Realistic power simulations compare point- and area-based disease cluster tests

One can roughly divide disease cluster tests into area-based (using regional data) and point-based (using exact locations). We have compared the power of two area-based methods (Moran's I and I* (pop), a new method) to that of two point-based methods (the Cuzick-Edwards test and Grimson's test), using three realistic simulations of disease (fox rabies in England, childhood leukaemia in North Humberside, England, and Lyme disease in Georgia). The naive belief that point-based methods should be better is not supported: for the complex data simulated here, I* (pop) and the Cuzick-Edwards test had higher power than Grimson's method or Moran's I. I* (pop) capitalizes on high inter-region variability, while Moran's I cannot.