A method for quantifying artefacts in mapping methods illustrated by application to headbanging

Maps of disease rates (and other quantities) often must contend with variance associated with variable population sizes and low incidence within spatial units. These characteristics can lead to substantial statistical noise that can mask underlying spatial variation. As Gelman and Price illustrated, most conventional mapping methods fail to address this problem, and in fact can introduce statistical artefacts; mapped quantities can show spatial patterns even when there are no spatial patterns in the underlying parameter of interest. Kafadar evaluated the performance of the headbanging algorithm for spatial smoothing (Tukey and Tukey, Hansen) for eliminating small scale variation and preserving edge structure. Here we perform a simulation study to investigate the artefacts of maps smoothed by unweighted and weighted headbanging. We find substantial artefacts that depend on the spatial structure of the statistical variation (for example, the spatial pattern of sample sizes) and on the details of the spatial distribution of geographic units. The methods used here could readily be adapted to study other spatial smoothers; we choose headbanging because (i) it is an important method used in practice, and (ii) its heavily computational nature is naturally studied using simulation (in contrast to the analytical methods used by Gelman and Price).