Improving Liver Allocation Using Optimized Neighborhoods

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.

Removing geographic boundaries from liver allocation: A method for designing continuous distribution scores

BACKGROUND

The Organ Procurement and Transplantation Network (OPTN) is eliminating geographic boundaries in liver allocation, in favor of continuous distribution. Continuous distribution allocates organs via a composite allocation score (CAS): a weighted sum of attributes like medical urgency, candidate biology, and placement efficiency. The opportunity this change represents, to include new variables and features for prioritizing candidates, will require lengthy and contentious discussions to establish community consensus. Continuous distribution could instead be implemented rapidly by computationally translating the allocation priorities for pediatric, status 1, and O/B blood type liver candidates that are presently implemented via geographic boundaries into points and weights in a CAS.

METHODS

Using simulation with optimization, we designed a CAS that is minimally disruptive to existing prioritizations, and that eliminates geographic boundaries and minimizes waitlist deaths without harming vulnerable populations.

RESULTS

Compared with Acuity Circles (AC) in a 3-year simulation, our optimized CAS decreased deaths from 7771.2 to 7678.8 while decreasing average (272.66 NM vs. 264.30 NM) and median (201.14 NM vs. 186.49 NM) travel distances. Our CAS increased travel only for high MELD and status 1 candidates (423.24 NM vs. 298.74 NM), and reduced travel for other candidates (198.98 NM vs. 250.09 NM); overall travel burden decreased.

CONCLUSION

Our CAS reduced waitlist deaths by sending livers for high-MELD and status 1 candidates farther, while keeping livers for lower MELD candidates nearby. This advanced computational method can be applied again after wider discussions of adding new priorities conclude; our method designs score weightings to achieve any specified feasible allocation outcomes.

The Precise Relationship Between Model for End-Stage Liver Disease and Survival Without a Liver Transplant

BACKGROUND AND AIMS

Scores from the Model for End-Stage Liver Disease (MELD), which are used to prioritize candidates for deceased donor livers, are widely acknowledged to be negatively correlated with the 90-day survival rate without a liver transplant. However, inconsistent and outdated estimates of survival probabilities by MELD preclude useful applications of the MELD score.

APPROACH AND RESULTS

Using data from all prevalent liver waitlist candidates from 2016 to 2019, we estimated 3-day, 7-day, 14-day, 30-day, and 90-day without-transplant survival probabilities (with confidence intervals) for each MELD score and status 1A. We used an adjusted Kaplan-Meier model to avoid unrealistic assumptions and multiple observations per person instead of just the observation at listing. We found that 90-day without-transplant survival has improved over the last decade, with survival rates increasing >10% (in absolute terms) for some MELD scores. We demonstrated that MELD correctly prioritizes candidates in terms of without-transplant survival probability but that status 1A candidates' short-term without-transplant survival is higher than that of MELD 40 candidates and lower than that of MELD 39 candidates. Our primary result is the updated survival functions themselves.

CONCLUSIONS

We calculated without-transplant survival probabilities for each MELD score (and status 1A). The survival function is an invaluable tool for many applications in liver transplantation: awarding of exception points, calculating the relative demand for deceased donor livers in different geographic areas, calibrating the pediatric end-stage liver disease score, and deciding whether to accept an offered liver.

Heterogeneous Circles for Liver Allocation

BACKGROUND AND AIMS

In February 2020, the Organ Procurement and Transplantation Network replaced donor service area-based allocation of livers with acuity circles, a system based on three homogeneous circles around each donor hospital. This system has been criticized for neglecting to consider varying population density and proximity to coast and national borders.

APPROACH AND RESULTS

Using Scientific Registry of Transplant Recipients data from July 2013 to June 2017, we designed heterogeneous circles to reduce both circle size and variation in liver supply/demand ratios across transplant centers. We weighted liver demand by Model for End-Stage Liver Disease (MELD)/Pediatric End-Stage Liver Disease (PELD) because higher MELD/PELD candidates are more likely to be transplanted. Transplant centers in the West had the largest circles; transplant centers in the Midwest and South had the smallest circles. Supply/demand ratios ranged from 0.471 to 0.655 livers per MELD-weighted incident candidate. Our heterogeneous circles had lower variation in supply/demand ratios than homogeneous circles of any radius between 150 and 1,000 nautical miles (nm). Homogeneous circles of 500 nm, the largest circle used in the acuity circles allocation system, had a variance in supply/demand ratios 16 times higher than our heterogeneous circles (0.0156 vs. 0.0009) and a range of supply/demand ratios 2.3 times higher than our heterogeneous circles (0.421 vs. 0.184). Our heterogeneous circles had a median (interquartile range) radius of only 326 (275-470) nm but reduced disparities in supply/demand ratios significantly by accounting for population density, national borders, and geographic variation of supply and demand.

