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

Table 6 Performance comparison of geostatistical and Bayesian estimators: discriminatory power of models of uncertainty.

Estimators	Lung cancer		Cervix cancer
LOW RISK THRESHOLD (RR = 1)	Average	% best result	Average	% best result
BYM model	4.009	14	3.532	16
Point Poisson kriging (adjacent counties)	4.112	20	3.751	4
ATA Poisson kriging (adjacent counties)	4.186	36	3.915	38
ATA Poisson kriging (32 neighbors)	4.132	30	3.995	42
HIGH RISK THRESHOLD	RR = 1.1		RR = 1.25
BYM model	7.037	6	5.859	2
Point Poisson kriging (adjacent counties)	7.842	12	6.300	0
ATA Poisson kriging (adjacent counties)	8.059	36	6.721	6
ATA Poisson kriging (32 neighbors)	8.243	46	7.381	92

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. The reported statistic is the average probability of exceeding a risk threshold for counties with true risk above that threshold divided by the average probability for the remaining counties. A low (Relative Risk, RR = 1) and high risk threshold (RR = 1.1, RR = 1.25) were considered. Bold numbers refer to best performances: large probability ratio. The second column gives the percentage of realizations where the particular method yields the best results.

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