Should liver transplantation in patients with model for end-stage liver disease scores ≤ 14 be avoided? A decision analysis approach

Authors


  • The content is the responsibility of the authors alone and does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the US Government.

Abstract

Studies have shown that liver transplantation offers no survival benefits to patients with Model for End-Stage Liver Disease (MELD) scores ≤ 14 in comparison with remaining on the waitlist. The consensus of a 2003 transplant community national conference was that a minimum MELD score should be required for placement on the liver waitlist, but no minimum listing national policy was enacted at that time. We developed a Markov microsimulation model to compare results under the present US liver allocation policy with outcomes under a “Rule 14” policy of barring patients with a MELD score of ≤14 from the waitlist or transplantation. For probabilities in the microsimulation model, we used data on all adult patients (≥18 years) listed for or undergoing primary liver transplantation in the United States for chronic liver disease from 1/1/2003 through 12/31/2007 with follow-up until 2/1/2008. The “Rule 14” policy gave a 3% improvement in overall patient survival over the present system at 1, 2, 3, and 4 years and predicted a 13% decrease in overall waitlist time for patients with MELD scores of 15 to 40. Patients with the greatest benefit from a “Rule 14” policy were those with MELD scores of 6 to 10, for whom a 17% survival advantage was predicted from waiting on the list versus undergoing transplantation. Our analysis supports changing the national liver allocation policy to not allow liver transplantation for patients with MELD ≤ 14. Liver Transpl 15:242–254, 2009. © 2009 AASLD.

The Model for End-Stage Liver Disease (MELD) liver allocation system in the United States took effect on February 27, 2002 and has undergone continual review since its adoption. By using 3 laboratory values (international normalized ratio, serum creatinine, and serum bilirubin) to predict the probability of a patient with end-stage liver disease dying in 3 months, MELD scoring provides an objectivity that was previously lacking in liver allocation. Implementation of these 3 measurements was based on extensive statistical analysis, which in 2002 represented a “sea change”1 in how organ allocation policy was developed. Assessment of the proper time for transplantation was formerly accomplished by more subjective means (by evaluation of the degree of encephalopathy and ascites); basing such decisions on mathematical principles began a new approach.

Overall, the MELD system has worked extremely well since its inception,2–6 with occasional changes enacted during its ongoing evolution. There is leeway in the system for the development of various trends and practice patterns. A recent trend is to give a larger proportion of livers to waitlist candidates with higher MELD scores and fewer transplants to those with MELD scores ≤ 14.7 Yet, some centers transplant a high number of patients with low MELD scores. Current media attention has re-opened the issue of a minimum listing score or a minimum transplantation score.8

This topic was on the agenda at a national conference in December 2003, when the liver transplant community gathered to discuss outcomes after the first 18 months under the MELD system.9 A conference working group addressed these questions:

  • 1What is the risk/benefit of transplantation in patients with low MELD scores?
  • 2Should there be a minimum score for listing or transplantation?
  • 3What impact would a minimum score have on events on the waiting list (deaths, removals, or too sick to transplant)?

The general consensus of the conference was that a minimum MELD score of 10 should be required for placement on the waiting list,9 but no national policy was enacted. However, the conference participants also recommended regional sharing for patients with MELD scores ≥ 15 before local allocation to patients with MELD scores ≤ 14, and this was formalized in national liver allocation policy. This change was hoped to raise the minimum MELD score at transplantation.

In 2005, Merion et al.10 provided updated data on survival benefits of transplantation in patients with low MELD scores (addressing question 1 from the 2003 conference). These authors showed that liver transplantation offers no survival benefits to patients with MELD scores ≤ 14 in comparison with waiting on the list at least for the next year. This was confirmed in 2008 by Schaubel et al.11

Should a policy be enacted to disallow transplantation for patients with MELD ≤ 14 except for special circumstances, such as hepatopulmonary syndrome and pulmonary hypertension?12 If such a policy were adopted, what would happen to waiting list events? Would the organs diverted from the patients with lower MELD scores have a significant impact on overall survival of all transplant candidates (from the time on the waiting list through the posttransplant period)? Answers to these questions are needed before such a change can be enacted. Naturally, it is not possible to conduct a randomized controlled trial or large case series study with respect to the waitlist. In debating enactment, a decision analytical model is needed to predict the overall mortality and effects on the waitlist of such a change in policy.

Of the several types of decision analytical models available,13 we desired to construct a model that would accurately analyze the scenario of prohibiting entry onto the waitlist or transplantation of patients with MELD ≤ 14 to determine how this would affect the overall survival of liver waitlist patients from the time of listing until death with or without transplantation. We determined that our model would be based on actual probabilities of the US liver waitlist since 2003. The goal of our study is to provide the transplant community with needed information to facilitate discussion of this important aspect of national liver allocation policy.

