Transforming geographic scale: a comparison of combined population and areal weighting to other interpolation methods

Abstract

BackgroundTransforming spatial data from one scale to another is a challenge in geographic analysis. As part of a larger, primary study to determine a possible association between travel barriers to pediatric cancer facilities and adolescent cancer mortality across the United States, we examined methods to estimate mortality within zones at varying distances from these facilities: (1) geographic centroid assignment, (2) population-weighted centroid assignment, (3) simple areal weighting, (4) combined population and areal weighting, and (5) geostatistical areal interpolation. For the primary study, we used county mortality counts from the National Center for Health Statistics (NCHS) and population data by census tract for the United States to estimate zone mortality. In this paper, to evaluate the five mortality estimation methods, we employed address-level mortality data from the state of Georgia in conjunction with census data. Our objective here is to identify the simplest method that returns accurate mortality estimates.ResultsThe distribution of Georgia county adolescent cancer mortality counts mirrors the Poisson distribution of the NCHS counts for the U.S. Likewise, zone value patterns, along with the error measures of hierarchy and fit, are similar for the state and the nation. Therefore, Georgia data are suitable for methods testing. The mean absolute value arithmetic differences between the observed counts for Georgia and the five methods were 5.50, 5.00, 4.17, 2.74, and 3.43, respectively. Comparing the methods through paired t-tests of absolute value arithmetic differences showed no statistical difference among the methods. However, we found a strong positive correlation (r = 0.63) between estimated Georgia mortality rates and combined weighting rates at zone level. Most importantly, Bland–Altman plots indicated acceptable agreement between paired arithmetic differences of Georgia rates and combined population and areal weighting rates.ConclusionsThis research contributes to the literature on areal interpolation, demonstrating that combined population and areal weighting, compared to other tested methods, returns the most accurate estimates of mortality in transforming small counts by county to aggregated counts for large, non-standard study zones. This conceptually simple cartographic method should be of interest to public health practitioners and researchers limited to analysis of data for relatively large enumeration units.

Differences in Travel Time to Cancer Surgery for Colon versus Rectal Cancer in a Rural State: A New Method for Analyzing Time‐to‐Place Data Using Survival Analysis

“…We based our geocodes on the smallest geographic unit that had the most similar level of geographic quality across a study area regardless of urban or rural status, which in this case were Census 2010 ZIP Code Tabulation Areas (ZCTA). Patient origins (n = 885) were computed by matching the residential ZIP Code of the patients as listed in the cancer registry to the ZCTAs and then using the population‐weighted ZCTA centroid as their geocode 34 . Surgical locations were address‐level geocodes for any facility that performed any CRC surgery on an Iowa resident during the study period (n = 136).…”

Using Areal Interpolation to Deal with Differing Regional Structures in International Research

“…The issue of spatial data transformation between two different systems of spatial units is traditionally a challenging topic in geospatial literature [4,7,8]. In geostatistics, spatial data transformation is often referred to as the change of support problem (COSP) [5,7].…”

“…These measures express the amount of estimation involved in the data transformation process from one spatial system to another. The degree of hierarchy for the entire study area is equal to the proportion of all source zones (municipalities) that fall completely within any of the target zones (grids) [8,16]. It gives evidence of nesting.…”

“…where i = a source spatial unit (municipality), j = a target spatial unit (grid cell), w ij = the proportion of the municipality that overlaps the grid cell, and n = the number of source units (municipalities). The degree of fit for the entire study area is the proportion of sums of the maximal weight of each source unit (municipality) and the number of all source units (municipalities) [8,16]. It measures the extent of overlap between two spatial systems.…”

“…where max w ij is the maximum proportion of the municipality i to grid j overlap. As other researchers dealing with areal interpolation [8,17], we also use these two Simpson's measures to estimate the 'goodness of fit' between the real regional structure and the regular structures with different grid sizes. These goodness of fit statistics were used to choose the best fit target grid structure.…”