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An AHP framework for balancing efficiency and equity in the United States liver transplantation system


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An AHP framework for balancing efficiency and equity in the United States liver transplantation system
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Veerachandran, Vijayachandran M
University of South Florida
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Multi-criteria decision analysis
Data mining
Healthcare policies
Medical decision making
Dissertations, Academic -- Industrial engineering -- Masters -- USF
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ABSRACT: Liver transplantation and allocation has been a controversial issue in the United States for decades. One of the main concerns in the allocation system is the trade-off between the two main objectives, efficiency and equity. Unfortunately, it is difficult to reach consensus on how to develop allocation policies that aim at balancing efficiency and equity, among transplantation policy makers, administrators, transplant surgeons and transplant candidates.Our research identifies and classifies the outcomes of liver allocation into two major categories, efficiency and equity, that are, often times, conflicting. Previous researchers did not consider how to balance outcomes in these two categories. Our research uses Analytic Hierarchy Process, a Multi-Criteria Decision Analysis methodology, to build a framework that quantifies the decision-making process and help decision makers to reach a valid consensus in terms of balancing these outcomes. Latest available patient registration and follow-up data are used in data analysis. Results from this analysis serve as inputs for the simulation model that is capable of evaluating alternative hypothetical policies.This research addresses the deficiencies of the current liver transplantation policy and is intended to refine the policy that will result in a more balanced allocation system with respect to efficiency and equity. Our proposed methodology can be applied to incorporate further changes in policy selection and refinement.
Thesis (M.S.I.E.)--University of South Florida, 2006.
Includes bibliographical references.
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Veerachandran, Vijayachandran M.
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An AHP framework for balancing efficiency and equity in the United States liver transplantation system
h [electronic resource] /
by Vijayachandran M. Veerachandran.
[Tampa, Fla] :
b University of South Florida,
ABSRACT: Liver transplantation and allocation has been a controversial issue in the United States for decades. One of the main concerns in the allocation system is the trade-off between the two main objectives, efficiency and equity. Unfortunately, it is difficult to reach consensus on how to develop allocation policies that aim at balancing efficiency and equity, among transplantation policy makers, administrators, transplant surgeons and transplant candidates.Our research identifies and classifies the outcomes of liver allocation into two major categories, efficiency and equity, that are, often times, conflicting. Previous researchers did not consider how to balance outcomes in these two categories. Our research uses Analytic Hierarchy Process, a Multi-Criteria Decision Analysis methodology, to build a framework that quantifies the decision-making process and help decision makers to reach a valid consensus in terms of balancing these outcomes. Latest available patient registration and follow-up data are used in data analysis. Results from this analysis serve as inputs for the simulation model that is capable of evaluating alternative hypothetical policies.This research addresses the deficiencies of the current liver transplantation policy and is intended to refine the policy that will result in a more balanced allocation system with respect to efficiency and equity. Our proposed methodology can be applied to incorporate further changes in policy selection and refinement.
Thesis (M.S.I.E.)--University of South Florida, 2006.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
Title from PDF of title page.
Document formatted into pages; contains 67 pages.
Adviser: Nan Kong, Ph.D.
Multi-criteria decision analysis.
Data mining.
Healthcare policies.
Medical decision making.
Dissertations, Academic
x Industrial engineering
t USF Electronic Theses and Dissertations.
4 0 856


An AHP Framework for Balancing Efficiency and Equity in the United States Liver Transplantation System by Vijayachandran M. Veerachandran A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Industrial Engineering Department of Industrial and Ma nagement Systems Engineering College of Engineering University of South Florida Major Professor: Nan Kong, Ph.D. Jos Zayas-Castro, Ph.D. Kingsley Reeves, Ph.D. Date of Approval: November 1, 2006 Keywords: Multi-Criteria Decision Analysis, Data Mining, Healthcare Policies, SAS, Medical Decision Making, Modeling Copyright 2006, Vijaychandran M. Veerachandran


DEDICATION To my wonderful parents, Veerachandran and Jayalakshmi


ACKNOWELDGEMENTS I would like to thank my Father, Mother and Sister for thei r love and continued blessings throughout my coursework and rese arch. I thank Dr. Nan Kong for his easy accessibility and tolerance. His expectations and dedication to work has been a great source of inspiration and encouragement whic h is reflected through out this research. I would like to thank my committee memb ers Dr. Jose Zayas-Castro and Dr. Kingsley Reeves, for their continued support a nd guidance. Finally, I would like to thank all my friends for their support and good wishes in my studies.


i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT v CHAPTER 1 INTRODUCTION 1 1.1 Current State of Health-C are in the United States 1 1.2 Organ Allocation in the U.S 3 1.2.1 United Network for Organ Sharing 4 1.3 Liver Transplantation 4 1.3.1 Research Motivation 5 1.3.2 National Organ Transplant Act 6 1.3.3 Efficiency and Equity in Liver Allocation 7 1.4 Analytic Hierarchy Process 7 1.5 Research Contributions 8 CHAPTER 2 LITERATURE REVIEW 9 2.1 Introduction 9 2.2 Analytic Hierarchy Process 9 2.2.1 Methodology 11 2.2.2 An Overview of AHP Applications 12 2.3 Selection Theme 13 2.4 AHP in Health-Care 14 2.5 AHP in Medical Decision Making 15 CHAPTER 3 PROBLEM STATEMENT AND METHODOLOGY 17 3.1 Introduction 17 3.2 Current Liver Allocation System 17 3.2.1 United Network for Organ Sharing 18 3.3 Liver Transplantation Issues 20 3.4 Analytic Hierarchy Process 21 3.5 Illustrative Example 21 3.5.1 Decomposition and Developm ent of Hierarchy Structure 22 3.5.2 Evaluation of Hierarchy 23 3.5.3 Consistency Index and Consistency Ratio 26 3.6 Synthesis of Priorities 28 3.7 Overall Priority for Final Selection 29 3.8 Results 30


ii CHAPTER 4 MODEL DEVELOPMENT 32 4.1 Introduction 32 4.2 AHP Framework 32 4.3 Selection Criteria for Liver Transplantation 33 4.4 Liver Transplantation Outcomes 34 4.4.1 Efficiency Outcomes 35 Average MELD/ PELD Score 35 Average Waiting Time 37 Acceptance Rate 37 4.4.2 Equity Outcomes 37 Geographical Equity 38 Gender Equity 38 Racial Equity 39 4.5 Hierarchy Model 40 4.6 Discussion of Methodology and Application 40 CHAPTER 5 DATA ANALYSIS AND RESULTS 41 5.1 Introduction 41 5.2 UNOS Data 41 5.2.1 Patient Registration Data 41 5.2.2 Patient Follow-Up Data 42 5.3 Statistical Analysis System (SAS) 43 5.4 Data Patterns and Simulation Model 43 5.5 Extraction Procedure and SAS Data Sets 43 5.5.1 Organ Procurement Organization 44 5.5.2 Regions and Transplant OPOs 45 5.5.3 Discrete Distributions 45 5.5.4 Cold Ischemic Time 46 5.6 Data Variables and Hierarchy 46 5.7 Merge Transplant and Follow-Up Data 47 CHAPTER 6 CONCLUSIONS 48 6.1 Concluding Remarks 48 6.2 Future Extension 49 REFERENCES 50 APPENDICES 55 Appendix A: Statistical An alytics Systems Program 53 Appendix B: Donor and Transp lant OPO 63 Appendix C: Cold Ischemic Time vs. Distance 65


iii LIST OF TABLES Table 2.1 The Fundamental Scal es (Saaty and Vargas, 2000) 10 Table 3.1 Average Random Index (O akridge National Laboratory) 27 Table 3.2 Weights Among Alternatives with Respect to Criterion 29 Table 3.3 Sum Product of Matrix 30 Table 4.1 Classification of Effi ciency and Equity Outcomes 33 Table B.1 Donor OPO vs. Transplant OPO 63 Table C.1 Analysis for 0 5000 in range of 100 miles 65 Table C.2 ANOVA Table for Patients Arrivals 66 Table C.3 ANOVA for Distance vs. CIT 67


iv LIST OF FIGURES Figure 2.1 AHP Themes 13 Figure 3.1 Schematic Representation of Current Liver Allocation System 19 Figure 3.2 Evolution of Hierarc hy Model for Fruit Selection 23 Figure 3.3 Final Priority Weight s Alternatives by Criterion 30 Figure 4.1 Evolution of AHP Model for Balancing Efficiency and Equity 39 Figure 5.1 SAS Data Extraction Flow Chart 43 Figure C.1 Distance vs. CIT for 100 miles 66 Figure C.2 Arrival of MELD Patients / OPO 67


v AN AHP APPROACH FOR BALANCING E FFICIENCY AND EQUITY IN THE UNITED STATES LIVER TRANSPLANT ATION SYSTEM: A PILOT STUDY Vijayachandran M. Veerachandran ABSTRACT Liver transplantation and a llocation has been a controversial issue in the United States for decades. One of the main concerns in the allocation system is the trade-off between the two main objectives, efficiency an d equity. Unfortunately, it is difficult to reach consensus on how to develop allocation policies that aim at balancing efficiency and equity, among transplantation policy makers administrators, transplant surgeons and transplant candidates. Our research identifies and classifies th e outcomes of liver allocation into two major categories, efficiency and equity, th at are, often times, conflicting. Previous researchers did not consider how to balanc e outcomes in these two categories. Our research uses Analytic Hierarchy Process, a Multi-Criteria Decision Analysis methodology, to build a framework that quantif ies the decision-making process and help decision makers to reach a valid consensus in terms of balancing these outcomes. Latest available patient registration and follo w-up data are used in data analysis Results from


vi This research addresses the deficiencies of the current liver transplantation policy and is intended to refine the policy that will result in a more balanced allocation system with respect to efficiency and equity. Our proposed methodology can be applied to incorporate further changes in policy selection and refinement.