Abbreviations

HCC, hepatocellular carcinoma; MELD, Model for End-Stage Liver Disease; SEM, standard error of the mean; STAR, Standard Transplant Analysis and Research; UNOS, United Network for Organ Sharing.

PATIENTS AND METHODS

Choosing and Building an Accurate Decision Analytical Model

Decision analytical modeling is a statistical method for predicting results of critical questions when formal studies, such as randomized controlled trials, cannot be conducted. The basis of this method is to use probabilities of multiple events that can occur to develop the most likely results. This is different from logistic regression or the Cox proportional hazards model, both of which determine the significance of various factors in relationship to one another in predicting the outcome.

From all the decision analytical models available, including simple decision analysis, cost-effective analysis, sensitivity analysis, and Monte Carlo simulation (either probabilistic sensitivity analysis or microsimulation),13, 14 we needed to choose the one that would best meet our needs of answering the complex question of whether liver transplantation should be avoided in patients with MELD scores ≤ 14.

Because we had a diverse patient population to study, we chose to create a microsimulation model.13, 15, 16 A microsimulation model allows thousands of different patients to be run through the model. While progressing through the model, each individual patient generates individual outcomes. Running thousands of different patients through the model gives results that are statistically very stable. In constructing our model, we incorporated state transition modeling, or Markov modeling, to limit the length of the decision tree and to track the various states or conditions of the waitlist population.15, 16

An example of a simple Markov microsimulation model is shown in Fig. 1.13, 16

Figure 1.

Simple example of a Markov microsimulation model. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]

The model asks the following question: “life or death?” This model uses a bootstrap group, which is a representative sample of the entire population of interest.17, 18 One individual is randomly chosen from the bootstrap group to proceed through the model. After passing through the model, this individual is re-entered into the bootstrap group and can be randomly chosen again to proceed through the model. At all times, the bootstrap group represents the population being studied.

All patients start in the initial state, which in our model is “alive” (Fig. 1). The patients then pass through the various transitions and, on the basis of the various probabilities of the transitions, enter other states or return to the initial state. Each cycle (starting in one particular state, passing through a transition, and returning to the same state or a different state) has a time duration that is set according to the probabilities used. For example, the probability of dying in 3 months would be different from the probability of dying in 10 years. There is a final state, which in our model is “death,” (Fig. 1) when all the patients' courses have finished and the model is complete. As patients proceed through the model, they can collect “payoffs,” such as getting older, becoming sicker, and developing tumors, as determined by their characteristics and related probabilities.

The accuracy of the model is dependent on the decision tree structure to account for all the important events or transitions and the probabilities used. Most decision analytical models use probabilities obtained from various published sources. The premise is that the study populations and methods of data collection in published sources are similar to those of the population in question, but the possibility of differences remains a drawback to this method of establishing probabilities.19 However, obtaining probabilities from the literature is better than obtaining expert “guesstimates,” which are used in some studies. The best method of obtaining probabilities is to develop them directly on the basis of a similar population. We chose to develop our probabilities directly from the US liver transplant population.

Validation of the developed model confirms its accuracy. This is unlike logistic regression or Cox proportional hazards modeling, in which a test cohort is used to develop the model parameters and then the model is confirmed on a validation cohort. In decision analysis modeling, when the probabilities are developed from a similar population, the model can be validated. The events predicted by the model can be compared to actual events that occurred in the population from which the probabilities were developed to confirm the accuracy of the model. This is rarely done with analytical models. Before using our model for predictions, we confirmed our model by comparing the model's predicted events to the actual events from the transplant population studied.

After our model was validated, we then ran 2 evaluations. We ran the current liver allocation system for the United States and collected overall survival, posttransplantation survival, and waiting list events. We next ran an evaluation of not allowing patients with MELD scores ≤ 14 to be listed or transplanted. We then compared the 2 sets of “patient histories” with survival curves and standard statistical analysis.

Finally, we conducted a sensitivity analysis of all the event probabilities used in the Markov microsimulation model. This determined what probabilities had the largest influence on the results and what probabilities had no or very little influence on the final results.

Developing Probabilities from the Liver Transplant Population for the Markov Microsimulation Model

After receiving expedited approval by the University of Washington Institutional Review Board, we reviewed data from the Standard Transplant Analysis and Research (STAR) files of the United Network for Organ Sharing (UNOS); these data were based on Organ Procurement and Transplantation Network data as of February 8, 2008. UNOS maintains the STAR files as a registry to prospectively collect pretransplantation, transplantation, and follow-up data on all patients on the transplantation waiting lists in the United States. We used the STAR files to obtain characteristics of the US liver waiting list and liver transplant recipients to provide probabilities in our microsimulation model.

