Smoothed Maps

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Smoothed Maps
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This is a Smoothed Map
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Ideas Behind Smoothing

• To avoid arbitrary political boundaries
• To adjust unstable estimates towards a global
  mean
• To borrow strength from neighboring areas

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Spatial Smoothing Techniques

• 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.
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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, 5622-630,
1994.
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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, 29369-378, 1991. Mungiole M, Pickle
LW, Simonson KH. Application of a weighted
head-banging algorithm to mortality data maps.
Statistics in Medicine, 183201, 1999.
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Pickle et al United States Mortality Atlas
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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
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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.
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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.
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Smoothed Probability Maps
Provides contours of p-values
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Low Birth Weight in Des Moines, Iowa Rushton
Lolonis Statistics in Medicine 1996
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Spatial Filters / Kernel Smoothers
References
Kafadar K. Smoothing geographical data,
particularly rates of disease. Statistics in
Medicine, 152539-2560, 1996. Rushton G, Lolonis
P. Exploratory spatial analysis of birth defect
rates in an urban population. Statistics in
Medicine, 15717-726, 1996. Talbot TO, et al.
Evaluation of spatial filters to create smoothed
maps of health data. Statistics in Medicine,
192399-2408, 2000.
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Exploratory/Descriptive Techniques

• Maps of rates or relative risks
• Probability maps
• Smoothed rates or relative risks
• Smoothed probability maps

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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