1 CHAPTER 1 INTRODUCTION 1.1 Current Health-Care Scenario in the United States Improved public health policy and improve ments in medical care have increased the life expectancy of the av erage American from 49 years in 1900 to an all time high of 77.4 years in 2002 [1]. More amounts are spend for health-care awareness and improvement. The United States remains the leading nation in global healthcare spending: an average of $ 4,500 per person [2]. On a per capita basis, health spending in the U.S. is 50% higher than in the s econd-highest spending country, Switzerland, according to the Organization of Economic Co-operation and Development (OECD) figures [3]. In 2005 the U.S. healthcare i ndustry grew as a more demanding population sought the best healthcare th ey could afford. The Center for Medicare and Medicaid Services (CMS) reports that he alth care expenditure in the United States is expected to continue growing to 16.2% of the Gross Domestic Product (GDP) in 2005, up from 16% in 2004 [4] [7]. By 2015 health ca re expenditure in the United St ates is project ed to reach $4 trillion and contributes to 20% of the GDP [5 ]. This makes the health-service industry the largest in the U.S. The aforementioned data suggests that even a small improvement in health-care or associated services might have significant effect on the overall economy and life expectancy.


2 World Health Organization (WHO) stat istics show that the U.S. ranks 37th out of 191 countries in performance metrics for ov erall levels of population health, system responsiveness, health inequa lities or disparities among the population and di stribution of the financial burden [6]. In 2005, the costs of h ealth insurance premiums continued to rise in the U.S., rising costs are likely to affect the country's healthcare industry [7]. The U.S. Census Bureau stated that 46 million American s now lack health insurance. Expenditure on health services more than doubled in 2005 from ten years earlier. Rising costs of a health insurance is a growing concern; more and more people are liv ing without adequate health insurance, Nearly 46 million people in U.S. have no health insurance, which means these individuals will be deprived of proper treatment solutions in times of necessity [8]. The Business Communication Company (BCC) reports that more than half of the health care expenditure in the United States are for organ failures or tissue loss, an amount that exceeds $600 billion [9]. They also reported that over 215,000 people die in the U.S. every year from diseases that ar e treatable with transplantation. The National Foundation for Transplants reports the average cost for a kidney transplant ranges from $75,000 to $100,000, liver transplants from $250,000 to $275,000 and lung transplants from $200,000 to $250,000. The U.S. Organ transplantation was a $4.2 billion market in 2002 of which 76% is attributed to kidney and liver transp lantation. The market is projected to grow at a rate of 5% to $5.4 billion by 2007 [9].


3 1.2 Organ Allocation in the U.S. An organ transplant is the transplantati on of a whole or partial organ from one body to another, for the purpose of replacing the recipient's damaged or failing organ with a functioning one from the donor. Or gan donors can be li ving, or cadaveric. In the United States, there's a great shortage of donor organs: hearts, livers, lungs, kidneys, pancreases and small intestines. Even though there is an increase in the number of transplants and available liver s for transplantation, there is wide disparity between the number of organs needed for transplanta tion and number of organs available. Over 92,000 Americans are currently waiting for an or gan transplant at any given day, and this number is increasing and is expected to reach 100,000 by the end of 2010 [10]. In 2005, only about 28,000 organ transplants were perf ormed. On average, 114 people are added to the nation's organ transplant waiting list each day -one every 13 minutes. Nearly 6,500 people died in 2005 because no organs were available. Lack of available dono rs in this country lead to the death of 3,886 kidney patients, 1,811 liver patients, 457 heart patients and 483 lung patients in 2004 while waiting for life-saving organ transplants. Almost 10 percen t of the patients currently waiting for liver transplants are young people under 18 year s of age. On November 30, 2001, 2,348 children under age 18 were registered on the organ transplant waiti ng list. Candidates for kidney transplants top the wait ing list followed by liver candidates and lung candidates published by the United Network for Organ Sharing (UNOS), Our research focuses on the study of liver transplantation. Li ver transplantation remains the only treatment for end-stage liver disease (ESLD); however the number of patients who could benefit from a transp lant far exceeds the number of available


4 cadaveric donors. There is a wide disparity in the allocation of organs based on various characteristics for example patients with type O blood wait the longest for a liver transplant--an average of 1,243 da ys [13]. People with type AB wait the shortest time--an average of 210 days. Waiting time has clinically and statistically significant effect on the probability of graft failure outcomes following transplantation. For every fifty days of wait time on the list for a transplant the probabi lity of graft failure at one year increases in between 1% and 2%. 1.2.1 United Network for Organ Sharing The United Network for Organ Shari ng (UNOS) manages the nation's organ transplant system and oversees a comprehe nsive database of clinical transplant information under a contract with the fede ral government. UNOS maintains and operates the computerized organ sharing system by ma tching donated organs to patients registered on the national organ transplant waiting list UNOS seeks to increase organ donation through the education of the public to the dire need of organ transplants and the improvement of transplant success rate s through outcomes-ba sed research and policymaking [14]. The strength of the tran splant database relies on the active reporting of 412 UNOS member institutions. 1.3 Liver Transplantation Liver transplantation is necessary for the cure of most causes of acute or chronic liver disease. Liver transplantation is appr opriate to any acute or chronic condition resulting in irreversible liver dysfunction, provi ded that the recipient does not have other


5 circumstances that will preclude a successful tr ansplant. Cirrhosis is the main reason for more than 80% of transplantations performed in adults, (hepatitis C and alcoholic liver disease are the two most common diagnoses). According to (UNOS), there are more than 17,000 patients on the national waiting list fo r a liver transplant. Yet, in 2002, only 5,329 liver transplantations were performed [14] The large disparity between the number of available deceased donor organs and qualified recipients awaiting liver transplantation has created ongoing debate about selection criteria, the timi ng of transplantation, and attempts to expand the donor pool as a result of increasing mortality rates among listed patients. 1.3.1 Research Motivation UNOS data shows that 10 percent of the waiting population dies before a liver is available [14]. Unfortunately liver transplant ation ranks among the most expensive medical services and costs hundre ds of thousands of dollars [16]. The existing system of liver allocation gives more preference to pati ents living near donor, (i.e. more emphasis is placed on geography than trying to ensure urgency). Only organs which are not suited within an Organ Procurement Organization (O PO) is given out for regional allocation and later if there is no ma tch found in the region is offered nationally. There is very little rationale explaining the reason behind this. The existing system takes into account of medical factors including waiting time and HLA level medical severity calculated using Model For End Stage Liver Disease (MELD) score and blood compatib ility [21]. Efficiency is more and more emphasized in the existing policy and little effort is given to make the system equitable in terms of


6 geography, race gender and others, As a result the system that fails to address the equity issues associated. The risk of death among women, Asians, Hispanics and children are more than that of rest of the population due to a longe r waiting time for transplant than foreign nationals and repeat transplant patients [17]. There exists a wide disparity in waiting times across different regional allocation of livers ranging from 31 days to 207 days [18] [20]. The number of patients registered for tr ansplant doesn’t match with the rapidly growing mortality rate associated with shortage of organs. Procured livers remain transplantable only for a limited period of time based in the Cold Ischemic Time (CIT) normally ranging from 18 – 24 hours [19]. Two mo st important issues associated with allocation delays and maximum utilization of this scarce life saving resource are 1) Quality of match and 2) increase in rejecti on rate. About 10 to 15% of patients die while waiting for transplantation. Due to the severe shor tage of livers, an in crease in the quality of the allocation procedure and policy is critical for ESLD patients. 1.3.2 National Organ Transplant Act The responsibility of the Organ Proc urement and Transplantation Network (OPTN), formed by the National Organ Tran splant Act (NOTA) of 1984, ensures the national registry of organ tran splants is established with an emphasis on the development of equitable and efficient organ allocation policies [22]. NOTA asserts that a proper system to allocate donated organs for tr ansplantation among transplant centers and patients should be ranked according to establis hed medical criteria. The Senate Labor and


7 Human Resources Committee amended NOTA with the following: an equitable system is necessary such that individua ls throughout the country can have equal access to organ transplantation when appropria te and necessary [22]. The allocation of transplantable organs has been the subject of considerable debate throughout the transplant community during the last decade [23]. A debate whic h reached congress in 1998 remains unsettled since then. The UNOS is responsible for managing the national organ dona tion and allocation system. The current allocation procedure wa s approved for implementation on February 28, 2002 [14]. In the last six years there has been four changes in policy [24]. These multiple changes highlight the challenge in forming a consensus on allocation policy. 1.3.3 Efficiency and Equity in Liver Allocation The goal of a proper allocation policy is to identify a system which is equitable and efficient. In an equitable system, each individual on a transplant waiting list has an equal opportunity to rece ive a transplant subject to esta blished medical and demographic criteria. No discrimination or privilege for on e patient over anot her based on region, ethnicity etc. Efficiency implies the diminu tion of the wastage of donated livers available for transplantation. Equity in our research is measured in terms of the difference over efficiency outcomes. 1.4 Analytic Hierarchy Process The Analytic Hierarchy Process (AHP) is capable of combining qualitative and quantitative criterions in decision making pro cesses. The AHP model is successful in


8 practice and has numerous and diverse app lications. AHP’s capability of handling complex decision problems is well acknowle dged. AHP can handle complex and poorly defined problems which rigorous mathematical models display difficulty in solving. AHP has the ability to handle mix qualitative and quantitative criteria within the same decision framework. It also helps create a consensu s of scenarios or s ituations by converting qualitative decisions to quantitative data. AHP has the ability to handle both tangible and intangible attributes, define the structure of a scenario through its inherent hierarchical model and verify the consistency of end decisions 1.5 Research Contributions This research aims to balance the trade-o ff between efficiency and equity in liver transplantation, an issue that is heavily deba ted. This framework can also be used for making similar policies addressing the efficien cy and equity tradeoff. The AHP approach is used to quantify the deci sion making process and build l ogics with complex decision making criteria for policy selection. This res earch addresses the concerns regarding the need for a change in allocation policy, which needs to reduce or eliminate inequity in organ transplantation system. The latest data from UNOS is used in our research. This research uses AHP methodology for organ allocation. Even though numerous application of AHP can be found in complex medical decision analysis proce ss, as such none of the applications uses the capability of AHP in selection and ev aluation of organ allocation policies. Our research aims to address the concerns in liver allocation policy by tying efficiency and equity together, which previous researchers held separate.