Our population was all adult patients (≥18 years old) listed with UNOS or receiving their first liver transplant for chronic liver disease from 1/1/2003 through 12/31/2007 with follow-up until 2/1/2008. Patients receiving exception MELD points for hepatocellular carcinoma (HCC) were included; however, those receiving exception points for other indications were excluded because of the variability across the nation in patients and the manner in which points are given. Patients listed or transplanted for cholangiocarcinoma, multiple organ transplantation, retransplantation, and acute hepatic failure were excluded. Patients receiving donation after cardiac death livers were excluded. Patients without calculated MELD scores were excluded. All deaths were confirmed through the linking of deaths reported to the Organ Procurement and Transplantation Network with deaths reported in the Social Security Death Master File in the STAR files. Our population was chosen to evaluate waitlist events and patients transplanted after spending time on the waitlist and was similar to populations in previous studies.20

All listed patients were evaluated for initial MELD score at listing, requirement for HCC exception points, MELD score at removal from waitlist, length of time on the list, and waitlist events as recorded in the STAR files, including reason for removal [transplantation, death while on list, being dropped off list (for possible reasons of medical unsuitability for transplantation, patient refusal of transplantation, too sick for transplantation, and other), and condition improved]. Liver transplant recipients were additionally evaluated for graft and patient survival. Waitlisted patients who were removed from the list for any of the aforementioned reasons were evaluated for patient survival.

Overall survival was defined as the interval between listing date and death, with or without liver transplantation. All living patients were censored at the time of their last recorded follow-up. Posttransplant survival was assessed from the time of liver transplantation until death or censoring at the time of follow-up.

Statistical Analysis

Continuous variables were given as the mean ± standard error of the mean (SEM), and categorical variables were presented as proportions. Nonparametric tests were used for testing continuous variables, and the chi-square test was used for categorical variables. The time to specific medical outcomes and survival curves were calculated with Kaplan-Meier survival analyses and compared with the log-rank test. Univariate sensitivity analysis was performed to check the influence of the various probabilities for factors influencing the overall survival of patients in our model. Ranges determined from the STAR data were used in the sensitivity analysis. The statistical software package JMP, version 7.0.2 (SAS Institute, Inc., Cary, NC), was used for determining the probabilities for the predictions. P values < 0.05 were considered significant. TreeAge Suite Pro Healthcare Version 1.4.1 (TreeAge Software, Inc, Williamstown, MA) was used to create the microsimulation model.

RESULTS

Final Markov Microsimulation Model

After several iterations, the final Markov microsimulation model that was validated included 7 health states: (1) on list, (2) death, (3) transplant, (4) drop off list, (5) retransplant, (6) HCC: drop off list, and (7) condition improved (Fig. 2). Each patient began in the “on list” state and proceeded through the model. The model encompassed the several health events that patients can experience while on the waitlist: transplantation, death during the transplant operation, death while on the waitlist, development of new HCC, dropping off the waitlist (for the possible reasons of medical unsuitability for transplantation, patient refusal of transplantation, too sick for transplantation, and other), and improved condition. Similar to the basis of the MELD score,21, 22 all probabilities of the model were for 3-month intervals. Thus, the time period for each cycle was 3 months. Patients were followed in the model for 4 years. A 4-year period was used to allow adequate time for a large percentage of patients to enter their final state. If an event did not occur for a patient, the patient would return to the “on list” state and repeat the aforementioned cycle until an event occurred. Once an event occurred, the patient would then move to that state and proceed through the associated events until death occurred or the 4-year time period ended. For example, if a patient “moved” to the transplanted state, the patient faced retransplantation or death over the course of the next cycles.

Figure 2.

Structure of the final Markov microsimulation model. Abbreviations: HCC, hepatocellular carcinoma; MELD, Model for End-Stage Liver Disease.

For our bootstrap group, we randomly chose 1000 patients from the population to run through our model to ensure adequate representation of the transplant population from the STAR files.17, 18 Each patient in the bootstrap group had data available on the following 3 characteristics: presence or absence of HCC, calculated MELD at time of listing, and calculated MELD score at transplantation. The trial or “clinical course” of 100,000 individual “patients” was run through our model. This number of trials was selected to allow the model to reach statistical stability. No discounting or quality adjustments were made.

Our model followed patient events that occurred after entry onto the liver transplant waiting list or attainment of a MELD score of ≥6 with chronic liver disease. In using our model to analyze the present US liver allocation system,23 chronic liver disease patients with a calculated MELD score were run through the model and encountered various health events. In the model of the allocation system that does not allow patients with MELD scores ≤ 14 to be waitlisted or transplanted (“Rule 14”), the patients with MELD ≥ 15 proceeded on the list and progressed through the various events as previously described. The patients with MELD ≤ 14 stayed off the list until reaching a MELD score of 15, at which point they were entered onto the list. The extra organs that had previously gone to the patients with the MELD scores of 6 to ≤14 were distributed to all other groups in proportion to the prior probabilities, and this increased their probabilities for transplantation. While off the list, these patients “experienced” an average quarterly increase in calculated MELD as determined directly from the STAR data.

