Heterogeneous Circles for Liver Allocation

Abstract

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.

FIG. 1.

Geographic variation in liver supply and demand. The circles (A) indicate the location of the supply of livers at each ZIP code where at least one deceased donor liver was recovered and transplanted between 07/2013 and 06/2017 (livers recovered and transplanted in AK, HI, and PR are not shown), while the stars (B) indicate the liver transplant centers in the continental United States.

FIG. 2.

Distribution of heterogeneous circle radii around each transplant center.

FIG. 3.

Transplant center and circle size. (A) The 20 transplant centers with the largest circles were AZMC (662 nm), CASF (665 nm), AZUA (666 nm), AZCH (666 nm), AZGS (666 nm), CASU (675 nm), CAPC (678 nm), CALL (745 nm), CACL (766 nm), CASD (773 nm), CACH (774 nm), CAGH (777 nm), CAUH (777 nm), CACS (778 nm), CAUC (791 nm), ORUO (855 nm), ORVA (855 nm), WASM (889 nm), WAUW (890 nm), and WACH (894 nm). (B) The 20 transplant centers with the smallest circles were FLTG (179 nm), FLFH (180 nm), IAIV (232 nm), MOBH (233 nm), INIM (233 nm), MOSL (236 nm), MOCH (237 nm), TNVU (238 nm), MOCG (239 nm), LAWK (245 nm), FLUF (245 nm), OHUC (250 nm), GAEH (253 nm), FLSL (255 nm), ILLU (256 nm), FLBC (256 nm), OHCM (256 nm), KYUK (256 nm), FLCC (261 nm), and OKBC (264 nm).

FIG. 4.

Average distance livers would travel. (A) Using homogeneous 500 nm circles, each location indicates the average distance a liver would travel based on its recovery location and on the homogeneous circles. Livers will require roughly the same travel distance throughout the continental United States. (B) Using heterogeneous circles, each location indicates the average distance a liver would travel based on its recovery location and on the heterogeneous circles. Compared to homogeneous 500 nm circles, livers require more travel in the West and the less travel in the East.

FIG. 5.

Average distance livers would travel in the northeast. (A) Using homogeneous 500 nm circles, each location indicates the average distance a liver would travel based on its recovery location and on the homogeneous circles. Livers recovered near high-demand areas such as Philadelphia and New York City will travel approximately 200–250 nm on average. (B) Using heterogeneous circles, each location indicates the average distance a liver would travel based on its recovery location and on the heterogeneous circles. Livers recovered near high-demand areas such as Philadelphia and New York City will only travel approximately 100–150 nm on average.

FIG. 6.

The variance and range of supply/demand ratios across transplant centers using homogeneous and heterogeneous circles (A) The dots indicate the variance in the supply/demand ratios across transplant centers using homogeneous circles of the size indicated on the x-axis. The star indicates the variance in supply/demand ratios for the designed circles, located at the median radius size. (B) The dots indicate the range of supply/demand ratios across transplant centers using homogeneous circles of the size indicated by the x-axis. The star indicates the range of supply/demand ratios for the designed heterogeneous circles, located at the median radius size.

FIG. 7.

Distribution of supply/demand ratios for heterogeneous circles (gray) and homogeneous circles of radius 500 nm (X).

FIG. 8.

Comparing definitions of demand. The x-axis indicates demand as the number of candidates listed with, or who first achieved, a MELD/PELD 15 during the study period, whereas the y-axis indicates the MELD-weighted demand. Each point represents a transplant center. For this work it is only the relative demand and not the magnitude of the demands that matter. Therefore the high value suggests that these definitions are roughly equivalent.