August 1998
Organ transplantation allocation policy analysisBy A. Alan B. Pritsker
Replacement of human organs has evolved over the last 30 years into a successful life-saving medical technology [4]. My objective in writing this article is to provide information about the policy implications of organ transplantation, specifically liver transplantation. The scarcity of liver organs for transplantation has reached critical levels in the United States; 1,131 patients died in 1997 while waiting for a transplant.
During the past three years, I have been directing a project that involves building and using a large-scale simulation model to evaluate policies for distributing and allocating recovered livers to terminally ill liver patients, that is, individuals who will die without receiving a transplant. Throughout the country, organ procurement is performed by 63 organizations (OPOs), and transplants are performed at 106 transplant centers. The OPOs and transplant centers are organized into 11 regions.
Approximately 4,000 liver donations were made in the United States in both 1996 and 1997. As of March 1998, about 10,000 individuals were on the waiting list for a liver transplant and another 8,000 new patients are expected to be added to the list this year.
In addition, the spread of hepatitis C is reaching epidemic levels and liver transplantation is currently the only complete treatment for it. Clearly, a donated liver is a scarce resource and the allocation of livers is a difficult problem involving a decision that will determine who will live and who will die. This decision needs to be made in an objective manner that uses all available information and considers all possible outcomes.
United Network for Organ Sharing (UNOS)
UNOS was founded in 1986 and is the organization responsible for the nationwide operational system for maintaining patient waiting lists and for running the program that implements the policy for allocating donated organs to waiting patients. UNOS is a not-for-profit organization that uses volunteers from the transplantation community for its Board of Directors, officers and voting committee members. The UNOS staff collects data, performs research, publishes reports and, in general, supports the transplantation community with the goal of providing the best possible service and healthcare to patients requiring transplants. A national system for collecting and publishing transplantation data called the Organ Procurement Transplantation Network (OPTN) was established by Congress. OPTN is funded through the Department of Health and Human Services (DHHS) which has contracted with UNOS to perform the OPTN project.
In 1995, UNOS contracted with Pritsker Corporation to develop a procedure for comparing proposed alternative liver allocation policies. The program that was developed is referred to as the UNOS Liver Allocation Model or ULAM [5].
Recent Policy-Setting Activities
Throughout 1995 and 1996, new liver allocation policies were debated by members of the transplantation community; primarily in UNOS committees. In 1997, the UNOS Board of Directors adopted a new liver policy that rejected the sickest-patient-first approach while creating new status definitions for patients. These actions apparently triggered a political reaction that currently involves the executive and legislative branches of the U.S. government. It is common to see articles in newspapers such as the New York Times and Washington Post and to see television programs such as NIGHTLINE present issues concerning organ transplantation policy crafting and setting. DHHS held hearings in December of 1996 and issued a new regulation on April 2, 1998 that would regulate organ transplantation policy (see "Policy Comparisons Using ULAM" section). The regulation was published in the Federal Register as OPTN: Final Rule [1]. Congressional hearings were held on June 18 to discuss and analyze the Final Rule.
After a review of ULAM, a comparison of the current policy and a policy consistent with the Final Rule will be given based on ULAM outputs.
Overview of ULAM
ULAM was developed within the AweSim simulation environment using the Visual SLAM simulation language [7]. A general flowchart of the model is shown in Figure 1. Modular modeling techniques are used to allow component models or submodels to be inserted as new data is collected and as new component models are developed. Starting on the left of Figure 1, we see that the arrivals to the system are donors and patients. Either historical or generated streams of arrivals can be processed with ULAM. Historical information was available from 1990-1995, and this data is stored within ULAM. Non-homogeneous Poisson processes (NHPPs) were used to characterize the arrival streams of donors to 63 OPOs and of patients to 106 Liver Transplant Centers. (For details of the procedure, see [3].) The characteristics of each donor are determined using a bootstrapping technique which randomly selects the characteristics of a generated donor from all donors in the 1990-1995 time frame. The characteristics of a donor include: age, weight, race, sex and blood type. A similar bootstrapping approach is employed for new patient arrivals.