Population and Bootstrap Group

Of 53,788 patients listed for a liver transplant with UNOS from 1/1/2003 through 12/31/2007, our population contained 38,880 adult patients (≥18 years old) listed for primary liver-only transplantation for chronic liver disease with an initial calculated MELD score. The population was stratified into 6 groups: 5 groups according to their initial calculated MELD score (scores of 6–10, 11–14, 15–22, 23–30, and 31–40) and 1 group receiving exception MELD points for HCC. The number and percentage of each group are shown in Table 1. Of the population group, 17,736 patients received transplants. Of those receiving liver transplants, 2121 (12%) had final MELD scores ≤ 14. The bootstrap group, randomly chosen by computer from the population and used in the microsimulation model, naturally had group proportions similar to the population (Table 1).

Table 1. Numbers and Percentages of the Population and Bootstrap Group
Stratified GroupPopulationBootstrap GroupP
  1. Abbreviations: HCC, hepatocellular carcinoma; MELD, Model for End-Stage Liver Disease.

Number38,8801,000 
Calculated MELD   
 6 to 106,616 (17%)166 (16.6%)0.8
 11 to 149,406 (24.2%)242 (24.2%)0.99
 15 to 2211,384 (29.3%)300 (30%)0.6
 23 to 303,791 (9.8%)93 (9.3%)0.7
 31 to 402,778 (7.2%)73 (7.3%)0.9
Exception HCC4,905 (12.6%)126 (12.6%)0.98
Transplanted17,736 (45.6%)460 (46%)0.8

Probabilities of Waiting List Events and Transplant Events

Probabilities of events required for the model were determined for each group directly from the events recorded in the STAR files. The probabilities of certain events in the microsimulation model—being entered onto the waitlist, receiving a transplant, and being taken off the waitlist—were determined from actual probabilities for 90-day intervals from the population of listed and transplanted patients from 1/1/2003 through 12/31/2007 (Table 2). For example, a patient with a MELD score of 31 to 40 had a 56.1% chance within the first 3 months after listing of being transplanted, a 10.8% chance of dropping off the waitlist, and a 27.8% chance of dying while on the list. Our population included data collected over 5 years, but transplant survival probabilities were determined for only 4 years to ensure that all recipients had at least 1 year of follow-up. For example, patients with MELD scores of 15 to 22 had a 4% chance of dying in the first 90 days following transplantation, a 2% chance of dying at 90 to 180 days, and a 3.2% chance of dying at 181 to 365 days. For these patients, the probabilities of dying in years 2, 3, and 4 following transplantation were 5%, 3.1%, and 4.4%, respectively. The posttransplantation survival curves for the 6 groups revealed 4 groups (11–14, 15–22, 23–30, and 31–40) stratifying into survival curves in order of their MELD groups (Fig. 3). Interestingly, for recipients transplanted with calculated MELD scores of 6 to 10, posttransplantation survival was lower than that of the groups with MELD scores of 11 to 14 and 15 to 22 but similar to the posttransplantation survival of the group with MELD scores of 23 to 30. [These patients received significantly higher risk donor livers (data not shown)]. Patients with exception HCC points also had lower survival (Fig. 3). Because of the small numbers and variability in results between groups, the retransplantation mortality, retransplantation rate, death off list, and death with condition improved were calculated for all patients as 1 group regardless of the MELD score or HCC status at transplantation.

Table 2. Probabilities (%) Used in the Markov Microsimulation Model as Determined from the Standard Transplant Analysis and Research Files
Event6 to 1011 to 1415 to 2223 to 3031 to 40Exception HCC
  • NOTE: Baseline values and ranges are included when available.

  • Abbreviation: HCC, hepatocellular carcinoma.

  • *

    The 4-year percentage includes the first 90 days.

  • Four categories (medical unsuitability, patient refusal, too sick for transplantation, and other) were combined.

  • The 90-day probability was converted from a 4-year probability.

  • §

    Because of the small numbers and variability in results between groups, the retransplantation mortality, retransplantation rate, death off list, and death with condition improved were calculated for all patients as 1 group, regardless of the Model for End-Stage Liver Disease score or HCC status at transplantation.

