A methodological framework for optimally reorganizing liver transplant regions

Heterogeneous donor circles for fair liver transplant allocation

The United States (U.S.) Department of Health and Human Services is interested in increasing geographical equity in access to liver transplant. The geographical disparity in the U.S. is fundamentally an outcome of variation in the organ supply to patient demand (s/d) ratios across the country (which cannot be treated as a single unit due to its size). To design a fairer system, we develop a nonlinear integer programming model that allocates the organ supply in order to maximize the minimum s/d ratios across all transplant centers. We design circular donation regions that are able to address the issues raised in legal challenges to earlier organ distribution frameworks. This allows us to reformulate our model as a set-partitioning problem. Our policy can be viewed as a heterogeneous donor circle policy, where the integer program optimizes the radius of the circle around each donation location. Compared to the current policy, which has fixed radius circles around donation locations, the heterogeneous donor circle policy greatly improves both the worst s/d ratio and the range between the maximum and minimum s/d ratios. We found that with the fixed radius policy of 500 nautical miles (NM), the s/d ratio ranges from 0.37 to 0.84 at transplant centers, while with the heterogeneous circle policy capped at a maximum radius of 500 NM, the s/d ratio ranges from 0.55 to 0.60, closely matching the national s/d ratio average of 0.5983. Our model matches the supply and demand in a more equitable fashion than existing policies and has a significant potential to improve the liver transplantation landscape.

Location of organ procurement and distribution organisation decisions and their impact on kidney allocations: a developing country perspective

Managing organ transplant networks is a complex task. It intertwines between locating the organ procurement and distribution organization (OPDO) (long-term decision) and allocating organs to the suitable destination (short-term decision). The literature lacks deliberation on the effect of those long-term decisions on short-term ones under the influence of clinical and non-clinical factors. This paper addresses this gap using a k-sum model for locational choice, and a discrete simulation approach for the allocation procedure for a real-life case study from a developing economy perspective. The study explores the trade-off between efficiency (distance-centric models) and equity (the result of time-centric allocation models). Our analysis of the efficiency of locational models and equity of the allocation policies reveal strong inter-dependence of both these decisions, a significant finding of this research. These findings offer an integrated model for high-level decision-makers, which can be used during the locational planning stage and provide input to design standard operating procedures for transplantation schemes.

Removing administrative boundaries using a gravity model for a national liver allocation system

Geographic disparities emerged as an increasing issue in organ allocation policies. Because of the sequential and discrete geographical models used for allocation scores, artificial regional boundaries may impede the access of candidates with the greatest medical urgency to vital organs. This article describes a continuous geographical allocation model that provides accurate organ access by introducing a multiplicative interaction between the patient's condition and the distance to the graft by using a gravity model. Patients with the most urgent need will thus have access to organs from farther away, while those in less urgent need may only have access to organs geographically closer. Compared to the previous French liver allocation scheme, the gravity model precluded transplantations for candidates with a Model for End-Stage Liver Disease (MELD) ≤ 14 for decompensated cirrhosis from 10.3% to 0.6%. Death and delisting while on the waiting list at 1 year also decreased from 30.1% to 22.4% for MELD ≥ 35. Waiting list (cumulative hazard ratio (CHR)  0.84 after adjustment) and posttransplant survival improved significantly (hazard ratio = 0.83 after adjustment). This new liver allocation system provides more equitable access to liver transplants and an efficient and safe alternative to administrative boundaries for geographical models in organ allocation.

