Shahid Rizwan, Bertazzon Stefania, Knudtson Merril L, Ghali William A
Department of Geography, University of Calgary, Calgary, AB, Canada.
BMC Health Serv Res. 2009 Nov 6;9:200. doi: 10.1186/1472-6963-9-200.
Several 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.
Road 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.
The 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.
Road 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.
在卫生服务研究中，已经采用了几种方法来估算距离。在本研究中，以心脏导管插入术服务为重点，使用欧几里得距离、曼哈顿距离以及鲜为人知的闵可夫斯基距离度量来估算从患者居住地到医院的距离。距离度量通常比实际测量产生的估计值准确性更低，但每个度量都提供了给定网络上的单一出行模型。因此，与实际测量不同，距离度量可直接用于空间分析建模。欧几里得距离最常被使用，但不太可能是最合适的度量。闵可夫斯基距离是一种更有前景的方法。用每个度量估算的距离与道路距离和出行时间测量值进行对比，并在空间分析建模中实施优化的闵可夫斯基距离。
从接受心脏导管插入术的每个患者的居住邮政编码计算到相关医院的道路距离和出行时间。对闵可夫斯基度量进行优化，使其分别近似出行时间和道路距离。然后使用描述性统计和可视化映射方法比较距离估计值和距离测量值。通过空间权重矩阵在识别与心脏导管插入术显著相关的社会经济因素的空间回归模型中实施优化的闵可夫斯基度量。
最接近道路距离的闵可夫斯基系数为1.54；1.31最接近出行时间。后者也是道路距离的良好预测指标，从而提供了从患者居住地到医院的最佳单一出行模型。在回归模型中交替实施欧几里得度量和最佳闵可夫斯基度量，并比较结果。闵可夫斯基方法比传统的欧几里得度量产生更可靠的结果。
道路距离和出行时间测量是最准确的估计值，但不能直接用于空间分析建模。欧几里得距离往往低估道路距离和出行时间；曼哈顿距离往往高估两者。优化的闵可夫斯基距离部分克服了它们的缺点；它提供了网络上的单一出行模型。该方法灵活，适用于分析建模，且比传统度量更准确；其使用最终提高了空间分析模型的可靠性。