Figure 1. Overview of ULAM
ULAM includes snapshots of the actual waiting lists of patients, which existed at the beginning of each year. Sampling from the arrival process described above simulates patient arrivals to a transplant center. Each patient is assigned characteristics and added to the waiting list.
One of the characteristics is a medical status which is coded as 1, 2A, 2B or 3. Status 3 is the least critically-ill patient. They require a Child-Turcotte-Pugh (CTP) score of 7 or above. The CTP score is based on clinical measurements. Status 2B requires a CTP score above 10 or a decompensating event; Status 2A requires a score of 10 or greater and a decompensating event. Status 1 is for an acute patient who needs a liver immediately (overdose of Tylenol or niacin, etc.); or a transplanted patient whose graft has failed within seven days of being transplanted; or a Status 2A patient that is less than 18 years of age.
A patient is transplanted and taken off the waiting list when a recovered liver is offered and accepted for that patient. An allocation policy organizes the patients waiting in accordance with the policy to be evaluated. This requires candidate lists of patients to be created based on the patient's medical status, and the location of OPOs, transplant centers and donor hospitals. Patients on a candidate list are prioritized in accordance with point-ranking schemes of the policy being evaluated. Points are typically assigned based on a patient's medical status, waiting time and blood type compatibility with the donor. For some policies, waiting time points are based on the time in a status. In addition, points may be assigned based on distance from the donor hospital, and on the density of population surrounding the donor hospital.
Continuing with Figure 1, a recovered liver has a quality characteristic which is assigned probabilistically based on historical data. The recovered liver is then offered to the patient in the first candidate subset that is ranked highest by the allocation policy if there is compatibility between the donor's and recipient's blood types, and liver weight and volume requirements. ULAM includes a Monte Carlo procedure for acceptance of an offered liver, where the probability of acceptance is a function of the medical status of the patient, the transplant center, and the quality of the liver offered. If the liver is not accepted, then the next highest ranking patient is offered the liver. This continues until the liver is accepted or all patients in all subsets have been considered. If the liver is not accepted by any patient, it is assumed to be used for research or other medical purposes.
When a patient accepts the liver, the patient is transplanted and removed from the waiting list. The future status of the transplanted patient is then determined. First, it is determined whether the graft will fail and the patient will relist based on historical outcomes of patients with similar characteristics. Patients are relisted at the transplant center that performed their transplant operation. Time-to-relist functions have been developed for each medical status using the Kaplan-Meier technique [2]. The relist data was derived from the 1991-95 time period which allowed a three-year follow-up period to determine if a patient was relisted. If not relisted, the patient's mortality following the transplant is determined based on (a) transplant center volume (larger centers have lower mortality rates); (b) patient condition as reflected by the patient's medical status; and (c) whether the patient had a previous transplant.
To model a patient's status change, a transition probability matrix, that is, a Markov chain, is constructed which models the probability of a change from one status to another in one day. The transition probabilities are estimated from a count of the number of times a patient made a transition in one day from one status to another divided by the total number of daily transitions from the particular status.
Verification, validation and acceptance
The verification and validation of ULAM has been reported elsewhere [5]; only a brief synopsis of verification and validation is given here. Verification involved a comparison of the ordered list of patients from match runs prepared by UNOS operations with the ordered list prepared by ULAM. Animations were then used to check the routing and disposition of patients. Figure 2 is a snapshot of the animation screen showing the delivery of livers from the hospital of the donor to the transplant center of the patient. The color of the livers and patients indicate their blood types. Also shown on the animation are the total distance traveled by all livers and the current simulated time. A second animation, Figure 3, shows the transitions from Status 3 to other statuses and the number of patients waiting in each status segregated by status at registration (Status 3 or other). Also shown are the current simulated time and the number of transplants, pre-transplant deaths and patients on the waiting list at the current time. These animations were useful in illustrating the operation of ULAM as well as verifying ULAM's operations.
