数学中国w, madio,net The Mas! Expensive is Not the Best 155 The Most Expensive is Not the best Hongxing Hao Xiangrong Zer Boliang Sun National University of Defense Technology Changsha, Chin Advisor: Ziyang mao Abstract Motivated to evaluate healthcare systems more accurately, we analyze existing evaluation methods. Most methods mainly focus on outcomes and their metrics often ignore intemal characteristics of the healthcare systems. We devise two methods: animproved World Health Organization(WHO) method and a comprehensive evaluation method Theimproved WHO method uses the same metrics as the WHOmethod which are determined by the outcomes of the healthcare system. Our im- provement is to use a grey comprehensive evaluation and the principle of minimum loss of information to combine the metrics, rather than simply combining them linearly. In our comprehensive evaluation method, we define five new metrics that concern both outcomes and characteristics of the healthcare system itself, including the effect of the government and the basic situation of a country. Then we use the equal-interval method to get a final score. Compared with other methods, this one does a better job in distinguishing countries and in sensitivit After comparing with other four countries that represent the four main modes of healthcare systems, we conclude that the most important reason why the highest cost can't make the U.S. the best is unfairness. Afterward, we use a neural network algorithm to predict what will happen to the us. if some values of the metrics change. We conclude that the U.S. can get the greatest benefit by improving fairness We finally consider a policy change, a"medical insurance voucher"as a method to increase insurance coverage and reduce unfaimess The UMAP Journnl29(2)(2008)155-168. Copyright2008 by COMAP Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or dassroom use is granted without tee provided that copies are not made or distributed for profit or commercial dvantage and that copies bear this notice. Abstracting with credit is permitted but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP
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数学中国w, madio,net 156 The UMAP Journal 29.2(2008) Introduction Many countries have recently introduced reforms in the health sector with the explicit aim of improving performance [Mathers et al. 2000: 2001] There is extensive literature on health-sector reform and recent debates have emerged on how best to measure performance so that the impact of reforms can be assessed [Goldstein 1996]. Measurement of performance requires an explicit framework defining the goals of a healthcare system and a suitable method to make a compelling evaluation So our goal is pretty clear Devise metrics to evaluate the effectiveness of a healthcare system Devise a method to combine the metrics Compare several representative countries. Restructure the healthcare system of the U.S. and build predictive models to test the chan Our approach is: Analyze factors that can affect the performance of a healthcare system. Search the literature on existing evaluation methods and find their short- Develop a comprehensive evaluation method that asks only for existing data or data easy to measure and collect Collect experimental data that can be used in our method. Compare current methods and determine their characteristics. Do a sensitivity analysis of variations of our models Restructure the healthcare system of the U.S. and build a model based on neural networks to test changes. Do further discussion based on our work Four Representative healthcare Systems The healthcare system, as an important part of the social security sys- m, is essential to promote the stability of society, and it reflects social justice. Due to the different histories, cultures, and status of human rights protection, healthcare systems vary from country to country. There are four representative healthcare systems[Ding 2005:
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数学中国 The Most is Not the Best 15 National insurance. The main countries using this system are the UK, Eastern Europe, and Russia. The government dominates, healthcare is free, with full medical treatment and complete coverage of the popula tion. But it doesnt have high efficiency or make use of the market, and it is a heavy burden to the government. Commercial insurance. The U.S. is the main country using this system, which makes the market the guideline of the healthcare system. Cost is high, and a large number of people fail to pay. Socialinsurance. This system features mandatory coverage and fairness, as in Japan, Germany, and Canada. It has high cost and slow service. Savings insurance. Singapore is the representative country. The main disadvantage is a low service efficiency. Costs rise rapidly, and it cannot achieve full coverage Analysis of the wHo Estimation Method The WHO,'s methuds focus un the outcomes of a healthcare system with out considering any characteristics of the system itself The metrics that the WHO uses to evaluate a healthcare system aim to measure goal attainment, and they include most of the outcomes that a healthcare system should produce Weaknesses The weights placed on each dimension are somewhat arbitrar The approach heavily penalizes countries with epidemic disease unre- Lated to the healthcare system. This approach does not look at how the system is organized and man- The WHO 2000 rankings do not look at access, utilization, quality, or cost-effectiveness In addition, according to Almeida et al. [ 2001, 1693: The measure of health inequalities does not reflect concerns about eqr uity Important methodologicallimitatiuns and controversiesare not acknowl-
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数学中国www, madio,net 158 The UMAP Journal 29.2(2008) The multicomponent indices are problematic conceptually and method ologically; they are not useful to guide policy, in part because of the opacity of their component measures. " Primary health care is declared a failure without examining adequate evidence, apparently based on the authors ideological position ."These methodological issues are not only matters of technical and scien- consequences. Improved WHO Method In the WHO methods, the weights in the construction of the composite index are used without considering uncertainty in the values of the different nen Weuse agrey comprahensive evaluation mode? toimprove the WHOmethod to make the evaluation more credible Methodology e Suppose that ck, for are the raw data of the metrics k= l,.m in suntry i, for i=1, ..,n, giving the n x m matrix=(c).We suppose cR=(ci,,,, c), a best possible situation, as a reference and compare the value of metric k in country i to this ideal via s(k)=min, Ic-cal+ pmaxiIct lc+k-eu+pmax Ic where p E(0, 1)is a differentiation coefficient that we generally can take to be.5. Using,(k), we get the evaluation matrix E=5()\s for them mtrppose W=(wi,., Wm)is a weight-distribution vector for the m metrics, with w the weight of metric k and >wk= 1. Based on the dis- cussion above, we get the grey comprehensive evaluation model R=W·E=(n1,…,rn ' S NOTE: This method, not known under this name in the US. was introduced by Deng Julong in Tutorial of Gray Systean Theory [in Chinese](1982). It uses ideas of TL Saaty's analytic hierarchy process and is well well-known in China(googling"grey aystem"gets 64,100 hits, induding The Journal of Grey Systemt, edited by Deng). For a numerical example, see Sun, Yan and Zong Sun, The grey comprehensive evaluation model for safety of construction sites, 2007 International Conference on winless CommunicatIons, Networking and Mobile Camping, 5240-5243
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数学中国w, madio,net The Most Expensive is Not the Best 159 where E is the transpose of E and r,=>=, wS ( k)is the relating de- gree. The vector R=(u ., r,.)contains the final scores of the countries healthcare systems. The larger r the better the system How to Determine the Weights Wewe want to determine the weight vector in a credible way. We use the principle of minimum loss I Wang et aL. 2000. Because our metrics ul, evaluate information from different aspects, combining all the metrics in a informatics We should maximize conservation of information. So we choose the most classical method: We calculate variance to represent information; the larger the variance, the more information. In the final scored=w u, we should choose the best weight w to make the variance of d reach the maximum: D(d)=w D(uw where D(d) is the variance matrix of d. when ww=l, D(d)achieves it maximum We use the method of Lagrange multipliers. Suppose that =2D(u)u-2)=0 入 which reduces to D(uw=Aw, 1 So Ais aneigenvalue of D(u with eigenvector w when ww=l, to make the maximum eigenvahtw= A reach the maximum, we should take Aas D() lue of D (u) In the real calculation, we do not know D(u), so we use the variance matrix D(u)=ou)of the sample(cin,., Cn)of u, to represent it, where (x-x)(
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