9 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction This chapter discusses the literature relate d to the research. In section 2.1 we will introduce Analytic Hierarchy Process (AHP), describe several applications, and summarize various solution techniques. In section 2.3 we will summarize previous studies that apply AHP to medical decision making problems. In section 2.4 will discuss previous decision making met hodologies in the national liver allocation system. Finally, section 2.5 will provide analysis on the previous studies addressing efficiency and equity in liver allocation. 2.2 Analytic Hierarchy Process AHP is a multi-criteria decision making tool that is flexible and used across wide variety of disciplines. It helps analyze both quantitative and qualitative aspects of a decision process. AHP was developed by Thom as L Saaty in 1970 [25]. An advantage of AHP over other multi-criteria decision making me thods is that the AHP can incorporate tangible as well as intangible factors, espe cially when the subjective judgments of different individuals constitute an important part of the decision process. The method is widely used in varying areas such as politic s, economics, sociology, and even in medicine because of the following advantages: 1) th is method can handle both quantitative and qualitative data all at once; 2) this method uses the eigenvector and eigen-value property,


10 which presents a computational advantage 3) a reduction in cognitive burden to decision makers when comparing with other similar me thods and 4) previous works have already verified the advantages of this method w ith numerous case studi es. AHP has broad application areas including planning, reso urce allocation, conflict resolution and optimization and selection of the best alternative [26]. This research uses the selection approach of AHP: selecting the best alternativ e from a set of given feasible alternatives. AHP utilizes a numeric scale to calibrate the measurement of quantitative as well as qualitative performances (Table 2.1), th e scale ranges from one to nine with one corresponding to least favored and progressi vely moving up the scale to nine which corresponds to very strongly favored. Table 2.1 The Fundamental Scales (Saaty and Vargas, 2000) Numerical Score Defi nition Explanation 1 Equal Importance Two activities equally contributes to the objective 2 Weak 3 Moderate importance Experience and judgment slightly favor one activity over another 4 Moderate plus 5 Strong importance Experience and judgment strongly favor one activity over another 6 Strong plus 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 8 Very, very strong 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation


11 2.2.1 Methodology AHP aids in formulating a multi-attribute decision problem in the form of a decision tree, where each of the hierarchy leve l involves a variety of criteria. It can be from a simple single level hierarchy to a multiple level (n) hierarchy. AHP addresses the decision problem of choosing the best al ternative by systematic and quantitative comparison of different criteria using pai r-wise comparison techniques. Mathematically, it determine the weights of the comparison pairs Ci for i = 1 to n ’ where n is the number of criteria. AHP exceeds the comparative judgment approach by relaxing the normality assumption of parameters. In this research, AH P is used in this research to develop and analyze trade off between conflicting outcomes in the course of structuring reciprocal pair-wise comparison matrices. AHP starts by breaking down the problem hierarchically; each level of the hierarchy consists of a few manageable elem ents. These elements are further sorted to another set of sub-elements. This process c ontinues until all speci fic elements of the problem are measured, which in turn repres ents the lowest level of the hierarchy. Structuring the problem hierar chically reduces the complex nature of the problem and helps identify the major components. It also helps us understand the problem in a better manner and sort the trivial and non trivial elements.


12 2.2.2 An Overview of AHP Applications The AHP model has found numerous successf ul applications. An overview of AHP in various areas is pres ented in Vaidya and Kumar ( 2004). These applications for AHP include decision making in personal, so cial, manufacturing, politics, engineering, education, government and health care app lications. The authors reviews several approaches used in AHP, selection, eval uation, priority, deve lopment, resource allocation, decision making, fo recasting, medicine [26]. In a review of the 150 top-tier journa ls, the most popular applications of AHP falls either in the combination of engineering application and selecti on approach or social application and selection approach. AHP has been used in many cases as a stand-alone application however variations of AHP such as fuzzy AHP or a combination of AHP with tools like linear programming, ar tificial networks and fuzz y set theory makes it more versatile and expands the application areas. The application of AHP is also seen a increasing trend as more and more top tier research publications like the European Journal for Operations Research (EJOR) have special editions and annual symposium for AHP being held due its incr eased application areas.


13 Figure 2.1 AHP Themes 2.3 Selection Theme Forman and Gass (2001) mention severa l AHP applications in selecting best alternatives from a given set of multiple alte rnatives in a multi-criteria environment. The application areas include pr oduct selection, vendor selec tion and policy decision. Their paper talks about application of AHP in more than 50 research decision situations within the Xerox Corporation; such as portfolio management, engineering design selection, technology implementation, market segment pr ioritization and customer requirement prioritizing [27]. Sharp (1987) discusses the application of AHP in their selection of lowest cost haulers to ha ndle the dispatches to reduce dispatch costs [29]. AHP has a significant role in group decision making, Dyer and Forman (2002) state the benefits of using AHP in group decision making through decomposition, comparative judgment and synthesis of priorities [30].


14 2.4 AHP in Health-Care AHP has been a powerful tool to h ealth care decision makers. Many common themes have been found in AHP aided decisi on making in the health care industry. This literature review will mainly discuss the application of AHP in clinical and medical decision evaluation. The problems mostly use the selection and decision making approach of AHP [26]. Application of res ource allocation and prioritization themes can be found in a) medical staff decision making b) identifying altern ative technologies to purchase, c) assisting patient s in their decision making pro cess. AHP is not only capable of analyzing economic and technical factors in the healthcare industry but also social and human factors [31[32] [33]. Ha riharan et. al (2005) presents an application of AHP for measuring and comparing the global performance in quality of intensive care units [34]. Different approaches have been taken in health care decision making problems using AHP, as demonstrated in the followi ng two examples. Wu, Lin and Chen (2006) apply AHP in optimal selection of locations for Taiwanese hospitals [35]. The model addresses the burgeoning health care quali ty consciousness among Taiwanese residents and improves scope of medical services consid ering a competitive advantage. Rosetti et al (2001) address decision problem for hospita l deliver systems that addresses economic and technical performance as well as social human and environmental factors. The model enables a better understanding of delivery and transportation requirements in medium and large size hospitals [36].


15 2.5 AHP in Medical Decision Making Min et. al (1997) propose a model whic h helps medical clinics improve service strategies in the competitiv e health care industry. Their research uses AHP for the comparative evaluation of quality benchmarking in health care service improvement [37]. A recent development in technology and bioethics enables an increased participation from patients in their own health care decision making, resulting in a shared decision making model Singpurwalla et al (1999) [39]. Liberatore et. al, (2003) uses AHP to model a shared decision making among patients and physicians for addressing the gr owing concern of prostate cancer in men. The model also successfully captures the decision-counseling pr otocol for cancer screening. The adaptability of AHP in mode ling complex problems is emphasized to fit the research. The paper describes the methodol ogy in three steps of which the first is identifying the alternatives available a nd personal criteria fo r evaluation. Secondly determining how the alternatives achieve the personal criteria based on analysis thirdly to determine the priority of the steps and fi nally deciding among alternatives. The study emphasizes the lack of training needed for patients who are involve d in decision making and the addresses the necessity of more application of AHP to personal decision making [39]. Applications of AHP in medical decision making and medical decision support can be found [40 [41] [42]. Cook, Staschak and Green (1990) work on the equitable allocation of livers for orthotropic transplantation they consider the major factors to logistics, tissue compatibility, waiting time, financial and medi cal status. They rate the patients in terms of main categories based on their rank in s ubcategories using pair-wise comparisons [33].


16 They state that the system lacks formal evaluation and is based on the intuition of individuals involved. While equity is heavily emphas ized, efficiency of the transplantation is poorly addr essed. Equitable provision and h ealthcare financing is one of the National Health Service’s (NHS) growing concerns since its ince ption (Sassi et al 2001). Awareness of widening health equities since the publication of Black report has raised equity to a high rank among policy makers.