Gerrymandering for Justice: Redistricting U.S. Liver Allocation

U.S. organ allocation policy sequesters livers from deceased donors within arbitrary geographic boundaries, frustrating the intent of those who wish to offer the livers to transplant candidates based on medical urgency. We used a zero-one integer program to partition 58 donor service areas into between four and eight sharing districts that minimize the disparity in liver availability among districts. Because the integer program necessarily suppressed clinically significant differences among patients and organs, we tested the optimized district maps with a discrete-event simulation tool that represents liver allocation at a per-person, per-organ level of detail. In April 2014, the liver committee of the Organ Procurement and Transplantation Network (OPTN) decided in a unanimous vote of 22-0-0 to write a policy proposal based on our eight-district and four-district maps. The OPTN board of directors could implement the policy after the proposal and public-comment period.Redistricting liver allocation would save hundreds of lives over the next five years and would attenuate the serious geographic inequity in liver transplant offers.

Improving Geographic Equity in Kidney Transplantation Using Alternative Kidney Sharing and Optimization Modeling

The national demand for kidney transplantation far outweighs the supply of kidney organs. Currently, a patient's ability to receive a kidney transplant varies depending on where he or she seeks transplantation. This reality is in direct conflict with a federal mandate from the Department of Health and Human Services. We analyze current kidney allocation and develop an alternative kidney sharing strategy using a multiperiod linear optimization model, KSHARE. KSHARE aims to improve geographic equity in kidney transplantation while also respecting transplant system constraints and priorities. KSHARE is tested against actual 2000–2009 kidney allocation using Organ Procurement and Transplant Network data. Geographic equity is represented by minimizing the range in kidney transplant rates around local areas of the country. In 2009, less than 25% of standard criteria donor kidneys were allocated beyond the local area of procurement, and Donor Service Area kidney transplantation rates varied from 3.0% to 30.0%, for an overall range of 27.0%. Given optimal sharing of kidneys within 600 miles of procurement for 2000–2009, kidney transplant rates vary from 5.0% to 12.5% around the country for an overall kidney transplant range of 7.5%. Nationally sharing kidneys optimally between local areas only further decreases the transplant rate range by 1.7%. Enhancing the practice of sharing kidneys by the KSHARE model may increase geographic equity in kidney transplantation.

The effect of the Statewide Sharing variance on geographic disparity in kidney transplantation in the United States

BACKGROUND AND OBJECTIVES

The Statewide Sharing variance to the national kidney allocation policy allocates kidneys not used within the procuring donor service area (DSA), first within the state, before the kidneys are offered regionally and nationally. Tennessee and Florida implemented this variance. Known geographic differences exist between the 58 DSAs, in direct violation of the Final Rule stipulated by the US Department of Health and Human Services. This study examined the effect of Statewide Sharing on geographic allocation disparity over time between DSAs within Tennessee and Florida and compared them with geographic disparity between the DSAs within a state for all states with more than one DSA (California, New York, North Carolina, Ohio, Pennsylvania, Texas, and Wisconsin).

DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS

A retrospective analysis from 1987 to 2009 was conducted using Organ Procurement and Transplant Network data. Five previously used indicators for geographic allocation disparity were applied: deceased-donor kidney transplant rates, waiting time to transplantation, cumulative dialysis time at transplantation, 5-year graft survival, and cold ischemic time.

RESULTS

Transplant rates, waiting time, dialysis time, and graft survival varied greatly between deceased-donor kidney recipients in DSAs in all states in 1987. After implementation of Statewide Sharing in 1992, disparity indicators decreased by 41%, 36%, 31%, and 9%, respectively, in Tennessee and by 28%, 62%, 34%, and 19%, respectively in Florida, such that the geographic allocation disparity in Tennessee and Florida almost completely disappeared. Statewide kidney allocations incurred 7.5 and 5 fewer hours of cold ischemic time in Tennessee and Florida, respectively. Geographic disparity between DSAs in all the other states worsened or improved to a lesser degree.

CONCLUSIONS

As sweeping changes to the kidney allocation system are being discussed to alleviate geographic disparity--changes that are untested run the risk of unintended consequences--more limited changes, such as Statewide Sharing, should be further studied and considered.