Received transplant      
 90 days5.28.730.159.156.148.2
 4 years*13.828.152.265.856.684.9
Dying during transplant      
 90 days0.020.040.070.20.50.1
 4 years*0.10.10.20.30.50.3
Dropping off list      
 90 days1.71.52.85.810.82.2
 4 years*13.312.19.87.911.34.4
Developing new HCC on list      
 90 days0.20.20.30.105.2
 4 years*0.20.30.40.50.86.3
Died on list      
 90 days11.95.614.827.80.8
 4 years*9.613.615.119.428.52
Condition improved      
 90 days0.150.10.20.61.20.04
 4 years*2.510.91.11.60.04
Posttransplant mortality      
 90 days5.7 (3.5–7.9)4 (3–5.1)4 (3.4–4.6)6.7 (5.8–7.6)9.5 (8.3–10.7)3.7 (3.1–4.3)
 180 days3.3 (2.7–3.8)1.4 (1.2–1.5)2 (1.9–2.1)3 (2.8–3.2)3.9 (3.6–4.1)2.4 (2.3–2.6)
 1 year5.6 (4.9–6.3)2.4 (2.1–2.7)3.2 (3–3.4)4.1 (3.9–4.3)5.9 (5.6–6.2)5 (4.6–5.3)
 2 years6.6 (5.8–7.4)2.6 (2.3–3)5 (4.7–5.3)5.6 (5.2–6)4.9 (4.6–5.2)9.3 (8.8–9.8)
 3 years3.4 (2.9–4)3.2 (2.7–3.7)3.1 (2.8–3.4)5.7 (5.2–6.2)2.3 (2.1–2.5)4.9 (4.5–5.3)
 4 years4.8 (2.4–7.2)4.4 (3–5.8)4.4 (3.5–5.3)4.1 (3.1–5.1)4.3 (3.4–5.2)5 (4.1–5.9)
Retransplant mortality      
 90 days11 (10.1–11.8)§§§§§
 180 days4 (3–5)§§§§§
 1 year2.9 (1.7–4.1)§§§§§
 2 years3.5 (2.1–4.9)§§§§§
 3 years2 (0.5–3.5)§§§§§
 4 years3.1 (1.5–4.7)§§§§§
Retransplant rate0.2§§§§§
Death off list25§§§§§
Death with condition improved0.3§§§§§
Figure 3.

Posttransplantation survival by Model for End-Stage Liver Disease group and exception hepatocellular carcinoma points.

For patients with MELD ≤ 14, the mean change in the calculated MELD score while on the waiting list for 90 days was 0.45 MELD points (95% confidence interval: 0.435–0.466).

Model Validation

To confirm the validity of our model, we compared the events on the waitlist predicted by our model (including the transplant rate, death rate on the list, rate of dropping off the list, and patient survival after transplantation) to the events actually observed in the population from the STAR files (Fig. 4). All predictions overlapped with no clinical differences, demonstrating the high validity of our model.

Figure 4.

(A) Comparison of the transplantation rate in the population with the rate predicted by the Markov microsimulation model. (B) Comparison of the waiting list death rate in the population with the rate predicted by the Markov microsimulation model. (C) Comparison of the dropped off list rate in the population with the rate predicted by the Markov microsimulation model. (D) Comparison of the transplantation survival rate in the population with the rate predicted by the Markov microsimulation model.

Comparisons Between the Present Allocation System and “Rule 14” Using Model

The Markov microsimulation model was run for the present US national liver allocation policy, and these results were compared to outcomes under a “Rule 14” policy of withholding patients with a MELD score of ≤14 from the waitlist. Patients with MELD ≤ 14 were assigned extra MELD points while they waited according to the average increase in MELD scores. When these patients' MELD scores reached 15, the patients were then allowed onto the waiting list. The extra livers that previously had gone to the patients with MELD scores ≤ 14 were equally distributed to all other groups in proportion to the previous probabilities, and this increased their probabilities for transplantation.

The “Rule 14” policy resulted in several survival differences from the present allocation system. The “Rule 14” policy gave a 3% improvement in overall survival for all patients over the present system at 1, 2, 3, and 4 years (Fig. 5A). Under the present system, patients with MELD scores of 6 to 10 experience 17% poorer survival at 3 years after transplantation in comparison with the scenario under “Rule 14” of remaining on the waitlist (Fig. 5B). Patients with MELD scores of 11 to 14 showed a small survival benefit under “Rule 14” extending to almost 2 years by not undergoing transplantation (Fig. 5C). Patients with MELD scores ≥ 15 showed 2% to 3% better overall survival after 1 year under the “Rule 14” system compared with the present national system (Fig. 5D).

Figure 5.

(A) Comparison of overall survival from the time of MELD score presenting under the present national allocation system with survival under a system withholding transplantation from patients with MELD scores ≤ 14 (“Rule 14”). (B) Comparison of the overall survival of patients with presenting MELD scores of 6 to 10 under the present national allocation system with survival under a system withholding transplantation from patients with MELD scores ≤ 14 (“Rule 14”). (C) Comparison of overall survival of patients with presenting MELD scores of 11 to 14 under the present national system with survival under a system withholding transplantation from patients with MELD scores ≤ 14 (“Rule 14”). (D) Comparison of overall survival of patients with presenting MELD scores of ≥15 or exception points for hepatocellular carcinoma under the present national allocation system with survival under a system withholding transplantation from patients with MELD scores ≤ 14 (“Rule 14”). Abbreviation: MELD, Model for End-Stage Liver Disease.