17 CHAPTER 3 PROBLEM STATEMENT AND METHODOLOGY 3.1 Introduction Allocating available livers to necessary patients involves a lot of discretion. Choosing an optimal liver allocation policy am ong a set of alternatives is a challenge given the subjective nature of this problem. The decision maker may not be able to make consistent decisions addressing the efficiency and equity in selecting policy. Decisions involved in selecting the best policy mu st consider various outcomes of liver transplantation including efficiency, equity a nd trade-offs between them [45]. This makes the problem a Multi-Attribute Decision Ma king problem (MADM). AHP is a MADM methodology which helps quantify the deci sion making process and gives decision makers the ability to reach a valid consen sus in decision making rather than depending totally on their intuition [25]. 3.2 Current Liver Allocation System This section provides an overview of the existing liver allocation system. Knowledge of the existing sy stem will help in understanding the difficulty faced by decision makers in allocating available liv ers to ESLD patients. UNOS operates the national system for organ transplantati on. It is responsi ble for managing and administering the proper allocation of availa ble organs for transplantation. The current liver allocation system was implemented in February 28, 2002 [20]. The policy has been


18 changed four times in the last six years [21] Numerous changes in such a small duration shows that there is a need for improvement in the liver allocation policy. 3.2.1 United Network for Organ Sharing UNOS is responsible for every organ tran splant performed in the United States. UNOS supervises the organ donation and proc urement via non-profit agencies called Organ Procurement Organizations (OPO). OPOs provide organ recovery services, manage the clinical care of the donors, ente r donor information in to the UNOS computer database to find a match and c oordinate the organ recovery process to hospitals located within designated geographical area in the U.S. OPO’s also promote organ donation in their communities by sponsoring workshops an d participating in community health fairs and events [14]. The national UNOS membership is divi ded into 11 geographic regions, each consisting of several OPOs. This regional configuration was developed to facilitate organ allocation and to offer individuals the oppo rtunity to identify concerns regarding procurement, allocation, and transplantation of organs that are unique to their region. The patients are divided in to two cate gories PELD and MELD based on the age. PELD score is for patients under 18 years of age. In our research we are focused on the adult liver allocation procedure. UNOS maintain s a patient waiting list that is used to determine the transplant candi dates among the patients. When a liver becomes available, the following factors are considered for its allocation: medical urgency of the patient, patients OPO, patient region, pa tient score from clinical an d medical urgency, and patient waiting time (Figure 3.1).


19 UNOS provides a framework of principl es for making policy decisions about organ allocation. Currently the existing systems follow a “sickest first” approach. Patients with severe medical urgency will be offered the liver first [47]. Figure 3.1 Schematic Representation of Current Liver Allocation System Figure 3.1 explains about the current liv er allocation procedure. Every liver available for transplant is first offered to those Status 1 patients located within the harvesting OPO based in descendi ng order of MELD score. If there are no suitable Status 1 matches within the harvesting OPO, the liver is then offered to Status 1 patients within the harvesting region. If a match still has not been found, the liver is offered to all nonStatus 1 patients in the harvesting OPO in descending order of MELD score. The search range is again broadened to the harvesting region if no suitable match has been found within the harvesting OPO. If no suitable matc h exists in the harvesting region, then the


20 liver is offered nationally to Status 1 patient s followed by all other patients in descending order of MELD score [14]. 3.3 Liver Transplantation Issues In the existing liver transplantation po licy, more emphasis is given in the geography of patient than balancing the equi ty issues associated with the model. A harvested liver is first distributed accord ing to medical condition and then by the proximity towards the transplant OPO. This results in wide inconsistency as a patient’s chance of living or dead is based on where they live than their medi cal urgency [20]. The condition becomes worse when current policy al low people to list in more than one geographical region, known as multi ple listing. Many patients who are able to list in more than one region stand a higher chance of obtaining a liver than people listed in only one region [21]. Any organ allocation policy should satisfy at least the following three performance goals: 1) identify and establish standardized criteria for measuring proper medical scores for eligibility of transplant patients before adding to the waiting list, 2) facilitate a fair comparison of patients acros s the waiting list. Geogra phical preference of the patients should be widely reduced and mo re emphasis should be give to the equity aspect [50]. A change in the increased emphasis on efficiency should be pushed by regulations to encourage a move to a more equitable system. There is less rationale in providing a liv er to a severe End Stage Liver Disease (ESLD) patient irrespective of the survival rate [20]. Two specific and somewhat conflicting goals should be considered for deci sion making in transplantation: efficiency


21 of the transplantation and equity in transpla ntation [22]. Which one should be given more emphasis, fairness surely give s higher preference to equit y, but utilization emphasizes on higher efficiency. We shall balance the e fficiency and equity of these conflicting outcomes and reach a more desirable decision making policy. 3.4 Analytic Hierarchy Process The AHP method by Saaty is based on two important theoretical principles: the fundamental scale for ratio comparison, and the eigenvector and ei gen value property [25]. Saaty utilizes a fundament al scale ranging from one to nine. The scale has its origin on the Weber-Fechner’s sensation (response) e quation “Law of stimulus of measurable magnitude” (i.e.0 log a b s a M ) where M denotes the sens ation and s the stimulus) (Fechner, 1966) [52] [53] When making pair-wise co mparisons, nearest integer approximation from the fundamental scales of one to nine is being used. This scale has been validated for effectiveness in many a pplications by numerous individuals through the theoretical justification of what s cale one must use in the comparison of homogeneous elements (Saaty and Vargas, 2000) [54]. The upper limit of nine is adopted following Miller (1956)’s “Magical number theory” [55]. Alternatives are compared based on this fundamental scales in a pai r-wise comparison fashion; then a decision matrix is composed [55]. 3.5 Illustrative Example We are using an example to explain th e AHP methodology. There is an age old adage which says apples cannot be compared with oranges. Our objective is to choose the best fruit from a set of alternatives, includi ng apple, orange and grapes. These can have


22 many criterions in common: color, quality, app earance, seediness, etc. We may prefer an orange for color criteria but for appearance criteria an apple and for quality criteria grapes. Strength of our preference for these characteristics may vary. Even though we may be indifferent to some at tributes there will be strong preference for some other attributes which may vary across circumstances. The challenge is to identify a set of alternatives which strongly fulfills the goal which satisfies entire set of objectives. The decision making is conc erned with weighing alternatives through pa ir-wise comparison. 3.5.1 Decomposition and Developm ent of Hierarchy Structure The AHP methodology suggests the developmen t of a hierarchical structure. The formulation of a decision hierarchy is a critical step in AHP because it helps to effectively frame a problem and simplify the anal ysis process. It also helps to decompose the problem into inter-related decision element goals, attributes and al ternatives. In our specific example the hierarchy structure consists of a three-level hier archy consisting of a final objective goal, level of attributes through which these alternatives are being evaluated including color, qu ality, appearance and seed iness and final level of alternatives, apple orange or gr ape to chose from (Figure 3.2).


23 BEST FRUIT QUALITY APPEARANCE COLOR SEEDINESS APPLE ORANGE GRAPES Figure 3.2 Evolution of Hierarch y Model for Fruit Selection 3.5.2 Evaluation of Hierarchy The second step in an AHP process is the evaluation of the hierarchy. 1) Identify the preference weights (judgm ents) by pair-wise comparison of the decision elements. 2) Synthesize the preference weights to determine the most preferred alternative. Let us consider the elements from C1 to Cn of some level in hierarchy. The weights of influence W1, to Wn are found on some element in the ne xt level. We will determine the pair-wise comparison matrix aij (i, j = 1, 2, n) which indicates the strength of Ci when compared with Cj. The matrix of these numbers aij is denoted A, or Goal Criteria Alternatives


24 1 / 1 / 1 / 1 1 / 1 / 1 1 / 1 13 2 1 3 23 13 2 23 12 1 13 12 n n n n n na a a a a a a a a a a a A (3.1) The matrix can be also be denoted as aij = 1/ aji ,, that is the matrix A is reciprocal. If at any level of hierarchy the attribute of Ci is of equal relative importance as Cj, then aij = 1, aji = 1; In particular aii = 1 for all i. If our judgment is perfect in all comparisons then aik = aij ajk for all i,j,k, and we can call matrix A as a consistent matrix. In a consistent matrix the comparisons are based on exact measurements and; If the weights W1, to Wn are already known. Then aij = j iw w (for i, j = 1, 2, …, n). (3.2) thus aij ajk = j iw w k jw w = k iw w = aik (3.3) This leads to aji = i j W W = / Wj i 1w = aij1 (3.4) Considering the matrix equation A.x = y (3.5) Where x = ( x1 . . . .xn ) and y = ( y1 . . . .yn ) i n 1 j ijy xi a (for i = 1, 2, …, n). (3.6) This gives us


25 aij i jw w = 1, (for i, j = 1, 2, …,n). Consequently wi wj an 1 j ijn (for i = 1, 2, …, n). Which is equivalent to Aw = n w (3.7) where A is a consistent matrix. In general, small deviation in aij may lead to large deviations both in Eigen value max and in iW (for i = 1,2, to n). It necessitates the need for stable solutions which satisfies the condi tion. The reciprocal matrix satisfies the conditions and gives a more stable solution. When considering th e reciprocal of the matrix A which is represented as A', from the pair-wise comparisons, the solution can be represented as A'w' = n w' (3.8) Several approximation methods are ava ilable to identify the weights of the comparison vector of which, the most r ecommended method geometric approximation is utilized in this research. This method mu ltiplies all the n elements in the pair-wise comparison matrix and the resulting weight s of corresponding alte rnatives normal the results obtained by taking the nth ro ot for matrix of n alternatives. From our example consider the priority vector matrix 1 4 / 1 9 / 1 7 / 1 4 1 5 / 1 5 / 1 9 5 1 3 / 1 7 5 3 1 A'


26 The multiplication of each row results in (105, 45/3, 4/25, and 1/252) respectively. Each value is raised to the power 1/n. In th is example n = 4. The result is represented by priority vector p ) 4 / 1 ( ) 4 / 1 ( ) 4 / 1 ( ) 4 / 1 (252 / 1 25 / 4 3 / 45 105 P = 0.251 0.632 968 1 3.201 These values are normalized using a linear normalization method. The sum of the all elements of column vector P is calculated, each element is then divided by that sum of elements. In our example, the sum of elements is found to be around 6.052. After normalization, the vector of weights is given by w. 6.052 0.251 6.052 0.632 6.052 1.968 6.052 3.201 w = 0414 0 1044 0 0.3251 5289 0 3.5.3 Consistency Index and Consistency Ratio Consistency of the decision is a big issue to be addre ssed in any decision making methodology. The matrix A (aij) is said to be consistent only if the principal eigen value max is equal to or close to the order of the ma trix (n). The sum of the eigen values of a matrix is equal to its trace which is also equal to n.


