Heterogeneous circles for liver allocation.

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. Using Scientific Registry of Transplant Recipients data from 07/2013-06/2017, we designed novel, heterogeneous circles to reduce both circle size and variation in liver supply/demand ratios across transplant centers. We weighted liver demand by MELD/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 150-1,000 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 (IQR) radius of only 326 (275-470) nautical miles, but reduced disparities in supply/demand ratios significantly by accounting for population density, national borders, and the geographic variation of supply and demand. In conclusion, large homogeneous circles create logistical burdens on transplant centers that do not need them, while small homogeneous circles increase geographic disparity. Using carefully designed heterogeneous circles can reduce geographic disparity in liver supply/demand ratios, compared to homogeneous circles of radius ranging from 150-1,000 nm.