The “Rule 14” system also resulted in a reduction of the amount of time on the waiting list for patients with MELD scores ≥ 15 to 40 (Fig. 6). The average decrease in waiting time was 25 days (a 13% reduction) for these patients. Patients with MELD scores of 15 to 22 had a 33-day 12%) reduction. (New patients being added from the MELD ≤ 14 group kept this reduction lower.) Patients with MELD scores of 23 to 30 had a 23-day reduction (29%) in waiting time, and those with MELD scores of 31 to 40 had a 16-day (70%) reduction in waiting time. Patients with exception points for HCC had a 140-day (87%) reduction in waiting time under the “Rule 14” system compared with the present system (Fig. 6).

Figure 6.

Percent reduction in time on the waiting list in a system withholding transplantation from patients with MELD scores ≤ 14 versus the present national allocation system. Abbreviations: HCC, hepatocellular carcinoma; MELD, Model for End-Stage Liver Disease. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]

Other changes would result from the “Rule 14” policy in comparison with the present national liver allocation policy. Of the patients with MELD scores of 6 to 10, 4.5% improved under the “Rule 14” policy and would not need a transplant over the 4-year period versus only 1.9% in the present system. The patients with MELD scores of 6 to 10 accumulated an average of 37 months ± 0.1 SEM before being placed on the waiting list. There was no difference in the improvement percentage and not needing a liver transplant in the patients with MELD scores of 11 to 14. These patients accumulated an average of 13.5 months ± 0.05 SEM before being placed on the waiting list. Larger changes were seen in the patients with an exception MELD score for HCC (Table 3). In 4 years, 26.1% more of these patients would receive transplantation, 13.7% fewer would be dropped off the list, and 4% fewer would die while on the waiting list. Patients with MELD scores of 15 to 22 showed the second largest change by receiving 5.1% more transplants, with 2% fewer dying in 4 years while on the list (Table 3).

Table 3. Changes in Waitlist Events from the Present National Allocation System to a System of Not Transplanting Patients with a Model for End-Stage Liver Disease Score ≤ 14
Listing EventPercent Change over 4 Years
15 to 2223 to 3031 to 40HCC
  1. Abbreviation: HCC, hepatocellular carcinoma.

Received transplant5.13.6126.1
Dropped from list−1.2−1.2−0.7−13.7
Died on list−2−2.20−4

Sensitivity Analysis

In a 1-way sensitivity analysis for overall patient survival for the microsimulation model, the probability of dying on the list had the main dominant effect (Fig. 7). There was no effect on overall survival regarding the probabilities used for the quarterly increase in MELD score for those ≤ 14.

Figure 7.

One-way sensitivity analysis of the effect of the probability of dying on the list on overall patient survival. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]

DISCUSSION

The main purpose of an organ allocation policy is to promote maximum survival for patients with end-stage organ failure. The first standard for any liver allocation policy is therefore to reduce overall mortality for all patients with liver disease and not just those receiving transplants. Another standard is to reduce stress for patients on the waiting list by reducing the waiting time, death rate on the waitlist, and drop-off rate. The MELD system for liver allocation in the United States meets these standards, but no system is perfect, and all systems will require constant modification as medical practice patterns change or evolve.

A current controversy is that some liver programs transplant a high percentage of patients with calculated MELD scores ≤ 14, to the potential detriment of patients with MELD scores both above and below 15.8, 24 Merion et al.10 pointed out a negative survival benefit of transplantation in patients with MELD ≤ 14. For this group of patients for a period of at least 1 year, the risk of dying from transplantation is higher than the risk of dying while on the waitlist.10 The question is therefore asked why patients with MELD scores ≤ 14, at a rate in our study of 12% of primary liver-only transplantations over a recent 5-year period, continue to be transplanted. Is it time to modify the national liver allocation policy in the United States to disallow transplantation of patients with low MELD scores, who would have little to no survival benefit from the procedure?

Our Markov microsimulation model suggests a modest advantage to patients with higher MELD scores if patients with lower MELD scores were not entered onto the liver waiting list until reaching a MELD score of 15. There is a significant benefit to patients with MELD scores of 6 to 10 in delaying entry onto the waitlist, while a smaller advantage can be seen for patients with MELD scores of 11 to 14.

While it is inevitable that any liver allocation policy might produce a higher risk of death in some patient categories, the main reason for changing a national allocation policy should be to raise the overall survival rate of all patients with chronic liver disease. On the surface, decreasing the size of the waiting list by removing all patients with lower MELD scores would essentially add >2000 donor livers that previously went to the patients with lower MELD scores in a 5-year period. This would effectively increase the transplant rate for the remaining waitlisted patients by 25% to 30% over a 5-year period. Under the current allocation system, reaching this same level by enlarging the deceased donor pool would provide potentially 2000 additional expanded criteria donors, possibly resulting in poorer survival. The same increased number of living liver donors would put 2000 more lives at risk. Our model predicted that raising the number of donor livers by 2000 would save 3% more lives over 4 years. This percentage may seem modest but at the national level translates to 1170 patients. This is more than the 65 saved lives predicted during a 6-month period as analyzed by the Liver Stimulated Allocation Model presented at the 2003 national conference.9 This value of 3% also seems low given the increased transplantation rate and decreased waiting times predicted by our model. This is understandable given that livers are diverted from the group with MELD scores of 11 to 14, who have the highest transplant survival, to the other groups with lower transplant survival. Survival for groups with MELD scores ≥ 15 and with HCC exception points would increase by 2% to 3%. We suggest that the cost to save these lives would be the travel costs and longer ischemia times in transporting the organs to the higher MELD patients; however, the few times when donor livers would be moved from one region to another seem a small price to pay. Overall, more lives would be saved.

