Defining hospital clusters and associated service communities in metropolitan areas.

According to traditional concepts of hospital governance, each institution is considered responsible for the care of a defined community. Evaluation of hospital performance and effective service planning both require that hospitals’ service communities be identified. However, in metropolitan regions it is difficult to associate a geographic population with any one hospital because of the wide choice of facilities available to area residents. The service community concept becomes more meaningful in these regions if several hospitals with overlapping geographic communities are defined as a cluster. This paper describes a two-step method for identifying hospital clusters and their associated service communities. The first step involves analysis of patient origin data to identify logical clusters of hospitals. Three algorithms for performing this analysis are presented. In the second step, analytical findings are reviewed by a panel of area planners and hospital experts who, considering additional qualitative factors, determine how the hospitals may be most appropriately grouped. Experience in using this method for hospitals in the seven-county region around Detroit, Michigan suggests that reasonable clusters can be identified, although clusters of central city hospitals are less well-defined than those in the suburban areas. The central purpose of this country’s nearly 6000 community hospitals traditionally has been to provide care to residents of the hospitals’ home communities. Although regional coordination of decisions concerning hospital size, location and services has been stressed since the late 1960s and emphasized particularly since the passage of PL 93-641 in 1974, governance of community hospitals remains a local, rather than regional, responsibility. At the iocal level, effective decision-making by a hospital’s governing board depends to a great degree upon the board’s knowledge of the needs of the hospital’s service community and this, in turn, requires that the service community be clearly identified and measured. As stated by the American Hospital Association, “careful appraisal by each institution of the area and people it plans to serve is essential to effective personal health services planning” [I]. In regions which contain few, geographically dispersed hospitals, identification of the population served by each hospital is reasonably straightforward.4 However, in metropolitan regions patients typically have numerous hospitals available within reasonable travel distance. When selecting hospitals for care, patients in these regions are often influenced by ethnic and religious factors, medical staff affiliations of their physicians, physician referral patterns, availability of special services at particular hospitals and other non-spatial considerations[3, S-81. Thus the concept of each intThe research described in this paper was supported through a grant from the W. K. Kellogg Foundation. Additional details on the research, including algorithms used, are available in the Hospital Performance Measures Project, University of Michigan Program and Bureau of Hospital Administration, Technical Paper Number 5. SSee, e.g. 1241. stitution possessing its own distinct service area is rarely meaningful for metropolitan hospitals. Nevertheless, evidence suggests that geography remains an important concern in these patient decisions[9]. Residents of a suburban community are more likely to utilize hospitals located in or near that suburb than to travel to central-city hospitals. In few cases do patients leave a relatively self-sufficient group of hospitals in one suburban area to seek hospital care in another suburb. And city residents tend to use city hospitals, with some preference given to hospitals located in the general vicinity of the patients’ residences. Where several adjacent neighborhoods, small suburbs or other areas located within an urban region are served by a common set of hospitals, the set of hospitals can be defined as a cluster, with the combined areas constituting the cluster’s service community. While this cluster concept does not provide for identification of populations uniquely associated with individual hospitals, it does allow meaningful service communities to be defined for groups of hospitals and it can demonstrate the necessity for coordinated organization and delivery of services by neighboring institutions. The purpose of this paper is to present an approach for defining hospital clusters and their service communities. Methods to test the existance of hospital groups serving overlapping geographic communities (clustering) will be reviewed. Using data from a statewide patient origin study, clustering methods are applied to hospitals in the metropolitan area around Detroit, Michigan. This region contains 82 hospitals and is composed of seven counties with populations ranging from 82,000 to 2.48 million. Identification of hospital clusters and service communities was the first step in a multi-year project to evaluate the impact of presenting annual evaluative data on hospital performance to areawide planners, hospital 45 46 J. W. THOMAS et al. administrators and hospital trustees. With cluster service communities defined, measures can be obtained which relate performance to size and other characteristics of the communities being served.t CLUSTER DEFINITION METHODS A cluster will contain one or more hospitals which (together) account for most or all of the hospital care provided to residents of an identifiable community. For a well-defined cluster, it can be shown based on objective analysis of patient origin data that patients from the geographic community surrounding the group of hospitals are likely to use one or more of those facilities for care. Additionally, the grouping should be considered generally consistent with known qualitative factors such as: formal and informal cooperative efforts among hospitals, inter-hospital competition, general community perceptions of hospital service areas and other commercial and political commonalities. Consistent with above characteristics, a two-step approach to the specification of clusters was formulated. The first step of the clustering process requires analysis of patient