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

Table 5 Performance comparison of geostatistical and Bayesian estimators: goodness and precision of models of uncertainty.

Estimators	Lung cancer		Cervix cancer
GOODNESS STATISTIC	Average	% best result	Average	% best result
BYM model	0.949	48	0.950	48
Point Poisson kriging (adjacent counties)	0.941	28	0.951	24
ATA Poisson kriging (adjacent counties)	0.922	14	0.939	16
ATA Poisson kriging (32 neighbors)	0.914	10	0.927	12
AVERAGE WIDTH OF PI
BYM model	2.544	14	0.816	4
Point Poisson kriging (adjacent counties)	2.439	20	0.813	0
ATA Poisson kriging (adjacent counties)	2.348	12	0.745	0
ATA Poisson kriging (32 neighbors)	2.313	54	0.691	96
% ACCURATE AND PRECISE PI
BYM model vs Point PK (adjacent counties)	9.35	6	12.73	8
BYM model vs ATA PK (adjacent counties)	7.53	4	6.22	2
BYM model vs ATA PK (32 neighbors)	7.35	4	4.30	4
Point PK (adjacent counties) vs BYM model	34.87	36	28.02	32
ATA PK (adjacent counties) vs BYM model	28.12	24	36.02	20
ATA PK (32 neighbors) vs BYM model	27.66	26	40.28	34

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 last statistic, based on the pair wise comparison of methods, reports the percentage of probability intervals (PI) that are jointly more accurate and precise. Bold numbers refer to best performances: goodness close to one, narrow probability intervals, and high percentage of accurate and precise PIs. The second column gives the percentage of realizations where the particular method yields the best results.

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