The “Rule 14” model predicts a 13% decrease in overall waitlist time for patients with MELD scores of 15 to 40. As shown by us and by others,9, 25 shorter waiting times result in fewer deaths or drop-offs from the waitlist. The most affected group is patients with exception points for HCC; with more time to wait on the list, they are exposed to more organs. These patients died on the list at a lower rate than the MELD groups; thus, they are influenced the most by the diversion of extra organs from the low-MELD groups. The group second-most influenced in actual days by a “Rule 14” policy is patients with MELD scores of 15 to 22. This group can also afford to wait on the list longer than groups with MELD scores of 23 to 30 or 31 to 40, and they live long enough to take advantage of the “extra” organs. All patients on the waiting list will face reduced stress from shorter waiting times and a higher transplant rate.

The benefit of a “Rule 14” policy for the group with MELD scores of 11 to 14 seems intermediate. Under the present system, as shown by Merion et al.,10 this group has a survival advantage in waiting on the list for about 1 year, but after 1 year, the group has a survival advantage in transplantation. Under “Rule 14,” the model predicts that this group's survival advantage in not being transplanted would be extended to almost 2 years, at which time the survival of waiting would equal that of transplantation. For other events occurring in this group, such as improving or dying while on the waitlist, we found no difference between the allocation policies. It might be best for this group to be evaluated by a liver center and followed on a regular basis. This would allow exception points to be given, if needed. Also, if rapid deterioration occurred, meeting the window of reaching a MELD score of 15 and being allowed on the list would be better achieved.

The group that would benefit the most from deferring transplantation is the group with MELD scores of 6 to 10. Our model projects a 17% difference in survival in favor of waiting on the list compared with transplantation for this group. This group could wait an average of 3 years, with few patients dying. Remarkably, 2.6% more patients in this group would improve while waiting and not need a liver. For an average waiting list, this would amount to about 100 patients improving and not needing a liver transplant for the average time period before being allowed on the waitlist. A policy of not allowing transplantation for patients with MELD ≤ 14 would greatly benefit this group.

There is further controversy with the group with MELD scores of 6 to 10 because some centers are giving these patients a high number of extended criteria donor livers. It has been suggested, and we have confirmed, that this group receives significantly more high-risk donor livers than any other group.7, 11, 26 Apparently, liver programs give the high-risk livers to low-MELD patients in an attempt to obtain better survival from the suboptimal donor livers. What would happen to these high-risk donor livers if a policy were instituted of not allowing low-MELD score patients on the transplant list? Would the high-risk donor livers be given to recipients with higher MELD scores who would have a favorable survival benefit?10 How would that influence posttransplantation survival for that MELD group? Would the extended criteria donor organs be discarded, with the result of no increase in the transplant rate? To sacrifice an available liver, even if the liver is an extended criteria donor liver, in view of the huge organ shortage seems unthinkable, yet this may sometimes be in the best interest of a specific recipient. We have instituted a study to find where to use these extended criteria donor livers besides in the low-MELD population.

The HCC exception group would need further consideration if “Rule 14” were instituted. Presently, the HCC exception group can wait on the list longer because fewer of these patients die or drop off the list. This increased length of time on the list without the occurrence of events allows these patients under “Rule 14” to be exposed to more donor livers. As seen under our “Rule 14” model, this group has a 140-day decrease in time on the list, a 26.1% increase in the transplant rate, a 13.7% decrease in the drop-off rate from the list, and a 4% decrease in the death rate on the list. With the poorer transplant survival rate at 4 years of this group of patients, this would arguably not be a fair system to maximize transplant benefit, as some have already questioned under the present system.27 We suggest that institution of “Rule 14” would necessitate consideration of lowering the exception points given to patients with HCC.

The predictions in our study are based on our Markov microsimulation model, which has certain strengths and weaknesses. Decision analytical modeling is limited by the model structure (model uncertainty) and the probabilities used for the model events (parameter uncertainty).15 We believe that one of the strengths of our model is the use of data directly from our population, rather than relying on published data that include different time frames and groups of patients, which can introduce bias.19 Another strength is that our model was given external validity when we made predictions that we corroborated with the STAR file data. While there is disagreement on whether MELD scoring can predict posttransplantation survival,2, 28–41 we stratified groups by MELD scores and HCC exception points and predicted the posttransplantation survival of these groups. We believe that it is a strength of our study because the allocation policy would move transplants to the higher MELD groups and any possible increase in mortality would need to be captured. We used 4-year study periods to determine long-term effects, which capture the latest trends in liver allocation policy. Finally, the bootstrap group is not uniform but mirrors the actual listed patients, and this allows for more precise predictions of actual events.