27 The human involvement of AHP makes it difficult for any one to give the precise values of the pair-wise comparison ratio j iw w, rather only an estimate. Therefore, Saaty replaces the equation Aw = nw with Aw = max w. where max is the largest or principal eigen value of matrix A. Saat y defines the difference between max and n as a Consistency Index (CI). CI is calculated by 1 n n CImax (3.9) The consistency index of randomly generate d reciprocal matrix for the ratio scale 1 to 9, with reciprocals forced is called as Random Index (RI). At Oak Ridge National Laboratory, Saaty generated an average ra ndom index (RI) for matrices of order 1-15 using a sample size of 100. RI increases as the order of the matrix increases and is shown in the following table as the sample size was only 100 and statistical fluctuation of indexes from one order to the other (Table 3.2). Table 3.1 Average Random Index (O akridge National Laboratory) N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 RI 0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51 1.48 1.56 1.57 1.59 The ratio of C.I to average R.I for matrix of the same order is defined as Consistency Ratio (C.R). C.R = C.I / R.I (3.10)


28 Lower the consistency ratio will increase the consistency of the decision. Saaty recommends using matrices of consistency ratio s less than 0.1. If the consistency ratio is greater than 0.1 such a matrix should be elim inated to calculate the weight so that the decision made is more rational. Thus AHP methods use a combination of C.R and powerful pair-wise comparison to reso lve irrational humanistic responses. Ideally, aij = j iw w (for i, j = 1, 2, …, n). We use judgments which are quantified, and all the allowances must be integrated. Deviations in the ratio aij and the number n, now denoted by max, leads to max n 1 j j ij max iw a 1 w i = 1, 2, …, n (3.11) A small deviation in aij can lead to a very large de viation in final weights. The consistency in decision should be maintained throughout for accurate measurement of the selection criteria. 3.6 Synthesis of Priorities Once we have obtained weights of criteri a, the next step is to prioritize the alternatives based on the criteria. For each crit erion the alternatives are prioritized based on the decision matrix and priorities are obtained. Pair wise comparison of criterion color is shown as follows 1 9 3 9 / 1 1 3 / 1 3 / 1 3 1 A' .6923 .0796 .23076 W' The matrix and the weights based on one of the criterion color as shown in the above equation. The weight is obtained via the method previously mentioned. Similarly


29 we can obtain the weights for other criteri a including quality appear ance and seediness (Table 3.3). Table 3.2 Weights Among Alternatives With Respect to Criteria Evaluation Color Quality Appearance Seediness Weights 0.1647980.1851840.437111 0.212907 Apple 0.2307690.1428570.177276 0.0704176 Orange 0.0769230.7142860.0852256 0.751405 Grapes 0.6923080.1428570.737498 0.178178 3.7 Overall Priority for Final Selection Finally, the priority weights of each alternative can be calculated by weights per alternative multiplied by weights of the corr esponding criterion. The highest score of the decision matrix implies the best choice of fru it. Synthesizing the priorities will give us the weights of the criteria and the priorities of the alternatives ba sed on each individual criterion. Now we have to obtain the overall priority ranks which will help us in making the decision. For obtaining the overall ranking of alternatives we multiply the corresponding alternatives with the weight s of the criterion weights. Ranking = Priorities Weight s of Criteria (3.12) The weight of alternativ e apple based on the criter ion color is obtained by 0.038030 16472 0 230769 0 color on based apple of Weight Similarly weights of other alternativ es are also obtained by sum product


30Table 3.3 Sum Product of Matrix SUM PRODUCT Color Quality Appearance Seediness Results Apple 0.03803 0.0264 0.0774892 0.014992 0.15696 Orange 0.012676 0.1322 0.037253 0.159979 0.34218 Grapes 0.11409 0.0264 0.3223684 0.037935 0.50084 3.8 Results According to the decision matrix final sc ores, grapes are the most preferred due to its high priority weight, Orange is the next recommended alternative. Through the illustration of this AHP model, it is found that the fruit selection problem can be solved in a structural and simple manne r without involving much comp lexity. The sensitivity of each fruit with respect to the attributes and main criteria also can be obtained. The final priority weights of each fruit can be seen in Figure 3.3. The step by step computations and comparison matrices of all the attributes are shown. The important results are also shown in Figure 3.3. 0 0.1 0.2 0.3 0.4 0.5 0.6 Color QualityAppearanceSeedinessGlobal Evaluation Apple Orange Grapes Figure 3.3 Final Priority Weight s Alternatives by Criterion


31 The final priority weights of different criteria shows that the appearance of the fruit carries the highest priority and it is followed by seediness, quality and color, respectively. The factors that contribute mo st in fruit selection are appearance and seediness.


32 CHAPTER 4 MODEL DEVELOPMENT 4.1 Introduction This chapter discusses decision making i nvolved in finding a trade-off between efficiency and equity outcomes which were modeled in a Multi-Criteria Decision Analysis framework using Anal ytic Hierarchy Process. Addi tionally, important decision criteria related to efficiency and equity invo lved in deciding the be st policy are detailed. The criteria discussed include average MELD score, waiting time, racial and geographic equity which require consider able amounts of atte ntion. We attempt to generalize the model for all organ transp lantation including liver, ki dney, and tissues etc. 4.2 AHP Framework Balancing efficiency and equity in U.S. liver transplantation can be modeled as a multi-criterion decision problem which include s both qualitative and quantitative factors. Reaching a consensus in selecting a policy is more complex when there are conflicting attributes involved. AHP ba sed methodology will be discusse d to tackle the different necessary but conflicting criteria. In our rese arch criterion like efficiency and equity including the sub criterions involved in th e selection of altern ative policy based on existing liver transplantation scenario. In this research AHP is used to identify a consensus in which how much a system should be balanced in terms of efficiency and


33 equity outcomes. This resear ch concentrates on a widely divided category of organ transplant’s outcomes; i.e. efficiency a nd equity. The aim of the National Organ Transplant Act (NOTA) is to develop a policy which is effici ent and equitable. Categorized outcomes are as shown in (Table 4.1). The table comprises some of the major outcomes which, we believe, affect an efficient and equita ble distribution of harvested organs. Table 4.1 Classification of Effi ciency and Equity Outcomes Efficiency Equity Average Cold Ischemic Time (Hours) Race No. of Previous Transplants Ethnicity Category Age in Years at Time Of Listing Gender Recipient Length of Stay Post Transplant State of Residency at Registration Recipient Died (1=Dead,0=Alive) Cold Ischemic Time (Hours) No. of Days on Liver Waiting List Average MELD Score Age In Years At Time Of Listing Recipient Length of Stay From Transplant to Discharge Recipient Days Between Previous And Current Transplant Allocation Type: Local/Regional/National/Foreign We categorize the measurable outcomes in to two main subsets: Efficiency and Equity. In the preliminary step for finding th e optimal policy we break down the decision problem into further criteria. These criteria will aid in building the hierarchy model, thus facilitating the easy understa nding of the problem and easing application of AHP methodology.