Redesigning Organ Allocation Boundaries for Liver Transplantation in the United States

Geographic disparities in access to and outcomes in transplantation have been a persistent problem widely discussed by transplant researchers and the transplant community. One of the alleged causes of disparities in the United States is administratively determined organ allocation boundaries that limit organ sharing across regions. This paper applies mathematical programming to construct alternative liver allocation boundaries that achieve more geographic equity in access to transplants than the current system. The performance of the optimal boundaries were evaluated and compared to that of current allocation system using discrete event simulation.

Addressing geographic disparities in liver transplantation through redistricting

Severe geographic disparities exist in liver transplantation; for patients with comparable disease severity, 90-day transplant rates range from 18% to 86% and death rates range from 14% to 82% across donation service areas (DSAs). Broader sharing has been proposed to resolve geographic inequity; however, we hypothesized that the efficacy of broader sharing depends on the geographic partitions used. To determine the potential impact of redistricting on geographic disparity in disease severity at transplantation, we combined existing DSAs into novel regions using mathematical redistricting optimization. Optimized maps and current maps were evaluated using the Liver Simulated Allocation Model. Primary analysis was based on 6700 deceased donors, 28 063 liver transplant candidates, and 242 727 Model of End-Stage Liver Disease (MELD) changes in 2010. Fully regional sharing within the current regional map would paradoxically worsen geographic disparity (variance in MELD at transplantation increases from 11.2 to 13.5, p = 0.021), although it would decrease waitlist deaths (from 1368 to 1329, p = 0.002). In contrast, regional sharing within an optimized map would significantly reduce geographic disparity (to 7.0, p = 0.002) while achieving a larger decrease in waitlist deaths (to 1307, p = 0.002). Redistricting optimization, but not broader sharing alone, would reduce geographic disparity in allocation of livers for transplant across the United States.

Foreigners traveling to the U.S. for transplantation may adversely affect organ donation: a national survey

The aims of this study were (1) to determine attitudes among the American public regarding foreigners coming to the United States for the purposes of transplantation, and (2) to investigate the impact this practice might have on the public's willingness to donate organs. A probability-based national sample of adults age > or =18 was asked whether people should be allowed to travel to the United States to receive a transplant, and whether this practice would discourage the respondents from becoming an organ donor. Among 1049 participants, 30% (95% CI 25-34%) felt that people should not be allowed to travel to the United States to receive a deceased donor transplant, whereas 28% felt this would be acceptable in some cases. Thirty-eight percent (95% CI 33-42%) indicated that this practice might prevent them from becoming an organ donor. In conclusion, deceased-donor transplantation of foreigners is opposed by many Americans. Media coverage of this practice has the potential to adversely affect organ donation.

Geographic variation in organ availability is responsible for disparities in liver transplantation between Hispanics and Caucasians

The aims of this study were to determine whether disparities in waiting list outcomes exist for Hispanics and African Americans during the post-MELD era, and to investigate interactions between disparities and geography. Scientific Registry of Transplant Recipients data were used to compare Hispanics and African Americans to Caucasians listed between 2003 and 2008. Endpoints included (i) receipt of a liver transplant and (ii) death or removal from the waiting list for being too sick or medically unsuitable. Adjustment for possible confounders was performed using multivariate Cox regression, with adjustment for geographic variation using a fixed-effects multilevel model. In multivariate analysis, African Americans have similar hazard of transplantation and death/removal as Caucasians during the post-MELD era. However, Hispanics are less likely to receive a transplant than Caucasians despite adjustment for potential confounders (HR 0.80, 95% CI 0.77-0.83), while having a similar hazard of death/removal. This effect disappeared after adjusting for unequal regional distribution of Hispanics, who represent 8% of patients in donation service areas (DSAs) having median waiting times of < or = 155 days versus 19% in DSAs with median waiting times of >155 days. In conclusion, disparities in liver transplantation exist for Hispanics during the post-MELD era, caused by geographic variation in organ availability.

