There were 66,011 census tracts with a valid driving route to a hospital. The 114 remaining tracts mainly consisted of islands without ferries or bridges, along with a very small number where the selected point fell within a gated residential community.2
Straight-line distance predicted travel distance very well in nearly all locations, with the r2
for the United States as a whole equal to 0.94. The largest outliers were disproportionately located in Alaska, which has significant roadless areas and locations connected by ferry, but excluding Alaska did not alter the r2
. The detour index was 1.417 for the entire data set. Straight-line distance also predicted travel time very well, with r2
= 0.91 for the United States as a whole—reasonable given that travel distance and travel time are themselves highly correlated ().
Correlations between straight-line distance (km), travel distance (km), and travel time (min) for the fifty states of the United States, District of Columbia, and Puerto Rico (N = 66,011)
The r2 values are presented merely to establish that they are extremely high; their exact interpretation is confounded by the spatial autocorrelation of the observations. Of greater interest is identifying the number and location of tracts where the straight-line distance is a poor predictor of driving distance. Both the absolute and relative differences between the actual and predicted driving distances were used to measure this (). Over 90 percent of the tracts have good agreement using thresholds within 10 percent or 5 kilometers. For the remainder, positive relative errors represent locations where the actual driving distance exceeds the predicted driving distance; negative values represent the converse. Large positive relative errors are found near irregular shorelines, on islands, in very low-population-density wilderness areas, adjacent to other impassable physical features, or some combination of these. Large negative relative errors are in locations that are not close to a hospital but that have a very straight drivable route to the nearest one. The lowest possible relative error is 41.7 percent, the situation when a route follows exactly the shortest straight-line distance.
Differences between actual and predicted travel distance for the fifty states of the United States, District of Columbia, and Puerto Rico (N = 66,011)
The most extreme difference between straight-line distance and travel distance is found between Grand Marais, Minnesota, and Houghton, Michigan (). Here, an 8.5-hour drive through three states is required to cover a distance that via straight line is just 155 kilometers, yielding a detour index of 3.4. This example also misassigns the hospital that is truly closest, as the hospital in Duluth, Minnesota, would be reached before the one in Houghton. Other large differences are found at other locations in the western Great Lakes; between the eastern end of Long Island, New York, and Connecticut; and in remote parts of western states such as Utah and Idaho. The same type of pattern can be found within urban areas, albeit on a much reduced scale. In New York City, there is a section of Queens close to the East River where the closest hospital is 1.1 km across the river in Manhattan. With no bridge immediately nearby, driving this route requires traveling 9.4 km, a detour index of 8.5, but there are hospitals in Queens closer than this.
Example of incorrectly determined nearest hospital using straight-line distance.
The differences between straight-line distance and travel distance are further illustrated by mapping the outliers in Nevada, a state with some of the largest outliers (). The map reveals longer-than-expected travel distances in the mountainous suburbs west of Reno, where roads are sparse and serpentine. Meanwhile, in the small town of Elko, travel distances are shorter than expected owing to a very direct route to the nearest hospital—albeit one that is in an adjacent state, roughly four hours away. Overall, though, the two measures agree to within 10 kilometers for over 90 percent of the tracts.
Outliers in predicted travel distance based on straight-line distance, state of Nevada.
In terms of computational complexity, few studies involving geographic distance use as many points as we have used here (66,000 origins and 5,000 destinations). For studies larger than this, processing time could become an issue. In our study, identifying the nearest hospitals from each sample point and calculating the straight-line distances took about 1.5 hours using a desktop computer with dual 3.16 Ghz processors, 3.3 GB of RAM, and 250 GB of free drive space. Finding the travel times via the repeated calls to Google Maps took about five hours. Our approach would be inappropriate for the calculation of travel-distance or travel-time buffers, where very large numbers of travel routes would need to be evaluated. In contrast, the calculation of buffers based on straight-line distance is trivial.