Application and empirical analysis of TOPSIS method in comprehensive evaluation of healthcare efficiency
Zhou Xiaojian? , Jiang Guan Xu ○1, Zhao Xiaochun
Abstract: Purpose? To analyze the medical efficiency situation of a hospital in a multi-indicator comprehensive evaluation to provide a scientific basis for hospital management decision-making. Methods? Apply TOPSIS method to comprehensively evaluate 8 indicators reflecting medical efficiency of the hospital from 2005 to 2008 years. Results?The best medical work efficiency in 2008 year,?the worst medical efficiency in 2005 year, which is consistent with the actual work situation of the hospital in recent years. Conclusion The comprehensive evaluation of multiple indicators of medical efficiency by TOPSIS method can objectively reflect the degree of medical efficiency of hospitals in different periods and find out the reasons for the advantages and disadvantages, which is of great practical value to improve the level of hospital performance management.
Keywords: TOPSIS method, comprehensive evaluation of medical efficiency, empirical analysis
Chinese Classification Number?R197 Literature Identifier?B?Article Number
To adopt an objective and accurate evaluation method, to understand the medical efficiency of hospitals in a more comprehensive manner, is of great significance to improve the performance management level of hospitals. The actual work of medical and health care is in a complex situation, affected by a variety of internal and external factors, a single evaluation method is difficult to fully reflect the real situation of hospital management. For this reason, we can choose a comprehensive evaluation method for multi-dimensional evaluation. Comprehensive evaluation based on raw hospital data is an important symbol of hospital information management and an important means of modern hospital management.TOPSIS method? (Technique?for?Order?Preference?by?Similarity?to?Ideal?Solution) is an important comprehensive evaluation method, this paper focuses on exploring the application and empirical analysis of the TOPSIS method in the comprehensive evaluation of medical efficiency, which provides a scientific basis for the hospital management decision-making and helps to improve the hospital's The paper focuses on exploring the application and empirical analysis of TOPSIS method in the comprehensive evaluation of medical efficiency, providing scientific basis for hospital management decision-making and helping to improve the efficiency of hospitals.
The?synthesized?application?and?empirical?analysis?by?TOPSIS?method?in?evaluation?of?medical?efficiency/ZHOU?Xiao-jian,? JIANG?Guan-xu,?ZHAO?Xiao-chun?//Chinese?Hospital?Management
Abstract?Objective?To?provide?scientific?foundation?for?making? strategic?decisions?in?hospital?management?by?synthesized?evaluation?of?certain?hospital?medical?efficiency?with?multi-indexes.? Methods?Application?by?TOPSIS?method?in?synthesized?evaluation?of?medical?efficiency?with?8?indexes?during2005-2008.Results? Optimal?medical?efficiency?in?2008,?oppositely,?the?2005,?keeping?with?the?factual?working?situation?in?recent?years?.Conclusions? Application?by?TOPSIS?method?in?synthesized?evaluation?of?multi-indexes,?can?objectively?reflect?the?qualities?level?and?find?out? the?cause?of?quality,?is?of?important?utility?value?to?raise?the?hospital?performance?management.
Key?words?TOPSIS?method,? medical?efficiency,?synthesized?evaluation,?empirical?analysis
First-author's?address?postgraduate?school?of?Anhui?Medical? University,?Hefei,?230032,?China.?
1?The basic theory of TOPSIS method
1.1?The basic principle and idea of TOPSIS method
The TOPSIS method is a commonly used method of multi-objective decision-making analysis of finite programs in systems engineering. It is the key link to ensure and improve medical efficiency [1]. The basic principle is to rank the evaluation object by detecting its distance from the optimal solution and the worst solution, if the evaluation object is the closest to the optimal solution and at the same time is the furthest away from the worst solution, then it is the best; otherwise, it is the worst. Among them, each index value of the optimal solution reaches the optimal value of each evaluation index, and each index value of the worst solution reaches the worst value of each evaluation index. The basic idea is based on the normalized original data matrix, the positive ideal solution and the negative ideal solution in the finite scheme form a space, the scheme to be evaluated can be regarded as a point on the space, from which the distance between the point and the positive ideal solution and the negative ideal solution can be obtained Di+? and Di-, thus deriving the relative proximity Ci value of the program to be evaluated to the positive ideal solution, and evaluating the advantages and disadvantages of the program according to the size of ?Ci value [2].
