In summary, we have presented a new method of stochastic model reduction that allows for impressive improvement in time series prediction. The reduced model captures both the amplitude and phase accurately for a temporal scale that is many orders of magnitude longer than the typical relaxation time. Since sufficient statistics of disease data are limited due to short time series collection, the results presented here provide a potential method to properly model real, stochastic disease data in the time domain. Such longterm accuracy of the reduced model will allow for the application of effective control of a disease where phase differences between outbreak times and vaccine controls are important. Additionally, since our method is general, it may be applied to very high-dimensional epidemic models, such as those involving adaptive networks. From a dynamical systems viewpoint, the reduction method has the potential to accurately capture new, emergent dynamics as we increase the size of the random fluctuations. This could be a means to identify new noise-induced phenomena in generic stochastic systems. Comparison of distance measures in spatial analytical modeling for health service planning BACKGROUND: 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. METHODS: 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. RESULTS: 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. CONCLUSION: 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. Health service research is concerned with the investigation of how social, financial, organizational, technological, and behavioral factors affect access to health care, the quality and cost of health care, and ultimately health and well-being [1] . Distance plays a vital role in studies assessing spatial disease patterns as well as access to hospital services. In a highly complex health care environment, even micro-geographic differences in the availability of tertiary services can affect access to care [2, 3] . The study of distances from patient homes to the nearest hospital is an example where distance is often studied as a crude but objective indicator of geographic accessibility to hospital services [4] . In such situations, the measurement of actual travel distance (or travel time) on a road network is clearly the most appropriate method [5] . Health service research, however, encompasses a much broader investigation area, where spatial analytical models are employed to assist in the provision of effective accessibility to health care services. Distance is often used indirectly in these types of analysis as one of the parameters defining the model's thrust and its results.