344.3 Selection Criteria for Liver Transplantation Most decision makers cannot simultaneou sly handle more than 7 to 9 factors when making a decision involving alternatives that have multiple attributes. It is necessary to break down complex problems in to more manageable sub problems which help decision making. There is a large num ber of contributing but conflicting factors simultaneously affecting the process of reachi ng a decision. An orderly sequence of steps should be required whereby a complex problem is broken down into to sub-problems reducing complexity and produces an easy analysis. Liver transplantation has f our level of hierarchy. Th e following sections discuss the different decision criteria, attributes and the decision alternatives. The objective is to select a best liver allocation policy which balanc es efficiency and equity for the U.S. liver transplantation system. Appli cation of common criteria to all alternative policies makes pair-wise comparisons possible. The criteria which are considered are: 1. Efficiency 2. Equity 4.4 Liver Transplantation Outcomes Liver transplantation outcom es are divided into efficiency and equity outcomes. Our research focuses on efficiency and equity outcomes of the existing model for liver allocation. Efficiency refers to the utilitari an view towards the systems and intends to make the existing system efficiency orient ed. In the equity oriented approach, the egalitarian view argues for the equity of th e system in all terms including gender, race,


35 geography, etc. It is a challenge to devel op a decision to process that is capable of balancing efficiency and equity amongs t large number of alternatives. 4.4.1 Efficiency Outcomes The efficiency criterion is an important criterion in assessing the policy because it can determine the effectiveness of the system in terms of utilization of scarce resources. A good policy cannot be possible without maximum utilization of the available transplantable livers. Cons idering a high rejection of more than 45%, maximum utilization of transplantable livers should have a major influence [57]. While most of the medical factors incl uding medical urgency, waiting time and age have been taken in consideration some issues are not properly addressed; some of the major factors (attributes) affecting th is criterion can be stated as follows Average MELD/ PELD Score Efficiency of the system is attributed to the scoring model for calculating the severity of disease. The MELD score reflects the patient's risk of dying while waiting for a liver transplant based on clinical tests. The MELD and PELD scor es range from 6 to 40 and are based on objective a nd verifiable medical data. Th e MELD score is used for adults, while the PELD score is used for pati ents who are less than 12 years of age. The higher the MELD or PELD score, the grea ter the risk of dying from liver disease The MELD score calculation uses: Serum Creatinine (mg/dl)* Bilirubin (mg/dl) INR


36 MELD Formula MELD Score = 0.957 x Loge (creatinine mg/dL) + 0.378 x Loge (bilirubin mg/dL) + 1.120 x Loge (INR) + 0.643 Multiply the score by 10 and round to the nearest whole number. The PELD score calculation uses: Albumin (g/dl) Bilirubin (mg/dl) INR Growth failure (based on gender, height and weight) Age at listing PELD Formula PELD Score = 0.480 x Loge (bilirubin mg/dL) + 1.857 x Loge (INR) 0.687 x Loge (albumin g/dL) + 0.436 if patient is less than 1 year old +0.667 if the patient has growth failure Multiply the score by 10 and round to the nearest whole number. The likelihood of a critical ly ill person receiving a live r is higher than that of patient who has a higher recove ry chance. In the current sc oring system, the median wait time for re-transplant candidates is less than that of new transplant candidates. A factorization of the score can be done based on transplant history. One of the primary efficacy outcome is survival rate of patient s after transplantation. Additionally, the quality adjusted life years is another major outcome. Length of time in the waiting list and quality of the liver obtained also attribute a lot towards the efficiency issues. Average MELD score, length of hospitalization, reject ion rate are secondary factors for deciding the efficiency of a transplant.


374.4.1.2 Average Waiting Time The length of time spent on the waiting li st is another major attribute for the efficiency of the system. For a more efficien t system it is necessary that the average wait time be reduced. This is a major factor in the measuring MELD scores. The wait time determines the priority when there is a tie amongst patients of similar MELD or PELD scores. Acceptance Rate Higher acceptance rate is directly related to the efficiency of the policy. It is necessary for any alternative po licy to have a very low reject ion rate. There is a wide gap between the available livers for transplantation and number of patients in the waiting list. Liver transplantation is very expensive and costs hundreds of thousands of dollars. A higher acceptance rate can substa ntiate the high cost involved with liver transplantation and associated costlier post transplant medication. 4.4.2 Equity Outcomes Equity of the liver allocation system shoul d be viewed as equal as efficiency. The measurement of equity contributes toward th e fairness of a policy. Numerous criteria which we can measure equity; are blood group, race, insurance, health conditions, ethnicity, transplant OPO etc, as such important for any policy to be fair so that no policy should be biased on things beyond their control. Our research c onsiders, what we think, a major contribution toward the equitable allocation via as ge ography, race and gender. We consider the measurements as we view th eir inclusion as a means to create a more equitable policy. Equity outcomes in this rese arch are measured in terms of the difference


38 in scores of specific efficiency outcomes over patient. For example The difference in the MELD score across Hispanics Asians Whites and African Americans. Geographical Equity Geographical equity is one of the major c ontributions toward the fairness of liver allocation policies. The regional variability in wait time has prompted vigorous debate on organ allocation policy. Certain parts of the nation failed to be nefit from the regional bias of current liver allocat ion policy. It is necessary for an ideal policy to reduce the regional variability in allocation of livers. Gender Equity There is a wide disparity in the post transplant survival rate and acceptability of organs based on the male and female. Any idea l policy should be ab le to recognize and reduce this disparity to its bare minimum while maintaining an acceptable efficiency level. Racial Equity Another major equity criterion measured is race. No policy should disadvantage anyone for belonging to a certain race. Even though the current system does not explicitly account for racial consideration, it is observed that there is a high racial disparity in the number of transplants as we ll as the waiting time for peopl e belonging to a particular race. Any system should be fair in such a wa y that the difference among the race in terms of efficiency attributes shoul d be minimized or negligible.


39 For all the major equity criteria a nd corresponding sub criteria, pair wise comparisons are done in terms of the differen ce in the efficiency attributes. For example if we consider the geographical equity criter ion we will measure the difference in average wait time across the different regions based on the national average. Similarly pair wise comparison will be done for other criteria to obtain a quantitative justification in determining priorities among the criteria. 4.5 Hierarchy Model Figure 4.1 Evolution of AHP Model fo r Balancing Efficiency and Equity Policy Selection Efficiency Equity Average MELD score Acceptance Rate Average Waiting time Race Geography Asian Hispanic Afro-American Difference in Meld Score Difference in waiting time Gender Polic y A Policy B Policy x


404.6 Discussion of Methodology and Application The problem discussed is the U.S. Live r transplantation and allocation policy; searching for the best policy for balancing effi ciency and equity. The research takes into account the majority of possible criteria whic h can affect the decision maker. A detailed discussion on every criterion, sub criterions, attributes a nd alternative policy has been presented. Two critical criter ia have been identified. The methodology has been used further to select the numerous attributes (or sub-criteria) with for evaluating among alternative policies. The following steps have been considered to form the hierarchy: (1) Define the issues considering the U.S. liver transplantation. (2) Identify the overall objective of policy selection. (3) Identify the criteria and attributes that must be satisfied to fulfill the overall objectives. (4) Identify decision alte rnatives or outcomes. (5) Structure the hierarchy placing the objective at first level, criteria at second level, attributes at third level, and decision alternatives at fourth level.


41CHAPTER 5 DATA ANALYSIS AND RESULTS 5.1 Introduction In this chapter we will discuss about th e sources of data, da ta extraction methods, variables for analysis, simulation mo dels, and data analysis software. 5.2 UNOS Data The UNOS operates the national system fo r organ transplantation. As mandated by policy, all transplanting institutions must report certain information for each transplant performed. The UNOS liver committee selects th e relevant set of variables to be report, which are collected on standardized form s made available by UNOS. UNOS makes the information publicly available in electronic format. Two sets of latest data requested from UNOS. 1. Patient registration data 2. Patient follow-up data 5.2.1 Patient Registration Data This data is provided as a SAS cport file. A cport file is a sequential file containing one or more data sets or catalogs in SAS form at. "Transport format" is a format understood by all versions of SAS in all systems. The data cont ains waiting list / transplant files. UNOS Standard Transplant Analysis and Res earch (STAR) files for liver registrations and transplants were obtained. The transpla nt STAR file from UNOS


42 contains information on all waiting list regist rations and transplants of livers that have been listed or performed in the U.S. and reported to the OPTN since October 1, 1987. The data includes both deceased and living-donor transplants. There is one record per waiting list registration/transplant event. E ach record includes the most recent follow-up information (including patient and graft survival ) reported to the OPTN as of June 2006. The patient information dataset consists of 142,873 records and 418 variables. These variables are further classified into post tran splant clinical information, pre-transplant clinical Information, candidate information, donor information, waiting list data, etc. 5.2.2 Patient Follow-Up Data The follow-up STAR file contains one record for each pre-transplant measurement. There are multiple records per transplant for most cases. For instance, if a patient was transplanted in January 1998, the graft has not failed, and the patient has not been reported lost to follow-up database, we have many follow-up records with the same transplant identification number i.e. transpla nt id. Follow up records for 6 month, 1 year, 2 year, 3 year, 4 year, 5 year, and 6 year etc can be obtained for each patient. The variable for linking the follow-up data to th e transplant STAR file is TRR_ID. The number of record of patient ranges from one record to more than hundred records per patient based on number of visits or te sts conducted. The patient follow up dataset consists of 675,279 records and 20 variables. Most of the variables are from the waiting list category. 5.3 Statistical Analysis System (SAS)


43 The SAS system is an integrated syst em of software products provided by the SAS Institute that enables programmers to perform data analysis. In this research latest version of SAS 9.1.3 (released on April 2006) li censed to University of South Florida is used. 5.4 Data Patterns and Simulation Model The main objectives of data analysis ar e to understand the system and to obtain the inputs for a discrete-event liver transplantation simulation model. The simulation model is intended to replicate the real life system. Patient’s cumulative distribution can be obtained by using their MELD scores as input from the patient registration dataset. This data was extracted from corresponding SAS dataset by avoidi ng the duplicates and based on the year of focus. Appendix A pr esents the sas program to determine the variables for extraction and the procedure fo r extracting the data. The different outcome categories and configurations based the data input comprise the input for the simulation model that will be described later in the chapter. 5.5 Extraction Procedures and SAS Data Sets The SAS software package was used to extract the data from the database. SAS file is presented in Appendix A an d was used as the master program that aids in identifying the variables needed from each data file. These variables will be described in more detail in the next section. Figure 5. 1 illustrates the complete procedure used in extracting all data in tables.


