数学中国w, madio,net Evaluation and Improvement of Healthcare Systems 113 Evaluation and Improvement of Healthcare Systems Luting Kong Yivi Chen hao Ye Beijing University of Posts and Telecommunications Beijing, China Advisors: Qing Zhou and Zuguo He S umma ry To evaluate the effectiveness of healthcare systems, we describe metrics in three categories: resources, performance, and inequity. Inthe Incomplete- Induction Model, we use the Variance Analysis method to evaluate the sig nificance of each metric. The four most important metrics are the percentage of GDPspenton healthcare, the ratio of general government expenditure on health to private expenditure, health-adjusted life expectancy, and health We combine the metrics into two integrative metrics, the ratio of re sources to performance, and healthinequity, using the Analytical Hierarchy Process. The two metrics make up the Evaluation Vector. To compare the effectiveness of different health systems by means of the Evaluation Vector, we construct two comparison models In Model l, we compare based on relative disparity In Model 2, we introduce a coordinate system in which a vector stands for a healthcare system. The effectiveness of thesystem is reflected by the length of the vector: A smaller length stands for a better system. In Task IV and Task V, we choose Brazil for its good healthcare system nd India for its poor one. According to the two comparison models, both systems are better than that of the U.S. Then we analyze the relationshi etween resources and system effectiveness in order to explain why the Indian system is better In Task VI, we analyze the U.S. system and put forward suggestions A. The UMAP Journal 29(2)(2008)113-133. @Copyright 200 by COMAP, Inc. All rights reserved. advantage and that copies bear this notice, Abstracting with credit is permitted, but copys is granted without fee provided that copies are not made or distributed for profit or commen for compoments of this work owned by others than COMAP must be honored. To copy otherwis post on servers, or to redistribute to lists requires prior permission from COMAP
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数学中国www, madio,net 114 The UMAP Journal 29.2(2008) to improve it. Then we build a model to investigate the influence of the changes In addition, we measure the historical change in the system. Gen erally, its effectiveness is increasing, but the growth rate is slower recently We also analyze the strengths and weaknesses of each model. Solution of task 1 Description and Analysis We put forward a method to measure a country s healthcare system. To simplify the problem, we first abstract the system as a simplified input- output system( Figure 1). Input: Health care Output: resource Figure 1 Healthcare as a simplified input-output system. Sufficient resources should be put in to guarantee that the system func- tions well. Viewed in isolation, the more resources the system gets, the betterit will be. However, linked to output, the better system is not the one with more resources but the one with a low input-output ratio. Later we discuss how to use the metric of resources to measure a healthcare system Output reflects the systems performance: The better the system is, the more output it will produce; we define performance later How the system operates cant be igored, since that affects the whole health situation of the country, such as the distribution of resources and the health level in different areas. These factors will be expressed by the metric of Inequities. Metrics Resources A good healthcare system needs adequate resources: human resources, material resources, and financial resources Human resources are the population engaged in medical careers, includ ing physicians, nurses, pharmacists, and other health workers Material resources are the hardware facilities in the medical system, such as hospitals and hospital beds
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数学中国w, madio,net Evaluation and Improvement of healthcare Systems 115 Financial resources include three aspects The percentage of GDP spent on healthcare The percentage of total government expenditure spent on healthcare. The ratio of governme ding to private spending on health. Apparently, in a good health system this ratio is high. Performance Health level. The main objective of a health system is improving health [WHO 2001]. We choose disability-adjusted life expectancy(DALE) and infant mortality as criteria, the combination of which can be used to evaluate the level of health Disability-adjusted life expectancy. dale is the life expectancy at birth adjusted for disability [IWHO2001]. It is a comprehensive mea sure of the global burden of