1.2 Meaning of Positive Ideal Solution and Negative Ideal Solution in the?TOPSIS Method
The so-called Positive Ideal Solution is an envisioned optimal solution (program), whose values of each attribute reach the best value among the alternatives; while the Negative Ideal Solution is an envisioned worst solution (program), whose values of each attribute reach the worst value among the alternatives. The rule for ranking the solutions is to compare the alternatives with the positive and negative ideal solutions, and if one of the solutions is closest to the positive ideal solution and at the same time far away from the negative ideal solution, it is the best solution among the alternatives.
2. The basic method and empirical analysis of TOPSIS method
2.1 Collect raw data and establish judgment matrix. The raw data information mainly comes from the annual report of health statistics of the information management section of a general hospital in Hefei City from 2005?to 2008, the register of admitted and discharged patients, the inpatient case information and the case database. With n evaluation objects and m evaluation indicators, n*m raw data matrices can be obtained, as shown in Table 1.
Table 1?Raw Data Matrix
Evaluation Objects Indicator 1 Indicator 2?...? Indicator m
Object 1x11?x12?x1m
Object 2x21?x22?x2m
...?..?....Object nxn1?xn2?xnm
2.2?Selection of Evaluation Indicators and Determination of Their Weights
Selection of Bed Utilization Rate (%) x1?, Bed Turnover (%) x2, Average Hospitalization Days for Discharged Patients (days) x3, Annual Outpatient Visits per Health Technician (person-years/person-years) x4, Annual Discharges Per Health Technician (person-years/person-years) x5, Annual Outpatient Visits per Health Technician (person-years/person-years), and Annual Discharges Per Health Technician (person-years/person-years). visits (person/person-year) x5, annual surgical visits per health technician (person/person-year) x6, ratio of surgical patients to discharged patients (%) x7, number of admissions per 100 outpatients (person/hundred) x8***8 indicators. This paper utilizes hierarchical analysis to determine the weights of these 8 indicators. Hierarchical analysis (analytic?hierarchy?process, AHP) is a system analysis method combining qualitative and quantitative methods proposed by the American scientist T.L.Saaty in the 1970s.AHP uses the principle of system engineering to decompose the research problem and establish a low-order hierarchical structure; construct a two-by-two comparison judgment matrix; calculate the relative weights of the elements from the judgment matrix; calculate the relative weights of the elements from the judgment matrix; and calculate the relative weights of the elements from the judgment matrix. Calculate the relative weight of each element; and calculate the combined weight of the elements of each level; take the lowest level as the evaluation index to measure the degree of achievement of the target; calculate the comprehensive scoring index to evaluate the total evaluation target of the evaluation object, and determine the strengths and weaknesses of the evaluation object according to its size [3]. The evaluation indexes are compared and scored, and the scoring criteria are shown in Table 2:
Table 2?Objective Tree Diagram Hierarchical Evaluation CriteriaCompare and Score? Relative importance level says? Explanation
1
3
5
7
9
(2,4,6,8)? Equally important
Slightly important
Basically important
Definitely important
Absolutely important
The middle of two adjacent degrees
? Both contribute equally to the goal
Slightly more favorable evaluation of one than the other based on experience
More favorable evaluation of one than the other based on experience
One more favorable evaluation of one than the other based on experience and proven in practice
Importance is evident
Used when a compromise is needed
Indicator weights are calculated by the hierarchical analysis method In the case of a two-by-two comparison of the hierarchical performance indicators in each dimension, a judgment matrix is formed using a 1-9 ratio scale. Calculate the maximum characteristic root of the judgment matrix and its corresponding eigenvectors, and then carry out the consistency test, which is calculated by the formula: CI=? (λmax-m)/(m-1)? ,where λmax=?λi/m?,?λi=?aijWj/Wi?. where m is the number of sub-targets of the tested level; λmax is the maximum characteristic root; λi is the characteristic root of the pairwise comparison judgment preference matrix of the sub-targets of the level. After calculating the normalized weight coefficients, the calculated weight coefficients should be checked whether they are logical. When the judgment matrix order <2, the consistency index CI is usually used to test the relative priority of the indicators with or without logical confusion, and it is generally believed that when the CI <0.10 may be no logical confusion, that is, the calculated weights of the various weights can be accepted. Based on Saaty,s weight method in the hierarchical analysis method to determine the calculation of weights can be derived from the weights of the indicators are 0.21, 0.18, 0.11, 0.12, 0.08, 0.10, 0.11, 0.09 respectively?
