Estimating Spatial Intensity and Variation in Risk from Locations Coarsened by Incomplete Geocoding

The estimation of spatial intensity and relative risk are important inference problems in spatial epidemiologic studies. A standard component of data assimilation in these studies is the assignment of a geocode, i.e. point-level spatial coordinates, to the address of each subject in the study population. Unfortunately, when geocoding is performed by the pervasive method of street-segment matching to a georeferenced road file and subsequent interpolation, it is rarely completely successful. Typically, 10% to 30% of the addresses in the study population fail to geocode, potentially leading to a selection bias called geographic bias. Missing-data methods might be considered for dealing with this; however, since there is almost always some geographic information coarser than a point (e.g. a zip code) measured for the observations that fail to geocode, a coarsened-data analysis is more appropriate. This article develops coarsened-data spatial epidemiologic methods for use with incompletely geocoded data, which can reduce or even eliminate geographic bias. In particular, existing completedata methods for estimating intensity and variation in relative risk are modified so as to exploit the coarsened data. Both nonparametric (kernel smoothing) and likelihood-based estimation procedures are considered. The success of these procedures relies on modeling and estimating a function called the geocoding propensity function, to which considerable attention is given. Models based on the degree of rurality are featured, as it is well-known that the propensity of rural addresses to geocode is much lower than for non-rural addresses. Advantages of the coarsened-data analyses are demonstrated empirically.