Spatial Scan Statistic

It uses Monte Carlo hypothesis testing rather than analytic p-values. After computing the maximum likelihood ratio over all candidate windows in the real data, it generates many datasets under the null of no clustering (randomly allocating cases in proportion to population) and recomputes the same maximized statistic for each. The observed statistic's rank among the simulated maxima yields the p-value. Because each simulated dataset's statistic is itself a maximum over all windows, the null distribution already embodies the full multiplicity of the search, so the test is correctly sized despite scanning an enormous number of overlapping circles.

The maximum cluster size caps how large a scanning window can grow, typically expressed as a fraction of the population at risk (50% is the conventional default). A smaller cap focuses power on tight, local clusters and can split a large diffuse cluster, while a larger cap can detect broad excesses but may report implausibly large 'clusters' that cover much of the map. Because results depend on this choice, good practice is to run the scan at several maximum sizes and report sensitivity, choosing a value motivated by the plausible spatial scale of the disease process under study rather than accepting the default uncritically.

Use the scan statistic when the goal is detection and hypothesis testing: deciding whether discrete clusters exist and locating them with a p-value, as in surveillance and outbreak investigation. Use Bayesian disease mapping when the goal is estimation: producing a smooth, full-map picture of relative risk with stabilized small-area rates and uncertainty. The two are complementary, scanning answers 'is there a significant hot spot and where,' while mapping answers 'what is the estimated risk surface everywhere.' Many studies run both, using the scan to flag clusters and a smoothed map to characterize the underlying risk pattern.