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.

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In order to accurately assess air pollution risks, health studies require spatially resolved pollution concentrations. Land-use regression (LUR) models estimate ambient concentrations at a fine spatial scale. However, spatial effects such as spatial non-stationarity and spatial autocorrelation can reduce the accuracy of LUR estimates by increasing regression errors and uncertainty; and statistical methods for resolving these effects--e.g., spatially autoregressive (SAR) and geographically weighted regression (GWR) models--may be difficult to apply simultaneously. We used an alternate approach to address spatial non-stationarity and spatial autocorrelation in LUR models for nitrogen dioxide. Traditional models were re-specified to include a variable capturing wind speed and direction, and re-fit as GWR models. Mean R(2) values for the resulting GWR-wind models (summer: 0.86, winter: 0.73) showed a 10-20% improvement over traditional LUR models. GWR-wind models effectively addressed both spatial effects and produced meaningful predictive models. These results suggest a useful method for improving spatially explicit models.

h i g h l i g h t s PM 1.0 -components displayed significant intra-urban variability in Calgary, Alberta. Land-use regression models were developed for 30 elements in summer and winter. 12 elements had models with R 2 > 0.7 in both seasons; 24 had R 2 > 0.5 in both seasons. Industrial sources were major predictors, as well as traffic, land-use, and wind. Interspecies dependencies were similar for measured and modeled pollutant data. a b s t r a c tAirborne particulate matter has been associated with cardiovascular and respiratory morbidity and mortality, and there is evidence that metals may contribute to these adverse health effects. However, there are few tools for assessing exposure to airborne metals. Land-use regression modeling has been widely used to estimate exposure to gaseous pollutants. This study developed seasonal land-use regression (LUR) models to characterize the spatial distribution of trace metals and other elements associated with airborne particulate matter in Calgary, Alberta.Two-week integrated measurements of particulate matter with <1.0 mm in aerodynamic diameter (PM 1.0 ) were collected in the City of Calgary at 25 sites in August 2010 and 29 sites in January 2011. PM 1.0 filters were analyzed using inductively-coupled plasma mass spectrometry. Industrial sources were obtained through the National Pollutant Release Inventory and their locations verified using Google Maps. Traffic volume data were obtained from the City of Calgary and zoning data were obtained from Desktop Mapping Technologies Incorporated. Seasonal wind direction was incorporated using wind rose shapes produced by Wind Rose PRO3, and predictor variables were generated using ArcMap-10.1. Summer and winter LUR models for 30 PM 1.0 components were developed using SAS 9.2.We observed significant intra-urban gradients for metals associated with airborne particulate matter in Calgary, Alberta. LUR models explained a high proportion of the spatial variability in those PM 1.0 components. Summer models performed slightly better than winter models. However, 24 of the 30 PM 1.0 related elements had models that were either good (R 2 > 0.70) or acceptable (R 2 > 0.50) in both seasons. Industrial point-sources were the most influential predictor for the majority of PM 1.0 components. Industrial and commercial zoning were also significant predictors, while traffic indicators and population density had a modest but significant contribution for most elements. Variables incorporating wind direction were also significant predictors. These findings contrast with LUR models for PM and gaseous pollutants in which traffic indicators are typically the most important predictors of ambient concentrations.These results suggest that airborne PM components vary spatially with the distribution of local industrial sources and that LUR modeling can be used to predict local concentrations of these airborne BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/ 4.0/). Atmospheric Environment 106 (2015) 165e177 elements. These models will support ...

For reasons that are not well understood, Aboriginal people with end-stage renal disease (ESRD) have lower rates of kidney transplantation. We hypothesized that distance between residence location and the closest transplant center was greater in Aboriginal dialysis patients and would partially explain the lower rate of transplantation in this population. We studied a random sample of 9905 patients initiating dialysis in Canada between 1990 and 2000. We calculated the distance between residence location at dialysis inception and the closest transplant center. Cox proportional hazards models were used to examine the relation between residence location and the likelihood of transplantation over a median period of 2.3 years. The proportion of Aboriginal participants living 300 km from the closest transplant center was 25, 18, 18, and 39% respectively, compared with 55, 19, 11, and 15% among white subjects. The relative likelihood of transplantation was significantly lower for Aboriginal compared to white participants across all four distance strata, with no apparent effect of residence location. For example, the relative likelihood of transplantation was hazard ratio (HR) 0.47, 95% confidence interval (CI) (0.31-0.72) in Aboriginal participants residing 300 km from the closest transplant center. Results were similar for transplants from deceased donors and living donors, and in all seven regions studied. In conclusion, remote location of residence does not explain the lower rate of kidney transplantation among Aboriginal people treated for ESRD in Canada.