geographical data, particularly rates
of disease. Statistics in Medicine, 15:2539-2560, 1996.
Rushton G, Lolonis P. Exploratory spatial analysis of birth
defect rates in an urban population. Statistics in Medicine,
15:717-726, 1996.
Talbot TO, et al. Evaluation of spatial filters to create
smoothed maps of health data. Statistics in Medicine,
19:2399-2408, 2000.
Exploratory/Descriptive Techniques
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Maps of rates or relative risks
Probability maps
Smoothed rates or relative risks
Smoothed probability maps
Maps of rates and probability maps are
very useful for descriptive purposes
Problem
Maps of Rates: No statistical testing
Probability Maps: Multiple testing
Solution
Tests for Spatial Randomness: One test