Smoothed Maps

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

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

• 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 inDes Moines, Iowa

Rushton & LolonisStatistics in Medicine1996

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

Exploratory/Descriptive Techniques

• 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

ProblemMaps of Rates: No statistical testingProbability Maps: Multiple testing

SolutionTests for Spatial Randomness: One test