Evaluation And Optimization Model Of Urban Medical Resource Allocation In Spatial Perspective

[Purpose]This research aims to propose a theoretical framework for the allocation of urban medical resources from a spatial perspective.It attempts to incorporates spatial data,visualization methods and mathematical modeling ideas into the process of evaluation and optimization of medical resource allocation,and construct a mathematical model of optimal allocation.Based on the analysis and evaluation of the current situation of the allocation of medical resources in the sample cities,the model is empirically verified,and the optimization results of the model are evaluated,in order to provide references and basis for the optimal allocation of urban medical resources.[Methods]1.Literature research method.By searching terms “health resource allocation”,“spatial accessibility” and “resource allocation optimization model”,the main databases at home and abroad were searched to collate relevant literature and systematically sort out the status of research on concepts,theories,evaluation methods and optimization models related to health care resource allocation in the spatial perspective.2.Secondary data collection.Zhongshan City,Guangdong Province,was selected as the sample area,and hospital-level data were obtained from the Zhongshan City Health Statistics Report from 2014-2018.Resident and patient-level data were obtained from the data collection indicators of the Fifth Guangdong Health Services Survey and the inpatient electronic medical records data of Zhongshan City in 2018.Various spatial geographic data were mainly obtained through the Open Street Map(OSM)website and the Application Programming Interface(API)of Amap.3.Panel discussion.Twelve experts in regional health planning,hospital management,clinicians,health administration and urban planning respectively were selected to consult expert advices on the objective setting,basic assumptions and construction ideas of the mathematical model for optimal allocation of urban healthcare resources,as well as the specific parameter setting and possible obstacles encountered in the empirical study.4.Data analysis methods.Use mixed-integer linear programming methods in mathematical modelling to construct models for optimal allocation of urban health care resources in a spatial perspective.Descriptive analysis,Gini coefficient combined with Lorenz curve,Theil index,and Health Resources Agglomeration Degree(HARD)were used to describe and evaluate the current situation and fairness of medical resources allocation.Describe and evaluate the spatial accessibility of various medical resources with Geographic Information System(GIS),Hierarchical Two-step Floating Catchment Area Method(H2SFCA)and Cold Hot Spot Analysis.Based on GIS,the geographic distribution and sources of inpatients were visualized and analyzed by using kernel density analysis and descriptive analysis;the Branch and Bound(B&B)algorithm of the exact algorithm and the optimality principle were used to solve the mixed integer linear programming model,and the Gini coefficient and H2 SFCA were applied to evaluate the optimization effect of the model.[Results]1.Theoretical Framework of Medical Resource Allocation in Spatial PerspectiveThis study proposed a theoretical framework of medical resource allocation in spatial view,including elements of allocation goals,allocation levels,medical institution layout,medical institution categories,urban space and allocation effects.By enhancing the interregional equity and spatial accessibility of medical resource allocation in urban space,the interaction is strengthened between residents and medical resources in space,and the accessibility of medical and health services for residents is promoted,so as to improve the utilization of medical services and enhance the health outcomes of the population in the region.2.Evaluation and optimization model of urban medical resource allocation in the spatial perspectiveThis study constructs a mathematical model for the optimal allocation of urban healthcare resources with a spatial view.The model takes inter-regional allocation equity and optimal spatial accessibility as the optimisation objectives.The H2 SFCA model and the Gini coefficient formula are linearly transformed.The minimum gap between the allocated resources of each region and the percentage of population(or percentage of geographical area)of the city in which it is located and the minimum gap between the ratio of demand for healthcare services and the supply of healthcare resources for each settlement within the threshold of different levels of hospitals are taken as the criteria.3.Evaluation results of medical resource allocation(1)Regarding the evaluation results of equity,the Gini coefficients of hospitals,physicians,nurses and beds by population distribution in 2018 were 0.34,0.40,0.43 and0.42,respectively,and the Gini coefficients of hospitals,physicians,nurses and beds by geographical distribution were 0.45,0.59,0.61 and 0.57,respectively,and the equity of various types of medical resources by population distribution was better than that by geographical distribution.(2)With regard to the spatial layout of hospitals and the evaluation of the spatial accessibility of medical resources,45 settlements were served by tertiary hospitals within10 minutes,57 settlements in the 10-20 minute range,43 settlements in the 20-30 minute range,and 132 settlements greater than 30 minutes;the closest proximity indices of primary and undetermined hospitals and secondary hospitals are 1.23 and 1.29,respectively,with a uniform distribution,and the closest proximity index of tertiary hospitals is 0.63 with a clustered distribution;the high accessibility of physicians,nurses and bed resources is mainly accumulated in the central urban areas of West Street,Shiqi Street,East Street,Shaxi Town and the northwest area of Xiaolan Town and Guzhen Town,while the accessibility of other areas is generally low.