This article identifies and compares four different methods for dealing with inhomogeneous backgrounds in kernel density estimation. The four methods result from combinations of two bandwidth types (fixed vs. adaptive) and two adjustment sides (site side vs. case side). The fixed and adaptive bandwidths employ different uniform bases in density calculation (spatial extent vs. population support). The adaptive bandwidth's strength lies in identifying spatial extents of density variation. It also produces values that are more comparable between locations and more stable statistically. When making adjustments to address the background, the site-side method makes the adjustment at each site for which the density value is to be estimated, and the case-side method makes the adjustment at each case location. Within a disease-mapping context, the former measures population at risk around each site and the latter measures around each disease case. The case-side adjustment is more justifiable in an application like disease mapping. It is also less sensitive to spatial details of the background (a favorable feature) and considerably more computationally efficient. Lung cancer data from Merrimack County, New Hampshire, USA, are used to demonstrate and compare the results from the four methods, leading to the conclusion that the case-side-adaptive-bandwidth method is most advantageous.

Background: Geographic information systems have advanced the ability to both visualize and analyze point data. While point-based maps can be aggregated to differing areal units and examined at varying resolutions, two problems arise 1) the modifiable areal unit problem and 2) any corresponding data must be available both at the scale of analysis and in the same geographic units. Kernel density estimation (KDE) produces a smooth, continuous surface where each location in the study area is assigned a density value irrespective of arbitrary administrative boundaries. We review KDE, and introduce the technique of utilizing an adaptive bandwidth to address the underlying heterogeneous population distributions common in public health research. Results: The density of occurrences should not be interpreted without knowledge of the underlying population distribution. When the effect of the background population is successfully accounted for, differences in point patterns in similar population areas are more discernible; it is generally these variations that are of most interest. A static bandwidth KDE does not distinguish the spatial extents of interesting areas, nor does it expose patterns above and beyond those due to geographic variations in the density of the underlying population. An adaptive bandwidth method uses background population data to calculate a kernel of varying size for each individual case. This limits the influence of a single case to a small spatial extent where the population density is high as the bandwidth is small. If the primary concern is distance, a static bandwidth is preferable because it may be better to define the "neighborhood" or exposure risk based on distance. If the primary concern is differences in exposure across the population, a bandwidth adapting to the population is preferred. Conclusions: Kernel density estimation is a useful way to consider exposure at any point within a spatial frame, irrespective of administrative boundaries. Utilization of an adaptive bandwidth may be particularly useful in comparing two similarly populated areas when studying health disparities or other issues comparing populations in public health.

Travel time is an important metric of geographic access to health care. We compared strategies of estimating travel times when only subject ZIP code data were available. Using simulated data from New Hampshire and Arizona, we estimated travel times to nearest cancer centers by using: 1) geometric centroid of ZIP code polygons as origins, 2) population centroids as origin, 3) service area rings around each cancer center, assigning subjects to rings by assuming they are evenly distributed within their ZIP code, 4) service area rings around each center, assuming the subjects follow the population distribution within the ZIP code. We used travel times based on street addresses as true values to validate estimates. Population-based methods have smaller errors than geometry-based methods. Within categories (geometry or population), centroid and service area methods have similar errors. Errors are smaller in urban areas than in rural areas. Population-based methods are superior to the geometry-based methods, with the population centroid method appearing to be the best choice for estimating travel time. Estimates in rural areas are less reliable.

Characterizing geographic access depends on a broad range of methods available to researchers and the healthcare context to which the method is applied. Globally, travel time is one frequently used measure of geographic access with known limitations associated with data availability. Specifically, due to lack of available utilization data, many travel time studies assume that patients use the closest facility. To examine this assumption, an example using mammography screening data, which is considered a geographically abundant health care service in the United States, is explored. This work makes an important methodological contribution to measuring access—which is a critical component of health care planning and equity almost everywhere. We analyzed one mammogram from each of 646,553 women participating in the US based Breast Cancer Surveillance Consortium for years 2005–2012. We geocoded each record to street level address data in order to calculate travel time to the closest and to the actually used mammography facility. Travel time between the closest and the actual facility used was explored by woman-level and facility characteristics. Only 35 % of women in the study population used their closest facility, but nearly three-quarters of women not using their closest facility used a facility within 5 min of the closest facility. Individuals that by-passed the closest facility tended to live in an urban core, within higher income neighborhoods, or in areas where the average travel times to work was longer. Those living in small towns or isolated rural areas had longer closer and actual median drive times. Since the majority of US women accessed a facility within a few minutes of their closest facility this suggests that distance to the closest facility may serve as an adequate proxy for utilization studies of geographically abundant services like mammography in areas where the transportation networks are well established.