smoothed maps. this is a smoothed map ideas behind smoothing to avoid arbitrary political boundaries...
TRANSCRIPT
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Smoothed Maps
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Age a djuste d<0.750.75-0.850.85-0.950.95-1.051.05-1.15>1.25
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, 5:622-630, 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, 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.
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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 inDes Moines, Iowa
Rushton & LolonisStatistics in Medicine1996
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Spatial Filters / Kernel Smoothers
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.
References
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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
ProblemMaps of Rates: No statistical testingProbability Maps: Multiple testing
SolutionTests for Spatial Randomness: One test