Use of space-filling curves in generating a national rural sampling frame for HIV AIDS research

The classical geographic research problem of regionalization and resource allocation is most commonly tackled by means of location-allocation methods. This paper introduces the spatial-order method as an alternative for creating regions or clusters. The spatial-order method utilizes space-filling curves, also known as Peano curves, to determine the nearness or spatial order of areal units, such as counties. Given a capacity constraint, the areal units are grouped consecutively according to their spatial order values. We applied the method to create clusters of rural counties for a national sampling survey of HIV/AIDS patients in the United States. Using the criteria that each cluster had approximately 50 new IUDS cases in 1991-1993 and that contiguity of areal units was maximized, 226 clusters were created from the 1,853 rural counties or health districts. The rural clusters generated by this method have been adopted as the national rural sampling frame in the HIV Cost and Services Utilization Study (HCSUS) being undertaken by RAND. In addition to its simplicity and fast computational speed, the spatial-order method produces satisfactory results. With minor modifications, this method can be an efficient alternative to the location-allocation method for solving a wide variety of locational problems, such as routing, political districting, and facilities location and allocation. This paper also demonstrates how a classical geographic research methodology, with the enhancement of GIS, can contribute to the multidisciplinary study of a pressing societal problem in our nation.