Allocating kidneys in optimized heterogeneous circles

Recently, the Organ Procurement and Transplant Network approved a plan to allocate kidneys within 250-nm circles around donor hospitals. These homogeneous circles might not substantially reduce geographic differences in transplant rates because deceased donor kidney supply and demand differ across the country. Using Scientific Registry of Transplant Recipients data from 2016-2019, we used an integer program to design unique, heterogeneous circles with sizes between 100 and 500 nm that reduced supply/demand ratio variation across transplant centers. We weighted demand according to wait time because candidates who have waited longer have higher priority. We compared supply/demand ratios and average travel distance of kidneys, using heterogeneous circles and 250 and 500-nm fixed-distance homogeneous circles. We found that 40% of circles could be 250 nm or smaller, while reducing supply/demand ratio variation more than homogeneous circles. Supply/demand ratios across centers for heterogeneous circles ranged from 0.06 to 0.13 kidneys per wait-year, compared to 0.04 to 0.47 and 0.05 to 0.15 kidneys per wait-year for 250-nm and 500-nm homogeneous circles, respectively. The average travel distance for kidneys using heterogeneous, and 250-nm and 500-nm fixed-distance circles was 173 nm, 134 nm, and 269 nm, respectively. Heterogeneous circles reduce geographic disparity compared to homogeneous circles, while maintaining reasonable travel distances.