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We analyse the effect of using prevalence rates based on populations with different sizes in the power of spatial independence tests. We compare the well known spatial correlation Moran's index to three indexes obtained after adjusting for population density, one proposed by Oden, another proposed by Waldhör, and a third proposed by us in this paper. We find an effect of spatially correlated populations in the type I error probability on the test based on Moran's and Waldhör's indexes. We conclude also that the test proposed by Oden is powerful to test risk heterogeneity, but it has disadvantages when the interest is solely on the spatial correlation of morbidity risks. In this latter case, we recommend using our proposed test which is more powerful than the usual Moran's index applied directly to the rates.
Assunção et al. (Mon,) studied this question.