The spatial autocorrelation coefficient Moran's I under heteroscedasticity

The spatial distribution of rates used in epidemiology often raises questions concerning the randomness of the observed pattern. In order to provide a first answer to this kind of question, the well-known spatial autocorrelation coefficient Moran's I is frequently used. Unfortunately, under heteroscedasticity, that is, unequal variances of the rates due to different population sizes, the moments of the test distribution of Moran's I under H(0) differ from the usually used moments. To obtain a less biased test, it is proposed in this paper and validated by simulation results, to approximate the moments of Moran's I by means of incorporating population size into the covariance matrix of the rates.