The main limitation is that our model stratified patients on static patient MELD scores (initial MELD score at listing or MELD score at transplantation). Some have concerns that the MELD score has a limited capability for predicting mortality in the lower MELD groups.42 However, our model accurately re-created the mortality in this group over the past 5 years, and with a low mortality in this group, future predictions should not vary significantly. Likewise, a single MELD score at listing is reportedly unlikely to accurately reflect the mortality risk across the entire time of being on the list.1 By removing the group with low MELD scores, who wait the longest, from the list, the remaining patients with higher MELD scores have a shorter time period on the list, and this allows the higher MELD scores to better predict mortality on the list.42 We also used the transplant mortality rate for each group based on calculated MELD scores at the time of transplantation; however, with the sensitivity analysis showing no effect of posttransplantation mortality on the overall death rate, the actual MELD scores would have little influence. Another weakness of our model is that, in contrast to other studies,25 we used worsening MELD scores over time for those not allowed on the waiting list. The average increase of 0.45 for a 3-month period for those listed with a MELD score of 6 to 14 was obtained directly from the population from the STAR files. We confirmed that this increase, as previously reported, was modest over time for the patients listed with lower MELD scores compared to the higher MELD patients.10 In actual clinical practice, we believe that this is quite variable among different patient and diagnosis for end-stage liver failure groups. However, the sensitivity analysis revealed no effect on the quarterly change in MELD scores, so it likely has little influence on the overall outcome. An additional weakness of our study is related to our evaluation of the liver allocation policy on the national level for the potential national effect. In regions of low donor rates versus regions with higher donor rates, the analysis may have variable results. If the higher donor rate regions did not transplant patients with lower MELD scores and did not have patients with high MELD scores to transplant, then some livers would be transferred to a low rate region, improving the overall survival rate. In regions with relative donor shortages, where the patients predominantly transplanted are those with high MELD scores, “Rule 14” would seem to have little effect other than these regions receiving some livers from other regions. However, “Rule 14” would prevent programs from transplanting patients with low MELD scores. If these programs were located in a region that transplanted patients with higher MELD scores, organs would be diverted from programs transplanting patients with MELD scores ≤ 14 to programs transplanting patients with higher MELD scores. A final limitation of our study is that past behavior is used to predict future practice patterns. It is difficult to tell how a change in policy would affect future liver programs' behavior. This will be an interesting development to study in the future.

No system of liver allocation is perfect, and all will need changes along the way. We recommend a policy change to not allow patients with MELD ≤ 14 on the waiting list or to switch to a survival/benefit policy.11 Center-specific data should not be affected. Programs' risk scores should be increased by transplantation of patients with higher MELD scores; thus, the risk-adjusted data should remain stable. Few programs have no patients with MELD scores ≤ 14, but no doubt some organs would be allocated to other programs, and this would cause the transplant numbers at some programs to decrease. We suspect the biggest influence on programs may be financial; however, exactly who pays for transplanting patients with higher MELD scores and possible complications is controversial.43–45 All programs might experience possible lower costs with the decrease in waiting times and in not following the patients with MELD scores of 6 to 10. The bottom line is that patients on the waitlist would be better served.

Our analysis supports changing the UNOS liver allocation policy to not allow patients with MELD scores ≤ 14 to be transplanted. We predict that these changes in the liver allocation policy would provide a modest benefit to the entire waiting list while giving tremendous benefit to patients with MELD scores of 6 to 10. We believe that patients with chronic liver disease and MELD scores of 11 to 14 should be referred to a liver program to allow adequate time for these patients to be followed and placed on the liver waiting list.

We emphasize that the MELD system is not “broken,” nor are large numbers of patients dying unnecessarily under the present policy. The changes that we propose are in the form of fine-tuning to maximize transplant survival. The public nature of the UNOS data and the mathematical basis of the MELD system combine to allow statistical analysis for prediction of hypothetical scenarios, as we have done. We encourage others to explore potential changes in allocation policy with other models or methods. These opportunities to examine the data and perform statistical analyses facilitate open discussion to improve the system. Our proposal to limit waitlist entry and transplantation to patients with MELD ≥ 15 might just remedy the disparities in access to donor organs across the United States by increasing access to patients having little time to wait. If these changes quell the controversy of transplanting patients with low MELD scores and reassure the public that the US liver allocation system is fair (with periodic revisions), this may be the best result.

Acknowledgements

The authors thank Marilyn Carlson for her editorial assistance.

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