44 Figure 5.1 SAS Data Extraction Flow Chart The hexagonal blocks represents the processi ng steps, the square blocks represent the data sets and tabulated results. The purpose of the PR OC (Procedural) step is to perform operations on data obtaine d from data step. Finally, the results of the analysis were processed using Excel. The analyzed data serve as input to th e simulation model. The simulation model is a clinically based, discrete event simulati on model of ESLD in the United States. The model is used for policy evaluation. It used input clinical data obt ained from the analysis. The model is used to generate outcomes. The outcomes are evalua ted based on expert’s opinion to obtain the weights of the evaluation criteria. Imp acts on changes in policy to various outcomes can be m easured in this model. 5.5.1 Organ Procurement Organizations (OPO) Each OPO considered is classified eith er as a transplant OPO or a donor OPO depending on its functionality. For this resear ch it is necessary to fix the number of transplant and donor OPOs. We obtained all the distinct OP Os in use at any given time starting from its inception. We are able to identify 87 donor OPOs and 57 transplant OPOs. These are the variables that we obtained from the dataset:


45 CTR_OPO --Transplant OPO. OPO_CTR -Donor OPO. The dataset obtained is di splayed in appendix B. 5.5.2 Regions and Transplant OPOs The entire UNOS is divided into 11 re gions for geographi cal allocation and administrative purposes. Each OPO belongs to certain region based on the proximity. Each region consists of multiple OPOs. It is necessary to find the regional allocation of OPOs for all the identified transplant and donor OPOs. This information will be used to evaluate regional equity. We classified th e two major categories of OPOs to their respectable regions. Variables used from the dataset Region – Region which an OPO belongs to. CTR_OPO --Transplant OPO. OPO_CTR -Donor OPO. We are able to classify all OPOs into different regions base d on the analysis and the result will be obtained from appendix C. 5.5.3 Discrete Distributions This analysis provides the patient arrival rate for the simulation model. We fixed the number of transplant OPOs as 57 for th e research purpose. For 142,873 patient’s information which we obtained the patients tran splant OPOs, a discrete distribution based


46 on these OPOs was obtained. There is wide disparity in the number of transplants. Patients from New York and Calif ornia nearly attributes to th e 15% of all the transplants. 5.5.4 Cold Ischemic Time Cold Ischemic time is a major factor that determines the quality of transplant livers. Preservation methods are available for stor ing livers without much deterioration in quality for at least 12 hours [58]. We conducte d this analysis by fi nding the distance between the Donor and Transpla nt OPOs and the cold ischem ic time of patients for that transplant. We sorted the entire database based on the distance between the transplant center and the mean cold ischemic time is extracted. Few transplants have taken place when the donor and transplant OPOs are more than 2500 miles. For close analysis the OPOs are further subdivided to the distan ce of 100 miles for dist ance less than 2500 miles. For distance less than 500 miles we furt her divided the distance into sub categories of 50 miles. A normal distribution was fitted with 95% confidence interval. 5.6 Data Variables and Hierarchy A hierarchy model helps decompose the prob lem in several stages. The aim of the model is to obtain a policy among the alte rnative policy recommendations. How do we test the alternative policies? Alternative polic ies can be tested for efficiency and equity based on certain outcomes of the policy that are obtained from the simulation model. The model generates waiting list times a nd survival rates, graft failure, and retransplant rates under the current UNOS liver allocation strategy, which emphasizes the severity of disease and incorporates the MELD risk score. A set of outcomes for various policies being obtained from the simulation model.


47 The outcomes of the simulation model were reviewed by experts. These Experts include transplant policy makers, physicians, and or focus groups among patients. They suggest the importance of the outcomes. Valu es from the outcomes obtained from the survey can be used to calculate the weights. This will help prioritize the impact of allocation policy and the contribution of each po licy towards efficiency and equity of the model. 5.7 Merge – Registration and Follow-Up Data The main objective of this pa rt of the analysis is to create a library to store the extracted data and create a working data set fr om each of the two distinct data sets. As mentioned above, the database includes two data sets files, the patient registration data and patient follow-up dataset, necessary variab les from each file were chosen from the data sets and finally the files were merged by patient id number (wl_id in the database). Merging was done to obtain the patient file in formation where the necessary variables for analysis were found in two different datasets The was updated in every an alysis. Specific data sets are extracted from the database based on certain paramete rs for example based on year, MELD score, PELD score etc. In order to extract a specific set of data in a tabular format, smaller SAS programs were created. Sample sas program (Sub is presented in Appendix A. This program extracts the patient id, initial and final MELD scores Dates of visit to transplant center etc from the follow up file.


48 CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6.1 Concluding Remarks In this research we studied efficiency and equity, two major conflicting factors of the United States liver transplantation. This research aims to find a policy which balances efficiency and equity of current liver tran splantation. The probl em was modeled using Analytic Hierarchy Process. This research classifies the outcomes of liver transplantation into two major criteria: efficiency and equity. The majority of the attributes contributing towards these criteria have been identified Some of the attributes whic h contribute to efficiency are average MELD score, length of wait time, a nd patient rankings. Major attributes that contributed toward equity included geogr aphical location, race and gender. The AHP approach helps quantify the decision making process to build logics into a complex decision evaluation process that involves policy selection. The proposed model is capable of obtaining the weights of these defined attrib utes with the goal of establishing the major criteria regarding efficiency and equity. Results from our data analysis that used the latest UNOS data serve as inputs for a simulation model. The simulation model is cap able of evaluating different strategies for liver allocation; the resulting outcomes can be quantified for decision making purposed using the proposed model. The AHP me thodology helps decision makers reach a


49 consensus in a quantifiable method whereas pr evious methods heavily rely on intuition. This research studies the deficiencies of the current liver transplantation policy and proposes alternative strategies that may help policy makers search for a better policy to balance efficiency and equity. Measuremen t of alternativ e policies can be done using the simulation model. The proposed model is flexible enough to accept future changes in the U.S. liver transplantation policy. 6.2 Future Extensions Some of the extensions that can be made for this research are: 1. Selection of proposed policy ca n be done through AHP model. 2. Different perspectives (policy makers or patients) towards the allocation policies can be studied. 3. The optimality criterion can be included for future research.


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56Appendix A: Statistical An alytics Systems Program /* Initializing the CPORT File and Data Extraction*/ libname lib "C:\Documents and Settings\vveerach\Desktop\SAS\newdata" ; /* where you want the new data to go */ Filename tranfile 'C:\Documents and Settings\vveerach\Desktop\newdata\LIVER_PUBLIC_USE_WLHIST_CPORT_FILE' ; /* Where the transport file is stored now */ proc cimport library=lib infile =tranfile; run ; options fmtsearch = (newlib) /* this will enable SAS to find the formats in the catalog*/ libname lib "C:\Documents and Settings\vveerach\Desktop\SAS\newdata" ; /*Extracting the value coloumns from the table*/ proc sql ; create table anew as select x.WL_ID, x.ASCITES_DATE, x.MELD_PELD_LAB_SCORE from lib.Liver_wlhistory_data x; run ; proc sql ; create table meldnew as select distinct WL_ID,Date, meld_peld_lab_score, MELD_OR_PELD from Anew where meld_peld_lab_score and date is not missing; group by wl_id; run ; proc sort data =Anew; by WL_ID ASCITES_DATE; run ; data meld_prog_date; set Anew; by wl_id; retain dt 1 ; if first.wl_id then do ; days= 0 ; dt =ASCITES_DATE ; end ; else do ; days = ASCITES_DATE dt; end ; drop dt; where wl_id and ascites_date is not missing and meld_or_peld = 'MELD' ;


57Appendix A: (Continued) drop meld_or_peld; run ; proc print ; run ; proc sort data =meld_prog_date out =meld_prog_date_norepli nodupkey; by wl_id ascites_date; run ; data MELD_Progression; set d3; drop ASCITES_DATE; drop meld_or_peld; run ; proc freq data =d3; by wl_id; run ; /*New Programs*/ data newtab; set Anew; by wl_id; do ; days = ASCITES_DATE MDY( 01 01 1999 ); end ; drop dt; where wl_id and ascites_date is not missing; run ; proc print ; run ; data newtab_final; set newtab; where days >= 0 and _SCORE>= 6 ; run ; proc sort data =newtab_final out =result2 nodupkey; by wl_id ascites_date; run ; proc contents data =a.a; run ; proc sql ;


58Appendix A: (Continued) create table result3 as select WL_ID, Days, meld_peld_lab_score from result2; run ; /*Remove Missing*/ proc sql ; create table newtable as select distinct WL_ID,ASCITES_DATE, MELD_PELD_LAB_SCORE from Anew where ASCITES_DATE and MELD_PELD_LAB_SCORE is not missing; run ; data newtable1; set newtable; where ascites_date le mdy( 1 1 2003 ); run ; /*No Missing*/ proc sort data =newtable1 out =Followup_2003; by descending ascites_date; run ; proc sort data =followup_2003 nodupkey; by wl_id; run ; proc sql ; create table new as select distinct WL_ID,ASCITES_DATE, MELD_PELD_LAB_SCORE from Anew where ASCITES_DATE and MELD_PELD_LAB_SCORE is not missing; run ; data new1; set new; where ascites_date le mdy( 1 1 2002 ); run ; /*No Missing*/ proc sort data =new1 out =Followup_2002; by descending ascites_date; run ; proc sort data =followup_2002 nodupkey;