Figure 2. Animation of Liver Allocation
Figure 3. Animation of Transitions of Status 3 Patients
For validation, each component model output as well as the total system model output was compared to actual results over the 1992-94 time period. The validation runs produced results that were sufficiently close to actual results that a comparison of policies based on ULAM was deemed to be appropriate [5].
To gain acceptance from the transplantation community, I talked with many individuals and presented ULAM to a wide cross section of the transplantation community including the following UNOS committees: Allocation Modeling Oversight, Liver and Intestinal Organ Transplantation, Scientific Advisory, and Allocation Advisory. Throughout this period, suggestions and guidance were sought which resulted in changes and modifications. Additional runs were made to promote understanding and to improve ULAM.
Presentations were then made to the DHHS' Division of Organ Transplantation Oversight Committee and the UNOS Board of Directors. I also took a personal interest in the transplantation system by interacting with the operational center of UNOS where patient-donor matching is performed. I visited transplant centers where I watched a liver being transplanted and talked to patients who had just received new livers. I visited an OPO and gave a lecture on the use of modeling and simulation to assess policies. Although these are time-consuming activities, acceptance and auditing are important steps toward achieving implementation of model-based recommendations [9]. When involved in these activities, I discovered several friends who had transplantation experiences. I relate a few of these here to illustrate the widespread nature of the transplantation process.
During a discussion of processes for enhancing performance in complex systems with Tom Starr, a Xerox executive, I mentioned my transplantation work and Tom informed me that he had had a liver transplant in 1987. Tom's transplant surgeon, Dr. Ron Busittil of UCLA, is currently a member of the UNOS Liver Committee and has taken a keen interest in the use of modeling and simulation as a vital tool in evaluating proposed organ allocation policies. Dr. Busittil testified at the congressional hearings on organ transplantation in June 1998.
At a Winter Simulation Conference speakers' breakfast, Dr. Phil Heidelberger, a well-known operations researcher at IBM, told me that his mother received a liver transplant at the University of Wisconsin Hospital in Madison by Dr. Munci Kalayoglu in 1986. She was 65 when transplanted and continues to lead an active life.
At UNOS, the director of Patient Affairs is Bill Lawrence who received a liver transplant at the Johns Hopkins University Hospital in 1988 with Dr. Andrew Klein as his transplant surgeon. Dr. Klein is actively involved in the modeling effort and has provided guidance in evaluating proposed policies and performance measures.
My most emotionally moving experience occurred recently when Dr. Gary Hogg of Arizona State University came up to me and said, "Alan, you helped me with the most difficult decision of my life. I heard your talk on transplantation and discussed it with my wife, Judy. We both decided we would want to be donors. Two weeks later Judy was killed in a skiing accident. The most important aspect of donation for our family was that Judy, in death, could provide an extension of the meaningful and productive life of other individuals."
My discussions with these individuals brought home the life and death aspects of transplantation and made me a more dedicated researcher who could understand more fully the contribution of the modeling and analysis work I was doing.
Performance measures
In parallel with the modeling effort, a subcommittee of the Liver Committee was established to select performance measures, which could be used to balance equity and utility when selecting a policy. The project team, based on UNOS Principles for Organ Allocation [8], developed a categorization of performance measures according to utility and equity as viewed from medical, patient and system perspectives. The categorization of performance measures is presented in Table 1; this was a major step toward understanding and evaluating policies. The performance measure subcommittee selected the following subset of these measures as the most important for comparing policies: MU1, MU2, MU6, PU1, PU2, ME2, SU1, SE2, PE3 and SE3.
