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Table 3 Performance comparison of alternative estimators: mean square error of prediction. Results obtained on average over 100 realizations generated under two different population size scenarios and 3 types of risk map (1 = observed, 2 = smooth, 3 = random). Poisson kriging was conducted with the semivariogram estimated from the underlying risk values (true γR(h)) or the simulated mortality rates. Bold numbers refer to best performances outside the ideal case where the true semivariogram of risk is known.

From: Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging

Estimators WF population BF population
BREAST CANCER Scenario 1 Scenario 2 Scenario 3 Scenario 1 Scenario 2 Scenario 3
Observed rates 4.426 4.462 4.777 1178 1461 1321
Population-weighted average 3.249 1.085 8.159 8.093 3.753 11.40
Global Empirical Bayes 5.090 4.591 2.286 17.09 9.536 6.853
Local Empirical Bayes 1.514 0.811 2.424 8.631 5.543 11.02
Poisson kriging (true γR(h)) 0.828 0.593 2.376 6.154 3.534 9.648
Poisson kriging 0.857 0.625 2.452 7.107 3.741 10.03
CERVIX CANCER       
Observed rates 0.803 0.802 0.738 367 257 232
Population-weighted average 0.590 0.149 1.006 1.088 0.617 1.468
Global Empirical Bayes 0.556 0.496 0.318 1.387 1.079 0.906
Local Empirical Bayes 0.264 0.116 0.341 3.143 1.685 3.440
Poisson kriging (true γR(h)) 0.177 0.041 0.313 0.881 0.566 1.233
Poisson kriging 0.179 0.045 0.335 1.117 0.764 1.383