Effects of randomization methods on statistical inference in disease cluster detection

Monte Carlo methods are commonly used to assess the statistical significance of disease clusters. This usually involves permuting the observed outcome measure, such as the rate of disease, across the geographic units within the study area. When the variance of the disease rates is heterogeneous, however, randomizing the disease rate across the geographic units results in over-estimating the p-values in areas of low variance and under-estimating the p-values in areas of high variance. This bias results in under-ascertainment of clusters in urban areas and over-ascertainment of clusters in rural areas. As an alternative, randomizing the number of cases of disease or deaths proportional to the population at risk preserves the variance structure of the study area, therefore resulting in unbiased statistical inference. We compare results from randomizing rates with those from randomizing case counts, using county-level prostate cancer mortality data for the United States and ZIP-Code level prostate cancer incidence data for New York State, using the local Moran's I statistic.