disease and the trends of population health level [Mathers et aL. 2001 Infant mortality rates. Infant mortality rate is a significant indicator of medical level: High-medical-level countries have a low infant mortality rate Health-service coverage. Health-service coverage comprises several fac- ors, such as the immunization coverage of 1-year-olds and the percent- age of the population with pu ublic insurance A good health system should provide healthcare for all ofits citizens. Usually, developed coun- tries have high rates in the both of those Responsiveness. Responsiveness measures how the system performs relative to non-health aspects, meeting or not meeting a population,s expectation of how it should be treated [WHO 2001]. The notion of responsiveness is composed of seven elements, including [WHO 2001] respect for dignity, confidentiality, autonomy to participate in choices about ones own health, prompt attention, amenities of adequate quality access to social support networks, and freedom to select which individual or organization delivers ones The seven points above lead to a general metric of responsiveness. In part II we discuss how to combine them
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数学中国w, madio,net 116 The UMAP Journal 29.2(2008) Inequities in health. A healthcare system is not so perfect if the health level varies widely between different categories of the population, even in countries with a rather good health status on average [WHO 2001].To describe inequities in health, we use life expectancy in terms of age,race, gender, socioeconomic class, and so on. If every category has the same life expectancy, the system is fair in terms of health level Inequities in responsiveness. The same as health level: If some peo- ple are treated with courtesy and others are not, there are inequities in responsIveness. Fairness of financial contribution. To be fair, the expenditu household faces should be distributed according to ability to pay rather than by risk ofillness [WHO 2001]. That means that a household should not become impoverished to obtain healthcare, and rich households should pay more towards the system than poor households [Gakidou aL200 The Combination of Metrics We devise a composite measure of the three metrics: Resources, perfor Analytical Hierarchy Proces Divide layers. We divide the metrics into several layers as Figures 2-5 Resouree Performane Figure 2, Resources Figure 3. Performance Evaluation Vector. A good system should use the least resources pos sible to produce performance, therefore we use the ratio of resources to Performance to evaluate the system s effectiveness The other metric is the inequity index. Since the two metrics may not have the same magnitude. it is not appropriate to add or multiply them
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数学中国 Evaluation and Improvement of Healthcare Systems 117 Inequiti n heslth distribution 1 Figure 4. Figure 5. Evaluation. Hence, we form an evaluation vector (EV) consisting of the two metrics resources ev=performance, inequities This is our final composite measure to evaluate the effectiveness of a healthcare system. when both components of the vector are lower, the system is better. Determine Weights We specify the calculation of one metric, Resources; the others can be calculated in the same way. After comparing the effect of two criteria in the same layer to the higher layer, we can construct the conjugated-comparative matrix with Saaty's Rule Liang 1993]. For example, a12 can indicate the dif ference of the effect on resources between human resources and financial Resources. Let Mi be the conjugated-comparative matrix of Resources, while the elements of M, are Financial Resources 12 M2 11 After calculation of the matrix using thesummation method [Jiang 19931, e obtain the weight vectors t1=(.533,297,164),2=(.4133,26) So we can form the formulas Resources=. 539 x FR+. 297 x HR+. 164 x MR FinancialResources=.4l×Asp1+33×Asp2+26XAsp2 where our notations are defined in Table 1
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数学中国 18 The UMAP Journal 29. 2(2008) Table 1. Human resources Material resources Financial resources Tealth level HSK Health service coverage Responsiveness level DALE Disabihity-adjusted life expectancy HALE Health-adjusted life expectancy IMR equities of health equities metric Responsiveness metric FFD Fairness in financial distribution Seven aspects of responsiveness REL esources/ performance ratio Evaluation vector ength of the evaluation vector TH Total expenditure on health as of GDP GHtoPH Ratio of govemment expenditure on hea th care to private expenditure GHtoG Government expenditure on health as percentage of total government expenditure Formulas Using a similar method, we arrive at equations as follows Performance = 49 x HL + 31 x HCS+2 x RL HealthLevel=6 X DALE+4 x(1-IMRJ Responsiveness= I 7∑AP, Inequities=.4×lH+4xR+2×FFD with these formulas and our basic criterion, we easily get the evaluation vector to evaluate the effectiveness of a healthcare system. Strengths and Weaknesses The Analytical Hierarchy Process method is a good combinationof qual itative and quantitative analysis, and it gives the weights conveniently. But it possesses a certain subjectivity