| Listing of Potential Liver Allocation and Distribution Performance Measures | |||
| Medical Utility Measures | |||
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MU1 | Total (nonrepeated) transplants | |
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MU2 | Total deaths | |
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MU2.1 | Pre-transplant deaths |
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MU2.2 | Post-transplant deaths |
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MU3 | Total patients removed for other reasons | |
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MU4 | Percent of transplanted patients that survive | |
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MU5 | Total patients relisted | |
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MU6 | Number of life-years | |
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MU7 | Number of quality life-years | |
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MU8 | Size of the end waiting list | |
| Patient Utility Measures | |||
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PU1 | Probability of receiving a transplant | |
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PU2 | Probability of dying on the waiting list | |
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PU3 | Patient transitions from status at registration to other medical statuses | |
| System Utility Measures | |||
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SU1 | Distance organs travel | |
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SU2 | Size of the end waiting list | |
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SU3 | Total costs of transplantation | |
| Medical Equity Measures | |||
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ME1 | Total (nonrepeated) transplants | |
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ME2 | Differences in percent of status types transplanted | |
| Patient Equity Measures | |||
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PE1 | Differences in the probability of receiving a transplant | |
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PE2 | Differences in the probability of dying on the waiting list | |
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PE3 | Differences in waiting time measures | |
| System Equity Measures | |||
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SE1 | Impacts on geographic areas or individual centers | |
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SE2 | Local use of organs and its impact on organ donation | |
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SE3 | Differentials in size of waiting lists | |
Table 1
Policy Comparisons Using ULAM
ULAM was used extensively during 1996 to compare over 100 liver allocation policies [6]. In 1998, ULAM was updated with the most recent historical data collected by UNOS, and ULAM was used to compare the current policy put into place in 1997 (CP97) with a policy that is consistent with the DHHS Final Rule [1]. CP97 distributes livers to patients in local, regional and then national areas. In each area, the patients in the sickest status group are considered first. These patients are then ranked based on points assigned to waiting time and blood type compatibility. If the recovered liver is not allocated, the next sickest group of patients is then considered and so on. In contrast to CP97, the Final Rule sets forth the principles for the operation of the Organ Procurement and Transplantation Network (OPTN). One of the principles underlying the Final Rule is the following [1, p16288]: "Organs should be equitably allocated to all patients, giving priority to those patients in most urgent medical need of transplantation, in accordance with sound medical judgment." Note that this principle includes both a policy statement and an operational condition and this has caused much confusion regarding the intent of the principle.
Another principle underlying the regulation is [1, p16288]: "Transplant patients are best served by an allocation system that functions equitably on a nationwide basis." The preamble to the Final Rule also states that geographical boundaries should not determine who will be offered a transplant. These statements lead to the consideration of a single national list as an appropriate distribution procedure to be considered under the Final Rule regulation.
The Final Rule states that policies to be evaluated should be developed by the OPTN in conjunction with individuals in the transplantation community. A policy based on the above statements from the Final Rule is a Sickest Patient First allocation procedure using the entire national list of patients as the potential recipients of each recovered liver. This policy is referred to as SPF-Nat. Tables 2 through 5 provide a brief summary of some of the performance measure outputs from ULAM for the CP97 and SPF-Nat policies. (As a modeling note, in addition to summary and detailed reports, ULAM prepares a list of the disposition of each arriving patient.)
The outputs to be presented are based on 10, eight-year runs (1996-2003) with the first year's statistics cleared because outcomes for the first year reflect the prior policy and not the policies being evaluated. For example, the content of the waiting list is a function of the policy in use and it will take a period of time to clear out the effects of a previous policy before the actual impact of the new policy can be determined.
From Table 2, it is estimated that 25,024 different patients would be transplanted under CP97 and 23,515 different patients using SPF-Nat. This increase of 1,509 more transplanted patients occurs because SPF-Nat transplants sicker patients who have a higher chance of relisting and requiring another recovered liver. Also, the retransplanted patients tend to be sicker, have a lower survivability and require additional transplants.
| General Measures of Performance | |||||||||||||||||||||||||||||||||
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Table 2
Quantitatively, for the CP97 policy, it is expected that 2,414 more patients would survive for more than three years and the estimated percent who survive for 12 and 36 months are significantly higher. These higher survivability percentages occur because the CP97 transplants a mixture of patients some of whom are not the sickest. The estimates from ULAM for the percent transplants by Status 1, 2A, 2B and 3 for the CP97 policy are 6.7, 22.1, 48.0 and 23.2, respectively, and 18.1, 59.3, 22.2 and 0.3 for the SPF-Nat policy. (From these estimates, it is seen that only 22.5 percent of transplants under the SPF-Nat policy are to the two least-sick statuses. This indicates that patients in these statuses are required to transition to the sickest statuses to receive a transplant. On the first run of the set of 10, the number of transplants in Status 2A for CP97 was 6,083 and for SPF-Nat was 16,599, of which 8,916 originally registered as Status 3 but had to transition to Status 2A to be transplanted.