(3)In terms of the source of inpatient care,Xiaolan Town,Shiqi Street and Dongqu Street had the highest number of inpatient visits to tertiary hospitals,accounting for13.32%,12.53% and 13.57% of the local resident population respectively,while Fusha Town,Shenwan Town and Wuguishan Street had the lowest number of inpatient visits to tertiary hospitals,accounting for 5.52%,5.52% and 3.32% of the local resident population respectively.4.Optimization of medical resource allocation and its effect(1)In terms of the model solution results,in the equitable allocation scheme by town(street),the proportion of tertiary hospitals to the number of hospital beds in the city decreased from 39.1% to 10.6%,the proportion of physicians to the number of hospitals in the city decreased from 43.7% to 14.8%,and the proportion of nurses to the number of hospitals in the city decreased from 47.5% to 13.2%,while the number of medical resources in secondary hospitals and primary and unclassified hospitals increased significantly.The number of beds,physicians and nurses in the towns(streets)of Shiqi District and West District in the central city,and Xiaolan Town in the northwest area have decreased significantly,while the number of beds,physicians and nurses in the towns(streets)of Dongsheng Town and Henglan Town in the northwest area,Nanlang Town in the eastern area and Sanxiang Town and Shenwan Town in the south area have increased significantly;in the equitable allocation program by area,the proportion of beds in tertiary hospitals has dropped from 39.1% to 10.2%,the proportion of physicians has dropped from 43.7% to 14.8%,and the proportion of nurses has dropped from 47.5% to 13.2%.The number of beds in secondary hospitals has increased,while the number of doctors and nurses has decreased.The medical resources of the primary and unclassified hospitals have been greatly increased.The medical resources of the northeast and southern areas have been greatly improved,and the medical resources of the central urban area have been greatly reduced.(2)In terms of the effect of optimal allocation,in the equitable allocation scheme by town(street),the Gini coefficients of physicians,nurses and beds by population distribution decreased from 0.40,0.43 and 0.42 before optimization to 0.19,0.27 and 0.25,respectively,and the Gini coefficients of geographical distribution decreased from 0.59,0.61 and 0.57 before optimization to 0.14,0.07 and 0.07;the accessibility averages of physicians,nurses and beds increased from 0.0009,0.0013 and 0.0021 before optimization to 0.0010,0.0015 and 0.0030 after optimization,and the area of high accessibility areas in each town and street increased significantly and the area of low accessibility areas decreased significantly.In the equitable allocation scheme by area,the Gini coefficients of physicians,nurses and beds by population distribution decreased from0.26,0.27 and 0.16 before optimization to 0.12,0.12 and 0.12,respectively,and the Gini coefficients of geographic distribution decreased from 0.45,0.36 and 0.36 before optimization to 0.10,0.10 and 0.10 after optimization,respectively;the mean accessibility values of physicians,nurses and beds increased from 0.0009,0.0013 and 0.0021 before optimization to 0.0011,0.0015 and 0.0031 after optimization,respectively,and the area of the high accessibility value area within the city has grown significantly,and the area of the low accessibility value area has decreased significantly.[Conclusions]1.This study finds that the equity of medical resource allocation in hospitals in the sample cities is poor and there are large regional differences,and most medical resources are concentrated in the central city and northwestern area,and the equity of allocation by population is better than the equity of allocation by geography.2.The spatial distribution of medical resources of various types of hospitals in the sample city is uneven,with large differences among towns(streets)and a strong dependence of spatial accessibility on the distance from residents to tertiary hospitals,and the areas with high accessibility concentrated in the central city and some towns(streets)in the northwest area and poor accessibility in other areas.3.The optimal allocation model can significantly improve the inter-regional allocation equity and spatial accessibility results.After the adjustment of the optimal allocation model,the inter-regional equity and spatial accessibility of hospital resource allocation in the sample cities were significantly improved,indicating that the model results can provide a reference for policy makers.4.The mixed integer linear programming model for optimal allocation of medical resources with the spatial perspective,constructed with inter-regional allocation equity and spatial accessibility as optimization objectives,is applicable to the problem of optimal allocation of hospital medical resources in the sample cities,and its optimization performance is stable,which is recommended to be promoted in practice with good generalizability and extensibility.5.In regional health planning,a multidisciplinary approach can be used to scientifically formulate regional health plans;pay attention to spatial equity and optimise the spatial layout of medical resources;build regional medical consortia to create a fair access environment;and promote "Internet + healthcare" to improve the accessibility of medical services.[Innovation and Deficiency]1.Innovations(1)A theoretical framework is constructed for the allocation of healthcare resources in a spatial perspective.Based on the relevant concepts and theories,this study innovatively proposes a theoretical framework for the allocation of healthcare resources with a spatial perspective,which has certain theoretical innovations.(2)A mathematical model is constructed for the optimal allocation of urban health care resources in a spatial perspective.This study constructs a mathematical model for the optimal allocation of healthcare resources with the dual objectives of inter-regional allocation equity and spatial accessibility in a spatial perspective,which provides an important modelling tool for the optimal allocation of regional health resources and is both scalable and extensible.(3)An attempt is made to systematically analyse,evaluate and optimise the allocation of urban healthcare resources based on a spatial perspective.Based on the data of the sample cities,this study conducts a systematic research on the evaluation and optimisation of healthcare resources allocation in a spatial perspective,providing empirical experience for other cities to carry out regional health planning and optimisation of healthcare resources allocation in the context of the current promotion of new urbanisation and the Health China strategy.2.Deficiencies(1)Due to the unique administrative division and historical legacy of the medical service system in Zhongshan,the empirical part of this study only evaluates and optimizes the allocation of medical resources in its hospitals.In the next step,we hope to cooperate with relevant departments in other cities to extend the scope of evaluation and optimization to all medical service institutions within the city.(2)Due to objective data conditions,patient mobility between cities was not considered in the evaluation and optimisation for the convenience of modelling,and the determination of the objective function for equity was simplified.In future studies,the inclusion of resident health indicators and patient mobility factors will be considered for a more objective evaluation and optimisation.