2.3 Establish the original matrix based on the selected indicators and homotrendize it.
Based on the above selection of eight indicators reflecting medical efficiency x1, x2?, x3, x4, x5, x6, x7, x8 to establish the raw data matrix. As shown in Table 3.
Table 3?Raw matrix reflecting medical efficiency in a hospital from 2005 to 2008
IndicatorsYear?x1x2?x3?x4?x5x6?x7?x8
2005?78.3424.811.62513.322.145.7626.044.32
2006?82.6526.310.94535.224.096.5627.254.52?
2007?83.2127.19.05540.623.966.4026.714.86?
2008?85.4628.77.86525.122.096. 0627.425.02?
In the TOPSIS method of comprehensive evaluation of medical efficiency, some indicators are high-optimal indicators (i.e., the larger the value of the indicator, the higher the efficiency, such as the bed occupancy rate, the number of turnover of beds, etc.), and some indicators are low-preferred indicators (i.e., the smaller the value of the indicator, the higher the efficiency, such as the average hospital stay of hospital discharged patients), and then we should carry out the indicators of homothetic treatment (i.e., that is to say, the indicators are transformed into high-optimal indicators or indicators of high-optimal indicators, such as the average hospital stay of the patients). In this case, we need to homotrend the indicators (i.e., convert them into high or low indicators). In this paper, the inverse method is used to transform the indicators into high quality indicators. The formula is: x,nm = 1/xnm?, according to the formula will be transformed into a high-quality indicators of low-quality indicators, to get the same trend matrix, as shown in Table 4.
Table 4?Co-trendization processing matrix IndicatorsYear?x1x2?x3?x4?x5?x6?x7?x8
2005?78.3424.88.6513.322.145.7626.044.32
2006?82.6526.39.1535. 224.096.5627.254.52?
2007?83.2127.111.1540.623.966.4026.714.86?
2008?85.4628.712.7525.122.096.0627.425.02?
2.4 The same The matrix after trending is normalized and a normalization matrix Z is created.
When the original data is a high merit indicator, the normalization formula is: Znm=?xnm?/? (?x2nm)1/2?; When the original data is a low-optimal indicator, its normalization formula is: Znm=?x,nm?/? [? (x, nm)2]1/2?; After normalization, the normalization matrix Z is obtained. as shown in Table 5.
Table 5?Table of normalization matrix
IndicatorsYear?x1?x2?x3x4?x5?x6?x7x8
2005?0.00288?0.0087?0.01950.00046?0.01038?0.0374?0.00902?0.0491
2006?0.00304?0.0092?0.02060.00187?0.01130?0.0426?0.00944?0.0514
2007?0.00306?0.0095?0.02520.00048?0.01124?0.0416?0.00926? 0.0553
2008?0.00314?0.0100?0.02880.00047?0.01036?0.0394?0.00950?0.0571
2.5 Determination of the positive ideal solution and the negative ideal solution and their distances Di+ and Di- from the values of the indicators of each object of evaluation according to the normalization matrix Z.