With regard to estimates for the sharing of livers across the country, CP97 uses approximately 84 percent of the livers in local areas and 13 percent in the region of the donor, whereas the SPF-Nat policy uses more than 89 percent outside the donor's region. The following statistics were estimated from ULAM for miles traveled by a recovered liver. For the CP97, the median distance was 71 miles, the average distance was 157 miles, with 2 percent of the distances greater than 1,000 miles. For the SPF-Nat policy, the corresponding values are 930, 1,099 and 46 percent. Distance is a surrogate measure for both cold ischemic time (the time an organ is not supplied with blood which can degrade the quality of the organ) and organ recovery cost.
Table 3 provides estimates of the total deaths during the 1997-2003 simulation period. It is estimated for CP97 that 1,032 more deaths (17,237 minus 16,205) occur while patients are waiting. (Inactive status is temporarily not available to be transplanted.) For CP97, it is estimated that there will be 1,626 fewer post-transplant deaths (7,495 minus 5,869). Thus, the SPF-Nat policy has an estimated total number of deaths that is 594 more than the CP97 policy (1,626 vs. 1,032).
| Performance Measures Related to Deaths | |||||||||||||||||||||||||||
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Table 3
Figure 4 graphically depicts the number of deaths for each policy over time for a single run of ULAM. The plot for waiting list deaths illustrates that there is a greater increase in waiting list deaths over time for the SPF-Nat policy as compared to CP97. This occurs because the waiting list for the SPF-Nat policy increases at a higher rate as more transplanted patients relist. The estimated number of patients on the waiting list on Dec. 31, 2003 and the number who relisted during the simulation are 18,108 and 4,772 for CP97 and 20,103 and 5,557 for the SPF-Nat policy.
Figure 4. Number of Deaths, 1997 - 2003
The estimated median days from registration to transplant for those patients transplanted by a patient's status at transplant is shown in Table 4. (Other median waiting times were computed for incomplete cohort groups using Kaplan-Meier procedures.) With the SPF-Nat policy, half of the sickest patients are transplanted on the day that they register whereas the median for CP97 is 3.7 days. For all other status categories the median days to transplantation is smaller for CP97. An explanation for these median values is that few (0.3 percent) of Status 3 patients are expected to be transplanted in Status 3 under a SPF-Nat policy. Thus, they will wait longer to be transplanted (i.e., the patients must wait until they are the sickest on a national list.) Since there are not many transitions to Status 1 from the other statuses, Status 1 median times remain small.
| Median Waiting Days from Registration to Transplant for Transplanted Patients | |||||||||||||||||||||||||||
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Table 4
Table 5 presents the estimated years of life for the two policies. The patient life-years are categorized according to time spent on the waiting list and time spent after being transplanted. Since information is available in the simulation as to the final disposition of the patients, the patient life-years are further classified by active and inactive status on the waiting list and by relist, death and survival after a transplant. As can be seen from Table 5, CP97 provides 10,267 more patient life-years than the SPF-Nat policy. Of significance is that CP97 provides 20,314 more life-years in the highest quality-of-life category, that is, post transplant survival.
| Patient Life-Years on the Waiting List, Post Transplant and Total | |||||||||||||||||||||||||||||||||||||||
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Table 5
Based on these projected results and other medically based information, the UNOS Liver and Intestine Organ Committee overwhelmingly (18 for, 0 against, 2 abstentions) passed a resolution in May to not consider the SPF-Nat policy further. The measures of performance for the Current Policy (CP97) are good. However, the distribution of recovered livers to predefined local and regional areas first is not in direct compliance with DHHS' Final Rule. ULAM is currently being used by an ad hoc committee of the Liver Committee to search for a policy with the best performance. At Congressional Hearings held on June 18, Dr. L. Hunsicker, president of UNOS, and I testified and submitted the comparative results presented in this paper for the congressional record. At these hearings, DHSS Secretary Donna Shalala testified that a sickest-patient-first allocation method and a single national list distribution procedure were not required by the Final Rule regulation.