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数学中国w, madio,net Eualuation and improvement of Heaithcare Systems 119 Solution of task ll Modify the List of Metrics and Calculate Each In this task, we take the Us. as an example %everal small metricsBut data In Task I, we listed three total metrics and for some metrics are unavailable, so we need to modify our list of metrics. Data Disposal For the sake of consistency, we need to process the original data, which we denote as original Step 1: Find the maximum and minimum values in the whole table, denoted by Vmax and Vmia. The adjusted value is ad justed Step 2: If the metric has only one factor, we can simply use Adjusted. If the metric consists of several factors, we should give each one the weight as determined in Task I Neglected Metrics We neglect the metrics of responsiveness inequities and faimess of fi- nancial contribution because we lack data To quantify responsiveness, WHO surveyed 35 countries, giving scores in seven aspects; but data for the U.S. are absent [WHO 2007]. Thus, we delete this factor. without the metric of responsiveness, we should adjust he weights in calculating the metric Performance Performance=.613×HL+:387×HCs Selected metrics e Resources Human resources (Table 2) HR=25(physicians + nurses +dentists+pharmacists), where the numbers are measured per thousand of population. Material resources (Table 3): We choose hospital beds per 10,000 population to reflect the amount of material resources
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数学中国w, madio,net 120 The UMAP Journal 29.2(2008) Table 2. Human resources(per thousand of population Year: 2000 Physicians Nurses Dentists Pharmacists Ls 937183 88 Max, 35 countries 591 Min, 35 countries U.11 Normalized U.s. value Table 3 Maberial resources(hospital beds per 10,000 Year 2003 Beds US Max 35 countries 1324 Min 35 countries 2 Normalized US value 24 Financial resources(Table 4): TH- Total expenditure on health as of GDP GHtoPH Ratio of government expenditure on health care to rivate e diture GHtoG= Government expenditure on health as percentage total goverrment expenditure. FR= Financial resources = 33TH +, 41GHtoPH +. 26GHtoG Since by the usual calculation the normalization result for GHtoPH turns out to be extremely exceptional, we calculate it instead by In Voriginal-I In v Vadjused=n v-Inv Table 4 Financial resources as percentage of GDP. Year 2004 TH GHtoPH GHtoG s 1544471553189 Max 35 countries 166 Min, 35 countries 16129/87.1 14 Normalized U. S value 92 2 55
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数学中国w, madio,net Evaluation and improvement of Heaithcare Systems 121 Performance Health level (Table 5) Disability-adjusted life expectancy(DALE): In our data, there is no information about DALE. So we use HALE, health-adjusted life expectancy, to substitute for it. HL- Health level=.6HALB+, (1- IMR) w Infant mortality Table 5 Health leveL. HALE (2002) Infant mortality (2005) Male Female Ave per 1000 live births US 71 Max 35 countries 7 165 Min, 35 countries Normalized U.S. value 89 Health service coverage(Table 6) We choose percentage of immunization coverages to evaluate the level of health service coverage, plus TB treatment success Measles immunization coverage among one-year-olds with one dose of measles Diphtheria- immunization coverage among one- year-olds with three doses of diphtheria, tetanus toxoid and pertussis(DTP3 HepB3-immunization coverage among one-year-olds with three doses of Hepatitis B(HepB3) t TB- tuberculosis treatment success(%) Coverage=25(Measles+ Diphtheria +HepB+TB). Table 6 Health service coverage(percentages) Measles(2005) Diphtheria (2005) HepB3 (2005) TB (2004 US 9 61 Max 35 countrie 1D0 Min 35 countries 993g 20 Normalized US velue 97 61
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数学中国w, madio,net 122 The UMAP Journal 29.2(2008) bee choose probability of dying aged 0, then system 1 is better than system 2. Model Expansion In our function, the two metrics-resources/ performance ratio and in- quity index-have equal weight. They could be weighted otherwise
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