origin data to identify groupings of area hospitals that are most appropriate in terms of actual patterns of patient use. Three such techniques-the greedy algorithm, the max-flow/min-cut algorithm and the maxrelevance algorithm-are discussed below. The second step in the process is to submit the analytical results to a cluster review committee, a group of experts familiar with the local area. Based on members’ knowledge of hospital relationships and other factors influencing the reasonableness of proposed groupings, the committee is asked to decide whether the objectively determined clusters are in fact appropriate. Where several alternative groupings are equally plausible in terms of the objective criterion, committee members are asked to select the one that in their opinion is the most reasonable. Other adjustments, such as transferring a hospital from one cluster to another, may also be made by the committee. Thus the committee makes the final determination, using the patient origin data analysis as one important source of information. Analytic methods A number of methods described in the literature have been used for partitioning large regions, e.g. states or sub-state regions, into smaller non-overlapping areas such as hospital districts, health planning areas or medical service areas[l l-251. Generally, regions to be partitioned are composed of numerous small areal units such as census tracts, and each district of a region can be defined as a contigous subset of the region’s areal units. Several of the methods for defining districts may be applied to the problem of identifying hospital clusters, since hospitals located within a district could constitute a cluster and residents of the district then would make up that cluster’s service community. Techniques described by Poland and Lembke[l6], Ciocco and Altman[l2], Taliaferro and Remmers[24], Thomas [20] and Transaction Systems, Inc. [ 191, utilize conceptually similar approaches for defining district boundaries. With each of these methods, several areal tFor a discussion of performance measures and an overview of the project, see Griffith[lO]. In addition to the Southeastern Michigan Region, the project also focuses on Michigan’s six other Health Services Areas. The procedures described in this paper for clustering Southeastern Michigan hospitals were also employed in these other areas. units in the region (those containing hospitals and/or having a net inflow of patients above a specified level) are selected to be district centers. The remaining area1 units are then assigned, one by one, to districts. While these techniques differ in such respects as the types of patient-use data considered, the types of areal units employed and whether or not individual areal units can be split or reassigned, all utilize basically the same logic for assigning areal units to districts. The rule for selecting the next areal unit for assignment may be termed the “greedy” heuristic, since it selects the unit whose assignment appears, at that point, to offer the greatest reduction in cross-district-boundary patient traffic; that is, the areal unit and developing district that share the greatest amount of patient traffic are identified, and the areal unit is assigned to that district. Taliaferro and Remmers, Thomas and Transaction Systems, Inc. utilize computer-based algorithms for data analysis and district definition, while Ciocco and Altman’s and Poland and Lembke’s procedures were performed manually. Devise, in defining hospital planning districts for Chicago, employed an approach similar to that of Ciocco and Altman[lSl. Related procedures were also utilized by Gittelsohn and Wennberg[4] in Vermont and the Citizens’ Hospital Study Committee [18] in Northeastern Ohio. Instead of building up districts through sequential assignment of area1 units, the max-flow/min-cut procedure proposed by Thomas [20] divides a region into ever-smaller pieces. As a first step, the region (consisting, say, of N zip codes) is divided along zip code boundaries into two districts. Another cut is then made to yield three districts; the next cut yields four districts, etc. This process continues until a user-specified number of cuts are completed. With this algorithm, each areal unit in the region is considered to represent one node of a network and the capacity of the arc connecting areal units i and j in the network is defined to be the patient traffic, or flow, between i and j. Ford and Fulkerson’s[26] max-flowlmin-cut theorem then provides a basis for locating optimal cuts. Griffith’s[2] relevance index method, unlike the techniques discussed above, is used for defining service populations of individual hospitals rather than dividing regions into districts. With this method, the size of a hospital’s service population is determined by (a) multiplying each areal unit’s total population times the percentage of patients from the areal unit who utilize that hospital and the (b) summing these figures over all area1 units in the area. (Bailey[271 in 1952 labelled this the hospital’s “total effective population.“) The key measure in these calculations, the percentage of patients in an areal unit who use the hospital, is called “relevance index”. Although the relevance index method was intended only for calculating service communities of individual hospitals, a straightforward extention of the procedure may be used for defining hospital clusters. In areas containing several hospitals, relevance index values can be improved by selectively grouping hospitals into clusters, and the degree of improvement achieved can serve as a guide when determining which hospitals to cluster together. The first step of this modified procedure, which shall be termed the max-relevance algorithm, is to c_alculate a population-weighted average relevance index Rj for each hospital. Letting: Pi = population of area1 unit i; dii = number of patients from area1 unit i treated at hospital j; Oi = $dij = total patients from areal unit i; 4 = {il(dij/Di)r a}, t f se o areal units for which individual relevance values (dij/Di) of hospital j exceeds or equals a, where (I is specified 0 I a z 1; Then Rj = Defining hospital clusters and associated service communities in metropolitan areas 41 C Pi(dij/Di)/ C Pi. After Rj is calculated for each in-