CONCLUSIONS

Large homogeneous circles create logistical burdens on transplant centers that do not need them, whereas small homogeneous circles increase geographic disparity. Using carefully designed heterogeneous circles can reduce geographic disparity in liver supply/demand ratios compared with homogeneous circles of radius ranging from 150 to 1,000 nm.

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.

Migration of Patients for Liver Transplantation and Waitlist Outcomes

BACKGROUND & AIMS

Patients in need of liver transplantation may travel to improve their chance of receiving an organ. We evaluated factors to determine which transplant candidates travel to other regions to increase their chances of receiving a liver and effects of travel on waitlist outcomes.

METHODS

We performed a retrospective cohort study of all adult patients registered for primary deceased donor liver transplantation in the United States from January 2004 to December 2016. Zip code data were used to calculate the travel distance from a patient's residence to centers at which they were on the waitlist or received a liver transplant. Distant listing and migration were defined as placement on a waitlist and receipt of liver transplantation, respectively, outside the home transplantation region and greater than 500 miles from the home zip code. We assessed the effect of distant listing on outcomes (death and liver transplantation) and predictors of distant listing or migration using multivariable analyses.

RESULTS

There were 104,914 waitlist registrations during the study period; of these, 2930 (2.8%) pursued listing at a distant center. Of waitlist registrants, 60,985 received liver transplants, of whom 1985 (3.3%) had migrated. In a multivariable competing risk analysis in which liver transplantation was considered as a competing event, distant listing was associated with a 22% reduction in the risk of death within 1 year (subhazard ratio, 0.78; 95% CI, 0.70-0.88). Distant listing and migration were associated with non-black race, non-Medicaid payer, residence in a higher income area, and education beyond high school.

CONCLUSIONS

Placement on a liver transplant waitlist outside the home transplantation region is associated with reduced waitlist mortality and an increased probability of receiving a liver transplant. Geographic disparities in access to liver transplantation have disproportionate effects on patients who are minorities, have lower levels of education, or have public insurance.

Utilization of Declined Liver Grafts Yields Comparable Transplant Outcomes and Previous Decline Should Not Be a Deterrent to Graft Use

BACKGROUND

In the United Kingdom, up to 20% of liver graft offers are not used for transplantation, and the reasons for graft refusal are multifactorial and not consistent among transplant units.

METHODS

Liver grafts previously declined by other transplant centers in the United Kingdom but transplanted in our unit in Birmingham between 2011 and 2015 were analyzed. According to the indicated reason for previous declines, liver grafts were categorized into 3 refusal groups: "quality," "logistics," and "other reasons." Results were compared with a matched, low-risk cohort of livers primarily accepted and transplanted at our center.

RESULTS

During the study period, 206 livers (donation after brain death: n = 141 (68.4%); donation after circulatory arrest: n = 65 (31.6%) were transplanted, which were previously discarded by a median of 4 other UK centers. The majority of declines were donor quality (n = 102; 49.5%), refusals followed by logistics (n = 45; 21.8%), and other reasons (n = 59; 28.6%). Transplantation from both graft types (donation after brain death and donation after circulatory arrest) and all 3 refusal groups achieved equally good outcomes with an overall low complication rate. The incidence of primary nonfunction (2.4% vs 1.7%; P = 0.5483), in-hospital mortality (6.3% vs 4.1%; P = 0.2293) and 3-year graft (82.5% vs 84.1%; P = 0.6872) and patient (85.4% vs 87.6%; P = 0.8623) survival was comparable between livers previously declined and livers primarily accepted and transplanted at our center.