59Appendix A: (Continued) by wl_id; run ; /*Coverting days from January 2002 to number of days*/ data newtab; set followup_2002; do ; days = ASCITES_DATE MDY( 01 01 2002 ); end ; run ; proc sql ; create table finalfinal as select WL_ID, Days, meld_peld_lab_score from newtab; run ; /*Start New 2002 2003 2004 2005 */ data new1; set new; where ascites_date le mdy( 1 1 2003 ); run ; /*No Missing*/ proc sort data =new1 out =Followup_2003; by descending ascites_date; run ; proc sort data =followup_2003 nodupkey; by wl_id; run ; data newtab2003; set followup_2003; do ; days = ASCITES_DATE MDY( 01 01 2002 ); end ; run ; proc sql ; create table final_followup_2003 as select WL_ID, Days, meld_peld_lab_score from newtab2003; run ; data new1; set new; where ascites_date le mdy( 1 1 2004 ); run ;


60Appendix A: (Continued) /*Sorting and Ascending by removing the duplicates Missing*/ proc sort data =new1 out =Followup_2004; by descending ascites_date; run ; proc sort data =followup_2004 nodupkey; by wl_id; run ; data newtab2004; set followup_2004; do ; days = ASCITES_DATE MDY( 01 01 2002 ); end ; run ; proc sql ; create table final_followup_2004 as select WL_ID, Days, meld_peld_lab_score from newtab2004; run ; data new1; set new; where ascites_date le mdy( 1 1 2005 ); run ; /*No Missing*/ proc sort data =new1 out =Followup_2005; by descending ascites_date; run ; proc sort data =followup_2005 nodupkey; by wl_id; run ; data newtab2005; set followup_2005; do ; days = ASCITES_DATE MDY( 01 01 2002 ); end ; run ;


61Appendix A: (Continued) proc sql ; create table final_followup_2005 as select WL_ID, Days, meld_peld_lab_score from newtab2005; run ; /*Meld And PELD SCORE*/ data End2002; set Final_followup_2002; where MELD_PELD_LAB_SCORE>= 6 ; run ; data End2003; set Final_followup_2003; where MELD_PELD_LAB_SCORE>= 6 ; run ; data End2004; set Final_followup_2004; where MELD_PELD_LAB_SCORE>= 6 ; run ; data End2005; set Final_followup_2005; where MELD_PELD_LAB_SCORE>= 6 ; run ; /*CHANGE IN MONDAY*/ Data FINAL_FOLLOW_UP; set followup_all; by wl_id; do ; days = ASCITES_DATE MDY( 01 01 2002 ); end ; drop dt; where wl_id and ascites_date is not missing; retain ascites_date; run ; proc sql ; create table final_all_all as select WL_ID, Days, meld_peld_lab_score from final_follow_up; run ; data final_all; set final_all_all; where days > 0 ; run ;


62Appendix A: (Continued) proc sort data =final_all nodupkey; by wl_id days; run ; PROC SORT DATA =a.Final_2003; BY wl_id; PROC SORT DATA =a.Final_followup_2003; BY wl_id; DATA widedata; MERGE a.final_2003 a.Final_followup_2003; BY wl_id; RUN ; /*Merging the data sets from Patient Registration and patient follow up database*/ data three; merge a.Final_2003( in =fromdadx) a.Final_followup_2003( in =fromfamx); by wl_id; fromdad = fromdadx; fromfam = fromfamx; if fromdad= 1 and fromfam= 1 ; run ; PROC FREQ DATA =three; TABLES fromdad*fromfam; where fromdad= 1 and fromfam= 1 ; RUN ;




64 Appendix B: Donor and Transplant OPO Table B.1 (Continued) No Transplant OPO Donor OPO 45 TNDS-OP1 NVLV-OP1 46 TNMS-OP1 NYAP-OP1 47 TXGC-OP1 NYFL-IO1 48 TXSA-OP1 NYRC-OP1 49 TXSB-OP1 NYRT-OP1 50 UTOP-OP1 NYSB-IO1 52 VAOP-OP1 OHLB-OP1 53 VATB-OP1 OHLC-OP1 54 WALC-OP1 OHLP-OP1 55 WANW-OP1 OHMV-IO1 56 WISE-IO1 OHOV-OP1 57 WIUW-IO1 OKHM-IO1 58 OKOP-OP1 59 ORUO-IO1 60 PADV-OP1 61 PATF-OP1 62 PRLL-OP1 63 SCOP-OP1 64 TNDS-OP1 65 TNET-OP1 66 TNMS-OP1 67 TXAD-IO1 68 TXBC-IO1 69 TXFW-IO1 70 TXGC-OP1 71 TXLG-IO1 72 TXSA-OP1 73 TXSB-OP1 74 UNKN-OP1 75 UTOP-OP1 76 VAFH-IO1 77 VAOP-OP1 78 VATB-OP1 79 WALC-OP1 80 WANW-OP1 81 WASH-IO1 82 WISE-IO1 83 WISL-IO1 84 WIUW-IO1 85 WVMS-OP1 86 ZCAN-FOP 87 ZFOR-FOP


65 Appendix C: Cold Ischemic Time Vs Distance Table C.1 Analysis for 0 5000 in range of 100 miles Analysis for 0 5000 in range of 100 miles Distance Miles Mean CIT LCL UCL SD Var Range 0 100 8.0399 7.99318 .0874.5655 20.8438 50 100 200 9.2977 9.214 99.38 4.398 19.3424 150 200 300 9.8012 9.68689 .9164.5425 20.6343 250 300 400 10.0359 9.8478 10.225.2455 27.5153 350 400 500 10.1749 9.957 410.394.867 23.6877 450 500 600 10.3177 10.066 10.575.2922 28.0074 550 600 700 10.8373 10.542 11.134.8056 23.0938 650 700 800 11.1372 10.816 11.464.8368 23.3946 750 800 900 10.8209 10.495 11.154.9589 24.5907 850 900 1000 11.9619 11.467 12.465.2669 27.7402 950 1000 1100 10.8845 10.425 11.354.7745 22.7959 1050 1100 1200 11.6717 11.118 12.234.4073 19.4243 1150 1200 1300 11.5631 10.887 12.245.8062 33.712 1250 1300 1400 11.6803 10.831 12.535.2437 27.4964 1350 1400 1500 12.3073 11.746 12.873.9215 15.3782 1450 1500 1600 13.0943 12.239 13.955.6182 31.5642 1550 1600 1700 13.3862 12.533 14.245.2145 27.191 1650 1700 1800 13.096 12.307 13.893.8089 14.5077 1750 1800 1900 15.0422 14.351 15.735.2262 27.3132 1850 1900 2000 15.5607 14.48 316.635.563 30.947 1950 2000 2100 14.1942 13.371 15.025.2225 27.2745 2050 2100 2200 13.9505 12.719 15.186.2371 38.9014 2150 2200 2300 13.2455 12.156 14.344.5704 20.8886 2250 23002400 14.3079 11.91 16.714.9756 24.7566 2350 2400 2500 8.775 2.6667 14.883.8387 14.7356 2450 Only 14 readings for distance between t he transplant centers greater than 2500. Analysis for 0 500 miles in range of 50 miles Distance Miles Mean LCL UCL SD Var Range 0 50 7.7897 7.73517 .8444.6128 21.2779 25 50 100 8.7992 8.71198 .8874.3447 18.8764 75 100 150 9.247 9.13589 .3584.3716 19.1109 125 150 200 9.4103 9.293 9.5284.4444 19.7527 175 200 250 9.6498 9.506 79.7934.434 19.6604 225 250 300 9.96 9.7771 10.144.6427 21.5547 275 300 350 9.7486 9.498 9.9995.2697 27.7697 325 350 400 10.3845 10.107 10.665.2251 27.3017 375 400 450 10.262 9.9587 10.574.9757 24.7576 425 450 500 10.0516 9.7451 10.364.7187 22.2661 475


66 Appendix C: (Continued) Table C.2 ANOVA Table for Patients Arrivals SUMMARY OUTPUT Regression Statistics Multiple R 0.8874623 R Square 0.7875894 Adjusted R Square 0.761038 Standard Error 0.3801294 Observations 10 ANOVA Df SS MS F Significance F Regression 1 4.2862407 4.28624 29.6629 0.000611 Residual 8 1.1559871 0.1445 Total 9 5.442227 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 8.39059 0.24132 34.769 5. 1E-10 7.83410 8.947 0 7.83410 8.9470 X Variable 1 0.00455 0.00083 5.44637 0.00061 0.00262 0.006 4 0.00262 0.0064 Figure C.1 Arrival of MELD Patients / OPO Arrival Candidates/ MELD Score /OPO 0 5 10 15 20 25 30 35 40 147101316192225283134 MELD ScorePatients Transplant Candidate / MELD Score


67 Appendix C: (Continued) Table C.3 ANOVA for Distance vs. CIT SUMMARY OUTPUT Regression Statistics Multiple R 0.7255 R Square 0.5263 Adjusted R Square 0.5057 Standard Error 1.3935 Observations 25 ANOVA Df SS MS F Significance F Regression 1 49.627 49.627 25.56 4.066E-05 Residual 23 44.662 1.9418 Total 24 94.289 Coefficients Standard Error t Stat Pvalue Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 9.3651 0.5577 16.791 2E-14 8.2113027 10.51882 8.211303 10.51882 X Variable 1 0.002 0.0004 5.0554 4E05 0.0011543 0.002753 0.001154 0.002753 Figure C.2 Distance vs. CIT 100 miles Distance by CIT 0 5 10 15 20 050010001500200025003000 Distance in MilesCIT Hours Distance by CIT