Exciting Opportunities
This organ transplantation project illustrates how policy crafting involves broader issues with complex implications impacting diverse groups [6]. The future application of simulation in supporting policy-setting is highly dependent upon how modeling and simulation programs can foster meaningful executive communication and systematic understanding of the issues being considered. We were able to achieve these capabilities by adhering to the following four guidelines:
- Historical data is the base for component models;
- Data and models for policy analysis are kept up to date;
- Important operational procedures are imbedded in the program; and
- Continual communication and technical interaction with policy-crafters and decision-makers provided a means to achieve policy implementation based on model outputs.
| Congress Enters National Transplant Debate |
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Given that transplantable organs are a scarce resource, and that the number of patients on waiting lists for the life-giving organs far exceeds the supply, who should go to the front of the line? And how should the order of patients be determined?
Under the current system, organs are first offered locally, then regionally, then nationally. Waiting times vary widely because the number of patients and the number of available organs differs from area to area. Patients in some regions wait five times as long for a liver transplant as those in other regions. And that's not fair, says Health and Human Services Secretary Donna Shalala, whose department is exploring alternative allocation procedures, including a new program that will give the scarce organs to the sickest patients first, regardless of where they live. But hold on. If the goal of any transplant network is to save and prolong as many lives as possible, the HHS's idea may be counterproductive. If only the sickest people get organs, people could not get transplants until they were very sick, and more people would ultimately die because the sickest persons are the least likely to survive transplants. Complicating the matter even further is the reaction of certain states and transplant centers across the country who fear their constituents will suffer under the proposed changes. For example, some states such as Florida have worked hard to increase donations. Will the state continue its efforts if most of the organs are shipped out of state? Many transplant centers are concerned that the new policy will shift organs from their operations to large transplant centers that handle many of the sickest transplant candidates. The issue was given a formal airing in June before a Joint Hearing of the House Committee and Senate Labor and Human Resources Committee. Dr. Lawrence G. Hunsicker, president of the United Network for Organ Sharing, was among those who testified. UNOS is a private contractor to the HHS through the Organ Procurement and Transplantation Network (OPTN) and is charged with developing the nationwide operational system now in effect for maintaining transplant candidate waiting lists. As discussed in the accompanying article, computer-based simulation models have played a pivotal role in helping UNOS evaluate the potential impact of transplant policies on behalf of OPTN. Alan Pritsker, whose company built the sophisticated simulation models for UNOS, accompanied Hunsicker to the hearings to answer questions regarding the model. In his testimony, Hunsicker described Pritkser as "the father of modern computer simulation modeling," adding that Pritsker was given the job because of his "impeccable credentials as well as his objectivity." Hunsicker noted that Pritkser "constructed the UNOS Liver Allocation Model (ULAM) under the guidance of more than 100 members of the transplant community over the past three years and the oversight of an 8-person HHS modeling committee. Since that time, he has worked with the community to model more than 100 different allocation system in our attempt to reach the best allocation system across all measures." Hunsicker concluded by noting that "UNOS' data and predictions have been provided to HHS, including the results predicted by Dr. Pritsker's ULAM model for the allocation policy we believe is described in the Regulation. Many individuals who have reviewed those predictions have arrived at the conclusion that the results would, indeed, be quite adverse for patients. It is for that reason that UNOS has so ardently opposed the kind of allocation policy that we and many others believe is prescribed in the Regulation. In fact, after reviewing these findings, the UNOS Liver Committee voted unanimously against a single national list that transplants the sickest patients first." The new regulation favored by HHS is scheduled to take effect on Oct. 1, unless Congress changes the implementation date or intervenes. While the transplant community and politicians may disagree on an allocation policy, all agree that the country faces a shortage of organ donations. For a free brochure on organ donation, call 1-800-355-SHARE. Peter Horner, editor |
References
1. Federal Register, "Department of Health and Human Services: Organ Procurement and Transplantation Network," Final Rule, Vol. No. 63, p. 16288, April 2, 1998.
