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Smoothed Maps. This is a Smoothed Map. 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. Rates/RRs in disjoint areas such as counties Empirical Bayes

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Presentation Transcript
ideas behind smoothing
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
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.

empirical bayes
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
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.

spatial filters kernel smoothers
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 smoothers10
Spatial Filters / Kernel Smoothers

Larger Circles =

More smoothing and more stable estimates

Smaller Circles =

Less smoothing but higher geographical resolution

spatial filters kernel smoothers11
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 smoothers12
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
Smoothed Probability Maps

Provides contours of p-values

slide15

Low Birth Weight in

Des Moines, Iowa

Rushton & Lolonis

Statistics in Medicine

1996

spatial filters kernel smoothers16
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
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