美赛论文--历年数学建模优秀论文大全 超经典版本.doc

2008 国际大学生数学建模比赛参赛作品-WHO 所属成员国卫生系统绩效评估作品名称：Less Resources, more outcomes 参赛单位： 重 庆大学 参赛时间：2008 年 2 月 15 日至 19 日 指导老师： 何 仁斌 参赛队员： 舒强 机 械工程学院 05 级 罗双才 自动化学院 05 级 黎璨 计算机学院 05 级 2008 年国际大学生数学建模比赛参赛作品作者：舒强、罗双才、 黎璨ContentLess Resources, More Outcomes . 41. Summary . 42. Introduction . 53. Key Terminology . 54. Choosing output metrics for measuring health care system. 54.1 Goals of Health Care System . 64.2 Characteristics of a good health care system . 64.3 Output metrics for measuring health care system. 65. Determining the weight of the metrics and data processing. 85.1 Weights from statistical data . 85.2 Data processing . 96. Input and Output of Health Care System . 96.1 Aspects of Input . 106.2 Aspects of Output . 117. Evaluation System I : Absolute Effectiveness of HCS . 117.1Background . 117.2Assumptions. 117.3Two approaches for evaluation . 111. Approach A : Weighted Average Evaluation Based Model . 112. Approach B: Fuzzy Comprehensive Evaluation Based Model 1920 . 127.4 Applying the Evaluation of Absolute Effectiveness Method . 148. Evaluation system II: Relative Effectiveness of HCS . 168.1 Only output doesnt work . 168.2 Assumptions. 168.3 Constructing the Model . 168.4 Applying the Evaluation of Relative Effectiveness Method. 179. EAE VS ERE: which is better?. 179.1 USA VS Norway . 189.2 USA VS Pakistan . 1810. Less Resources, more outcomes. 1910.1Multiple Logistic Regression Model . 1910.1.1 Output as function of Input. 1910.1.2Assumptions. 1910.1.3Constructing the model. 1910.1.4. Estimation of parameters . 2010.1.5How the six metrics influence the outcomes?. 2010.2 Taking USA into consideration . 2210.2.1Assumptions. 2210.2.2 Allocation Coefficient a . 2210.3 Scenario 1: Less expenditure to achieve the same goal . 2410.3.1 Objective function：. 2410.3.2 Constraints . 2529 / 2910.3.3 Optimization model 1 . 2510.3.4 Solutions of the model . 2510.4. Scenario2: More outcomes with the same expenditure . 2610.4.1Objective function . 2610.4.2Constraints. 2610.4.3 Optimization model 2 . 2610.4.4Solutions to the model . 2715. Strengths and Weaknesses . 27Strengths . 27Weaknesses . 2716. References. 28Less Resources, More Outcomes1. SummaryIn this paper, we regard the health care system (HCS) as a system with input and output, representing total expenditure on health and its goal attainment respectively. Our goal is to minimize the total expenditure on health to archive the same or maximize the attainment under given expenditure.First, five output metrics and six input metrics are specified. Output metrics are overall level of health, distribution of healthin the population,etc. Input metrics are physician density per 1000 population, private prepaid plans as % private expenditure on health, etc.Second, to evaluate the effectiveness of HCS, two evaluation systems are employed in this paper:l Evaluation of Absolute Effectiveness(EAE)This evaluation system only deals with the output of HCS，and we define Absolute Total Score (ATS) to quantify the effectiveness. During the evaluation process, weighted average sum of the five output metrics is defined as ATS, and the fuzzy theory is also employed to help assess HCS.l Evaluation of Relative Effectiveness(ERE)This evaluation system deals with the output as well as its input, and also we define Relative Total Score (RTS) to quantify the effectiveness. The measurement to ATS is units of output produced by unit of input.Applying the two kinds of evaluation system to evaluate HCS of 34 countries (USA included), we can find some countries whichrank in a higher position in EAE get a relatively lower rank in ERE, such as Norway and USA, indicating that their HCS should have been able to archive more under their current resources .Therefore, taking USA into consideration, we try to explore how the input influences the output and archive the goal: less input, more output. Then three models are constructed to our goal:l Multiple Logistic RegressionWe model the output as function of input by the logistic equation. In more detains, we model ATS (output) as the function of total expenditure on health system. By curve fitting, we estimate the parameters in logistic equation, and statistical test presents us a satisfactory result.l Linear Optimization Model on minimizing the total expenditure on healthWe try to minimize the total expenditure and at the same time archive the same, that is to get a ATS of 0.8116. We employ software to solve the model, and by the analysis of the results. We cut it to 2023.2 billion dollars, compared to the original data 2109.8 billion dollars.l Linear Optimization Model on maximizing the attainment. We try to maximize the attainment (absolute total score) under the same total expenditure in2007.And we optimize theATS to 0.8823, compared to the original data 0.8116.Finally, we discuss strengths and weaknesses of our models and make necessary recommendations to the policy-makers。2. IntroductionToday and every day, the lives of vast numbers of people lie in the hands of health systems. From the safe delivery of a healthy baby to the care with dignity of the frail elderly, health systems have a vital and continuing responsibility to people throughout the lifespan. They are crucial to the healthy development of individuals, families and societies everywhere. Due to the irreplaceable role that the health care systems play in residents life, better health care system is needed. “Improving performance” is therefore the key words today.However, nowadays health care systems in many countries do not exhibit enough high effectiveness in guaranteeing residents good health and a long life expectancy. In some countries, their government invests large amount of money on the health care systems, however, they didnt archive what they should have been to archive. We try to explore an optimized system in this paper.3. Key