Comparison of distance measures in spatial analytical modeling for health service planning

Abstract

BackgroundSeveral methodological approaches have been used to estimate distance in health service research. In this study, focusing on cardiac catheterization services, Euclidean, Manhattan, and the less widely known Minkowski distance metrics are used to estimate distances from patient residence to hospital. Distance metrics typically produce less accurate estimates than actual measurements, but each metric provides a single model of travel over a given network. Therefore, distance metrics, unlike actual measurements, can be directly used in spatial analytical modeling. Euclidean distance is most often used, but unlikely the most appropriate metric. Minkowski distance is a more promising method. Distances estimated with each metric are contrasted with road distance and travel time measurements, and an optimized Minkowski distance is implemented in spatial analytical modeling.MethodsRoad distance and travel time are calculated from the postal code of residence of each patient undergoing cardiac catheterization to the pertinent hospital. The Minkowski metric is optimized, to approximate travel time and road distance, respectively. Distance estimates and distance measurements are then compared using descriptive statistics and visual mapping methods. The optimized Minkowski metric is implemented, via the spatial weight matrix, in a spatial regression model identifying socio-economic factors significantly associated with cardiac catheterization.ResultsThe Minkowski coefficient that best approximates road distance is 1.54; 1.31 best approximates travel time. The latter is also a good predictor of road distance, thus providing the best single model of travel from patient's residence to hospital. The Euclidean metric and the optimal Minkowski metric are alternatively implemented in the regression model, and the results compared. The Minkowski method produces more reliable results than the traditional Euclidean metric.ConclusionRoad distance and travel time measurements are the most accurate estimates, but cannot be directly implemented in spatial analytical modeling. Euclidean distance tends to underestimate road distance and travel time; Manhattan distance tends to overestimate both. The optimized Minkowski distance partially overcomes their shortcomings; it provides a single model of travel over the network. The method is flexible, suitable for analytical modeling, and more accurate than the traditional metrics; its use ultimately increases the reliability of spatial analytical models.

Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data

“…Curriero 2006, Money et al 2009); (2) landscape studies using kriging, where landscape-based distance metrics are derived (e.g. Jensen et al 2006, Lyon et al 2010; and (3) socioeconomic studies, where Minkowski distances have been used (Kent et al 2006, Shahid et al 2009). In general, empirical work indicates that there is no 'one-fit-all' distance metric, and the scope of possible distance metrics in spatial analysis is far larger than a single Euclidean choice.…”

The Minkowski approach for choosing the distance metric in geographically weighted regression

“…For example, Shahabi et al (2002) and Shahid et al (2009) use Minkowski distance to approximate road distances and TTs. Love et al (1988), cited by Miller and Wentz (2003), indicate that the value of p typically ranges from 1 to 2 for representing the true travel distance at urban and regional scales.…”

Geographic Accessibility to Health Services and Neonatal Mortality Among Very-Low Birthweight Infants in South Carolina

“…Among rural populations, road travel time based on GIS estimates was found to more closely reflect actual drive time as compared to straight-line distance (Jordan, Roderick, Martin, & Barnett, 2004). When comparing travel distances over larger geographic areas, straight line distance was shown to be a poor approximation for actual journey times (Shahid, Bertazzon, Knudtson, & Ghali, 2009). …”