Beyond utilitarianism: a method for analyzing competing ethical principles in a decision analysis of liver transplantation

BACKGROUND

The utilitarian foundation of decision analysis limits its usefulness for many social policy decisions. In this study, the authors examine a method to incorporate competing ethical principles in a decision analysis of liver transplantation for a patient with acute liver failure (ALF).

METHODS

A Markov model was constructed to compare the benefit of transplantation for a patient with ALF versus the harm caused to other patients on the waiting list and to determine the lowest acceptable 5-y posttransplant survival for the ALF patient. The weighting of the ALF patient and other patients was then adjusted using a multiattribute variable incorporating utilitarianism, urgency, and other principles such as fair chances.

RESULTS

In the base-case analysis, the strategy of transplanting the ALF patient resulted in a 0.8% increase in the risk of death and a utility loss of 7.8 quality-adjusted days of life for each of the other patients on the waiting list. These harms cumulatively outweighed the benefit of transplantation for an ALF patient having a posttransplant survival of less than 48% at 5 y. However, the threshold for an acceptable posttransplant survival for the ALF patient ranged from 25% to 56% at 5 y, depending on the ethical principles involved.

DISCUSSION

The results of the decision analysis vary depending on the ethical perspective. This study demonstrates how competing ethical principles can be numerically incorporated in a decision analysis.

Consequences of cold-ischemia time on primary nonfunction and patient and graft survival in liver transplantation: a meta-analysis

Introduction

The ability to preserve organs prior to transplant is essential to the organ allocation process.

Objective

The purpose of this study is to describe the functional relationship between cold-ischemia time (CIT) and primary nonfunction (PNF), patient and graft survival in liver transplant.

Methods

To identify relevant articles Medline, EMBASE and the Cochrane database, including the non-English literature identified in these databases, was searched from 1966 to April 2008. Two independent reviewers screened and extracted the data. CIT was analyzed both as a continuous variable and stratified by clinically relevant intervals. Nondichotomous variables were weighted by sample size. Percent variables were weighted by the inverse of the binomial variance.

Results

Twenty-six studies met criteria. Functionally, PNF% = −6.678281+0.9134701*CIT Mean+0.1250879*(CIT Mean−9.89535)2−0.0067663*(CIT Mean−9.89535)3, r2 = .625, , p<.0001. Mean patient survival: 93 % (1 month), 88 % (3 months), 83 % (6 months) and 83 % (12 months). Mean graft survival: 85.9 % (1 month), 80.5 % (3 months), 78.1 % (6 months) and 76.8 % (12 months). Maximum patient and graft survival occurred with CITs between 7.5–12.5 hrs at each survival interval. PNF was also significantly correlated with ICU time, % first time grafts and % immunologic mismatches.

Conclusion

The results of this work imply that CIT may be the most important pre-transplant information needed in the decision to accept an organ.

A novel model measuring the harm of transplanting hepatocellular carcinoma exceeding Milan criteria

No empirical studies have defined the posttransplant survival that would justify expansion of the Milan criteria for liver transplantation of hepatocellular carcinoma. We created a Markov model comparing the survival benefit of transplantation for a patient with >Milan HCC, versus the harm caused to other patients on the waiting list. In the base-case analysis, the strategy of transplanting the patient with >Milan HCC resulted in a 44% increased risk of death and a utility loss of 3 quality-adjusted years of life across the pre- and posttransplant periods for a nationally representative cohort of patients on the waiting list. This harm outweighed the benefit of transplantation for a patient with >Milan HCC having a 5-year posttransplant survival of less than 61%. This survival threshold was most sensitive to geographic variations in organ shortage, with the threshold varying from 25% (Region 3) to >72% (Regions 1, 5, 7 and 9). In conclusion, expansion of the Milan criteria will require demonstrating high survival rates for the newly eligible patients-approximately 61% at 5 years after transplantation. In regions with less severe organ shortage, a more aggressive approach to transplanting these patients may be justified.