Estimation of representative spatial probabilities and expected counts from baseline data can cause problems in applying spatial scan statistics when observed events are sparse in a large percentage of the spatial zones (e.g., zip codes or census tracts) found in the data records. In applications of scan statistics to datasets with fine spatial resolution, such as census tracts or block groups, such highly skewed data distributions are likely to occur. If the spatial distribution estimation process does not handle the zones with low counts correctly, bias in the determination of statistically significant clusters will occur.
In any 8-week baseline period, some of the sparse-data zones have no counts at all. If ignored, the zero-count spatial zones will result in division by zero in the loglikelihood ratio evaluation. The traditional method of setting a floor on the expected counts in each spatial zone leads to a loss of sensitivity when the number of zero count zones is a significant fraction of all the zones. One alternative method for estimating spatial probabilities is to add one count to the sum of baseline counts in each spatial zone. This method has been used in a study of spatial cluster detection using medical 911 call data from San Diego County with good results. However, when this method was applied to data with a more highly skewed spatial distribution, issues were uncovered which led to this investigation of alternatives.
Objective
Modifications to spatial scan statistics are investigated for prospective cluster detection at fine-resolution with highly skewed spatial distributions having many spatial zones with very few cases. Several alternative methods for the estimation of spatial probabilities and expected counts from counts in a baseline data window are evaluated with the Poisson spatial scan statistic and the space-time permutation scan statistic using goodness-of-fit statistics and cluster rates to compare performance.