CONCLUSIONS

Transplantation of declined livers can achieve comparable outcomes to primary liver low-risk graft offers. Previous refusal should not be taken as a barrier to use the graft, and with appropriate recipient selection, more lives could be saved.

Directed solutions to address differences in access to liver transplantation

The United Network for Organ Sharing recently altered current liver allocation with the goal of decreasing Model for End-Stage Liver Disease (MELD) variance at transplant. Concerns over these and further planned revisions to policy include predicted decrease in total transplants, increased flying and logistical complexity, adverse impact on areas with poor quality health care, and minimal effect on high MELD donor service areas. To address these issues, we describe general approaches to equalize critical transplant metrics among regions and determine how they alter MELD variance at transplant and organ supply to underserved communities. We show an allocation system that increases minimum MELD for local allocation or preferentially directs organs into areas of need decreases MELD variance. Both models have minimal adverse effects on flying and total transplants, and do not disproportionately disadvantage already underserved communities. When combined together, these approaches decrease MELD variance by 28%, more than the recently adopted proposal. These models can be adapted for any measure of variance, can be combined with other proposals, and can be configured to automatically adjust to changes in disease incidence as is occurring with hepatitis C and nonalcoholic fatty liver disease.

Patients From Appalachia Have Reduced Access to Liver Transplantation After Wait-Listing

BACKGROUND

The Appalachian region is medically underserved and characterized by high morbidity and mortality. We investigated disparities among patients listed for liver transplantation (LT) in wait-list outcomes, according to residence in the Appalachian region.

METHODS

Data on adult patients listed for LT were obtained from the United Network for Organ Sharing for July 2013 to December 2015. Wait-list outcomes were compared using cause-specific hazard models by region of residence (Appalachian vs non-Appalachian) among patients listed at centers serving Appalachia. Posttransplant patient and graft survival were also compared. The study included 1835 LT candidates from Appalachia and 5200 from non-Appalachian regions, of whom 1016 patients experienced wait-list mortality or were delisted; 3505 received liver transplants.

RESULTS

In multivariable analyses, patients from Appalachia were less likely to receive LT (hazard ratio [HR] = 0.86; 95% confidence interval [CI]: 0.79-0.93; P < .001), but Appalachian residence was not associated with wait-list mortality or delisting (HR = 1.03; 95% CI: 0.89-1.18; P = .696). Among liver transplant recipients, patient and graft survival did not differ by Appalachian versus non-Appalachian residence.

CONCLUSION

Appalachian residence was associated with lower access to transplantation after listing for LT. This geographic disparity should be addressed in the current debate over reforming donor liver allocation and patient priority for LT.

A Concentric Neighborhood Solution to Disparity in Liver Access That Contains Current UNOS Districts

BACKGROUND

Policymakers are deliberating reforms to reduce geographic disparity in liver allocation. Public comments and the United Network for Organ Sharing Liver and Intestinal Committee have expressed interest in refining the neighborhoods approach. Share 35 and Share 15 policies affect geographic disparity.

METHODS

We construct concentric neighborhoods superimposing the current 11 regions. Using concepts from concentric circles, we construct neighborhoods for each donor service area (DSA) that consider all DSAs within 400, 500, or 600 miles as neighbors. We consider limiting each neighborhood to 10 DSAs and use no metrics for liver supplies and demands. We change Model for End-Stage Liver Disease (MELD) thresholds for the Share 15 policy to 18 or 20 and apply 3- and 5-point MELD proximity boosts to enhance local priority, control travel distances, and reduce disparity. We conduct simulations comparing current allocation with the neighborhoods and sharing policies.

RESULTS

Concentric neighborhoods structures provide an array of solutions where simulation results indicate that they reduce geographic disparity, annual mortalities, and the airplane travel distances by varying degrees. Tuning of the parameters and policy combinations can lead to beneficial improvements with acceptable transplant volume loss and reductions in geographic disparity and travel distance. Particularly, the 10-DSA, 500-mile neighborhood solution with Share 35, Share 15, and 0-point MELD boost achieves such while limiting transplant volume losses to below 10%.

CONCLUSIONS

The current 11 districts can be adapted systematically by adding neighboring DSAs to improve geographic disparity, mortality, and airplane travel distance. Modifications to Share 35 and Share 15 policies result in further improvements. The solutions may be refined further for implementation.