2. Kaplan, E. & Meier, P., "Nonparametric Estimation from Incomplete Observations," JASA, Vol. 5, pp. 457-481, 1958.
3. Kuhl, M.F., Wilson, J.R. & Johnson, M.A., "Estimation and Simulation of Nonhomogeneous Poisson Processes having Multiple Periodicities," Proceedings, Winter Simulation Conference, pp. 374-383, 1995.
4. Phillips, M.G., Ed.. "Organ Procurement, Preservation and Distribution in Transplantation," 2nd Ed, UNOS, Richmond, Va., 1996.
5. Pritsker, A.A.B. et al. "Organ Transplantation Policy Evaluation," Proceedings, Winter Simulation Conference, pp. 1314-1323, 1995.
6. Pritsker, A.A.B., Daily, O.P., & Pritsker, K.D., "Using Simulation to Craft National Organ Transplantation Policy," Proceedings, Winter Simulation Conference, pp. 1163-1169, 1996.
7. Pritsker, A.A.B., O'Reilly, J.O., & LaVal, D.K., "Simulation with Visual SLAM and AweSim," John Wiley and Systems Publishing, 1997.
8. UNOS Statement of Principles and Objectives of Equitable Organ Allocation, Seminars in Anesthesia, Vol. 14, pp. 142-166, June 1995.
9. Withers, B.D., et al., "A Structured Definition of the Modeling Process," Proceedings, Winter Simulation Conference, pp. 1109-1117, 1993.
Alan Pritsker has been a member of INFORMS since 1959. He is the past chairman and CEO of Pritsker Corporation and a Distinguished Visiting Professor at Purdue University. Dr. Pritsker has written 12 books on modeling, simulation and industrial engineering and 150 technical papers. In 1985, he was elected to the National Academy of Engineering for development of the basic concepts underlying combined discrete/continuous simulation languages. In 1991, Dr. Pritsker received the Frank and Lillian Gilbreth Award, IIE's highest honor. He received a Doctor of Science, honoris causa, from Arizona State University in May 1992.
| Acknowledgments |
| I thank Dr. Patrick Daily of UNOS for organizing and participating in the ULAM project and for his comments and suggestions on this article. The members of the ULAM project are: Dave Martin, Janet Reust and Mary Grant of Symix Systems, Inc., Pritsker Division; Dr. Erick Edwards, Ann Harper, Sarah Taranto and Dr. Mary D. Ellison of UNOS; Jim Wilson of North Carolina State University and Michael Kuhl of Louisiana State University.
Contributions to the project came from many sources. Dr. Margaret Allen of University of Washington Medical Center was a prime mover and contributor to the modeling liver allocation as president of UNOS. Chairmen of the Liver and Intestine Organ Committee who contributed proposed policies and performance measures were: Dr. Ruud Krom of Mayo Clinic, Dr. John Roberts of the University of California, San Francisco, Drs. James Burdick and Andrew Klein of the Johns Hopkins University, Dr. Bruce Lucas of the University of Kentucky, and Dr. Jerry Turcotte of the University of Michigan. Judy Braslow, past director of the Division of Organ Transplantations, DHHS, provided guidance and direction for the development of ULAM and Dr. Richard Simon, National Institute of Health, performed a detailed review and analysis of ULAM as part of the government Modeling Oversight Committee. Walter Graham and Gene Pierce, executive directors of UNOS, provided guidance and a new allocation policy structure to be evaluated by ULAM. |
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