Kernel density estimation with geographically masked points

Abstract

Geographic masking displaces points to hide their identities. It has been used in health-related studies to protect patients' confidentialities. The main concern in this process is the balance between the protection of confidentiality and the preservation of the original spatial pattern. However, there is paucity in literature on quantification of this balance. We conducted a preliminary research on the most commonly used geographic masking method, the point dithering method, intending to quantify the original spatial pattern preserved under different dithering thresholds. We performed kernel density estimation (KDE) using a series of bandwidths to create density surfaces from both the original points and the dithered points, and then calculated Pearson's correlation coefficients between a density surface of the original points and its corresponding surfaces of the dithered points created with the same bandwidth. Using simulated data in New Hampshire, our test reveals a clear relationship between the bandwidth of KDE and the dithering threshold: When the bandwidth is 5 times the dithering threshold, the density surfaces of the original points and the dithered points are almost identical (in most cases the correlation coefficient ≫ 0.99). This relationship provides reference for choosing appropriate bandwidth in point pattern analysis, such as cluster detection, when working with dithered points.