The positive ideal solution Z+=(?zi1+,zi2+.... .zim+?) ;Negative ideal solution Z-=(?zi1-,zi2-.... .zim-?) where Eqs. i=1,2?...?n;?j=1,2?...?m?. Zij+? and ?Zij-? denote the maximum and minimum values of the evaluation object in the jth index, respectively. From the normalization matrix Z, we can determine the positive ideal solution Z+ (0.00314, 0.0100, 0.0288, 0.00187, 0.01130, 0.0426, 0.00950, 0.0571); the negative ideal solution Z- (0.00288, 0.0087, 0.0195, 0.0046, 0.01036, 0.0374. 0.00902, 0.0491); the distances Di+ and Di- between the indicator values of each evaluation object and the positive and negative ideal solutions, respectively, can be calculated using the following formula: Di+ = ? {? [wj(Zij-Zj+)]2}1/2; Di-=? {? [wj(Zij-Zj-)]2}1/2, where the equation wj denotes the weight coefficient of indicator j. If wj weights are equal, then wj=1? According to the Di+? and Di- formulas, and the weights of x1?, x2?, x3, ?x4?, x5?, x6, ?x7, and x8 to calculate the weighted Euclidean distances Di+ (0.004313,0.003225,0.001764, 0.001153) and Di- (0.001265,0.001921,0.002666, 0.0040).
2.6 Calculate the relative proximity Ci value based on the above Di+ and Di-values, and rank the order of the evaluation object's advantages and disadvantages according to the size of the Ci value.The Ci value is the relative proximity of the value of each evaluation index to the true ideal solution and the negative ideal solution, and is calculated as follows: Ci = ?Di-/(?Di++Di-), whose range of values is between [0?1], and the closer it is to 1, the closer it is to 1, the closer it is to the positive ideal solution. indicates that the evaluation object is closer to the positive ideal solution; the closer the value is to 0, indicates that the evaluation object is closer to the negative ideal solution. According to the above analysis of the hospital's medical efficiency in 2005-2008, the degree of good and bad (high and low) sorted, as shown in Table 6.
Table 62005-2008 years and the degree of proximity to the positive ideal solution and ranking
Year ?Di + Di - ?Ci ranking
2005 ?0.0043130.0012650.22684
2006 ?0.0032550.0019210.37333
2007?0.0017640.0026660.60182?
2008?0.0011530.0040?0.77621
As shown in the sorting results of Table 6, the hospital has the highest healthcare efficiency in 2008, and the hospital's healthcare efficiency has shown an increasing trend year by year since 2005, as Figure 1 can visually show the change of Ci value.
Figure 1: Changes in Ci value from 2005 to 2008
3. Analysis of results
3.1 According to the basic principle of TPOSIS method, the larger the Ci value is, the closer the evaluating object is to the ideal value and the higher the actual medical efficiency is. From the results of the four-year comprehensive evaluation of medical efficiency, we can see that 2008 was the most efficient year among the four years, while 2005 was the least efficient year, and 2005 was the most efficient year. while 2005 is the lowest year, the result is in line with the actual development of the hospital. The results are in line with the actual development of the hospital. The hospital began to implement full cost accounting at the end of 2004, and the hospital has done a lot of work to implement the idea of full cost accounting,? The hospital has done a lot of work to implement the idea of full-cost accounting, from strengthening the cost control of the hospital, to improving the efficiency of medical care. Improve the efficiency of medical care,? Expanding the scope of services, and attracting patients to visit the hospital. Attracting patients to receive a great effect,? Hospital work has been a significant development. Then in 2005, the hospital management year activities were carried out, and in the process of striving to meet the new standards, the hospital has been able to achieve great results. In the process of endeavoring to meet the new standards, the hospital's self-construction and comprehensive services have been greatly improved. The hospital's self-construction and comprehensive service capacity has been further improved and enhanced, and the efficiency of work has jumped to a new level. The work efficiency has jumped to a new level[4]. At the same time, the hospital has implemented reforms and innovations, improved competition and incentive mechanisms, effectively utilized various quantitative and efficiency quality indicators, and established a comprehensive efficiency evaluation system of the hospital, which has fully mobilized the enthusiasm and initiative of medical and nursing staff[5].
