How does Poisson kriging compare to the popular BYM model for mapping disease risks?

Table 4 Performance comparison of Bayesian and geostatistical estimators: Smoothing effect and prediction variance.

Estimators	Lung cancer		Cervix cancer
	Dispersion variance	Prediction variance	Dispersion variance	Prediction variance
True risk values	9.817	-	1.153	-
Global Empirical Bayes	6.059	-	0.537	-
Local Empirical Bayes	7.905	-	1.063	-
BYM model	7.034	2.791	0.757	0.347
Point Poisson kriging (adjacent counties)	7.835	2.542	1.006	0.338
ATA Poisson kriging (adjacent counties)	7.563	2.363	0.977	0.287
ATA Poisson kriging (32 neighbors)	7.400	2.297	0.830	0.237

Results obtained on average over 50 realizations generated for Regions 1 and 2. Poisson kriging was conducted using either adjacent counties (same neighbors as BYM model) or the 32 closest counties in terms of distance between population-weighted centroids. ATA kriging accounts for the shape and size of the counties in the analysis. Straightforward empirical Bayesian smoothers were also applied. The dispersion variance measures the variability of the set of risk estimates, while the prediction variance quantifies the uncertainty attached to county-level risk estimates.

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