TerminologylHealth Care System (HCS)Health Care System is such a system that has its input and output, representing total expenditure on health and its goal attainment respectively.lEvaluation of Absolute Effectiveness of Health Care System (EAE)It is a kind of evaluation system that only considers the outcomes of the health care system, saying nothing to do with the input (resources), and adapts the outcomes as measurement to effectiveness.lEvaluation of Relative Effectiveness of Health Care System (ERE)It is a kind of evaluation system that considers the outcomes of the health care system as well its inputs, and adapts units of output produced by unit of input as measurement to effectiveness.lAbsolute Total Score (ATS)Overall score for the evaluation of absolute effectiveness of health care systemslRelative Total Score (RTS)Overall score for the evaluation of relative effectiveness of health care systemslInput Metrics (IM)Metrics that are specified to assess input of HCSlOutput Metrics (OM)Metrics that are specified to assess output of HCS4. Choosing output metrics for measuring health care systemTable 1. Notation for goals and metricsGoals of Health SystemNotationMetrics for EvaluationNotationHealthU1Overall level of healthu1Distribution of health in the populationu2ResponsivenessU2Overall level of responsivenessu3Distribution of responsivenessu4Fairness in FinanceU3Distribution of financial contributionu54.1 Goals of Health Care SystemAccording to the World Health Report in 2000, the WHO pointed out the three goal of health care system, each goal with different priority WHO 2000.lBetter HealthBetter health is unquestionably the primary goal of a health system, with the highest priority.lFairness in financial contribution.Fairness in financial contribution is the second goal, with a relatively lower priority to health.lResponsivenessResponsiveness to peoples expectations in regard to non-health matters reflects the importance of respecting peoples dignity, autonomy and the confidentiality of information, and is the third goal ,with the lowest priority.4.2 Characteristics of a good health care systemGoodness&Fairness WHO 2000As the WHO defined what a good health care system was in its World Health Report in2000, a good health care system is a combination of Goodness and Fairness. A good health system, above all, contributes to good health. But it is not always satisfactory to protect or improve the average health of the population, if at the same time inequality worsens or remains high because the gain accrues disproportionately to those already enjoying better health. The health system also has the responsibility to try to reduce inequalities by preferentially improving the health of the worse-off, wherever these inequalities are caused by conditions amenable to intervention. The objective of good health is really twofold: the best attainable average level goodness and the smallest feasible differences among individuals and groups fairness. A gain in either one of these, with no change in the other, constitutes an improvement, but the two may be in conflict.4.3 Output metrics for measuring health care systemTo assess a health care system, we must measure the following five output metrics：lOverall level of healthWe use the measure of disability-adjusted life expectancy DALE to assess the overall level of population health. This measure converts the total life expectancy for a population to the equivalent number of years of good health.lDistribution of health in the populationWe use the index of equality of child survival to assess distribution of health in the population. It is based on the distribution of child survival across countries, and takes advantage of the widely available and extensive information on complete birth histories in the demographic and health surveys and small area vital registration data on child mortality.WHO defined it as followsWHO 2000： nn3 xi - x j Equality of child survival =1 - =i =1j =120.5（1） 2n x Where x is the survival time of a given child and x is the mean survival time across childrenlOverall level of responsivenessResponsiveness includes two major components:(1) Respect for people (including dignity, confidentiality and autonomy of individuals and families to decide about their own health);(2) Client orientation (including prompt attention, access to social support networks during care, quality of basic amenities and choice of provider). The level of responsiveness was based on a survey of key informants in selected countries. And WHO defined the index of Overall level of responsiveness as weighted average of its seven components: WHO 2000Level ofRe sponsiveness = 1 Dignit + 1 Confidentiality + 1 Autonomy333+ 1 Pr ompt attention +3 Quality of amentities（2）520+ 1 Access to social Support network +1 Choice of provider1020lDistribution of responsivenessWe use a simple approach to quantize the distribution of responsiveness. That is respondents in the key informant survey were asked to identify groups who were disadvantaged with regard to responsiveness. The number of times a particular group was identified as disadvantaged was used to calculate a key informant intensity score. Four groups had high key informant intensity scores: poor people, women, old people, and indigenous groups or racially disadvantaged groups (in most instances minorities). The key informant intensity scores for these four groups were multi- plied by the actual percentage of the population within these vulnerable groups in a country to calculate a simple measure of responsiveness inequality ranging from 0 to 1. The total score was calculated taking into account the fact that some individuals belong to more than one disadvantaged group.lDistribution of financial contributionThe fair financing measure estimates the degree to which health funding is raised according to the ability to pay for all m