3.2?From the magnitude of the change in the slope of the folded line in Figure 1 can be visualized, the magnitude of the change between 2005 and 2006 is not large, indicating that the hospitals to take various measures to improve medical efficiency is showing the effect; 2006-2007 the maximum magnitude of the change, indicating that the effect of the various measures to gradually increase the demand for medical services market is strong; 2007-2008 the magnitude of the magnitude of the change is again The largest change in 2006-2007 indicates that the effect of the measures is gradually increasing and the demand for medical service market is strong; the range in 2007-2008 tends to flatten out, indicating that the medical services provided by hospitals and the demand for medical services of patients are gradually moving towards a balance, which is fully in line with the health status of the population and the development of the medical service market in the region.
4Discussion
The TOPSIS method is used to evaluate the medical efficiency of hospitals. The method has no strict limitations on data distribution, sample size and the selection of evaluation indexes, and is characterized by flexible application, easy operation, intuitive results, etc. It can accurately reflect the differences of each evaluation object, and has a greater value of application in the comprehensive evaluation of multiple indicators of hospital work efficiency[6-7]? The TOPSIS method is used to comprehensively analyze and evaluate the eight indicators reflecting medical efficiency in this hospital for four years,? In order to obtain the relative proximity and ranking of each year to the ideal solution, we can not only see clearly the medical efficiency of each year, but also the medical efficiency of each year. We can not only clearly see the degree of medical efficiency in each year,? We can not only clearly see the degree of medical efficiency in each year, but also find out the reasons for the advantages and disadvantages,? thus providing a reliable basis for decision-making in health care [8]. However, the method also has its own limitations, is affected by outliers, to meet the requirements of the original data discrete degree is small, to reduce the impact of some evaluation index outliers on the analysis results, can be TOPSIS method and rank sum ratio method (RSR) combined application, to further improve the scientific nature of the evaluation results.
References:
[1]Liu?C,?Frazier?P,?Kumar?L,?Macgregor?C,?Blake?N.?Catchments?wide?wetland?assessment?and?prioritization?using ?the?multi-criteria?decision-making?method?TOPSIS?[?J?]. ?Environ?Manage,
2006,?38:316-326.
[2]? Sun ZQ. Comprehensive medical evaluation methods and their applications [M]. Beijing: Chemical Industry Press,2005.12.
[3]? Zhang DY, Zhang Z, Fan LH. Research on the performance evaluation index system of tertiary general hospitals in Heilongjiang Province[J]. China Hospital Management, 2007(5):26-27.
[4]Zhang Yunhong. Comprehensive evaluation of hospital effectiveness using TOPSIS method[J]. China Hospital Statistics,2007,14(3):256.
[5]Li Yumei,Shao Jianguo. Application of TOPSIS method to comprehensively evaluate changes in the quality of hospital medical work[J]. Journal of the Second Military Medical University, 2008, 29(12):1533
[6]?Van?Wink?B?L,?Klungel?O?H,?Heerdink?E?R?Boer?A.?A?comparison?of?two?multiple?-?characteristic? decision?-?making?models?for?the?comparison?of?antihypertensive?drug?classes:?Simple?Additive?Weighting?(SAW)?and?Technique?for? Order?Preference?by?Similarity?to?an?Ideal?Solution?(TOPSIS)[J?].Am?J?Cardiovascular?Drugs?,2006,6:251?-?258.
[7]Omit?S.? Soner,?S.Trans?shipment?site?selection?using?t?he?AHP?and?TOPSIS?approaches?under?fuzzy?environment?[J].Waste?Manage,?2008,?28. 1552-1559.
[8] Liao, Mingyun. Comprehensive evaluation of hospital bed efficiency using TOPSIS method[J]. Modern Medicine and Health, 2007,23(11): 1725.