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.

Logistical burden of offers and allocation inefficiency in circle‐based liver allocation

“…By contrast, an optimization perspective10–12 could mean applying computational tools to design continuous allocation scores that maximize transplantation benefits while enforcing constraints, say, that logistical complexity does not increase too much and that organs are distributed equitably. Furthermore, because increased burden varies greatly by geography, an optimization approach could be used to design a geographically heterogeneous continuous allocation score 13,14…”

“…Furthermore, because increased burden varies greatly by geography, an optimization approach could be used to design a geographically heterogeneous continuous allocation score. [13,14] Circle-based liver allocation is associated with a national increase of 2.0 h in mean distribution time. This delay in allocation is likely a delay in organ placement due to the increased number of centers required to place an organ.…”

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

“…Previously, optimization methods were used to redesign district boundaries [10][11][12] for liver distribution and design geographically heterogeneous circular distribution. 13 Stewart et al took a different approach to design a CAS for lungs, using rank-ordered logistic regression models that aimed to preserve the allocation ordering of candidates within match runs. 14 Bertsimas et al 7 have modeled continuous distribution similarly to our MELD-Distance score, using MELD/OPOM with a penalty for donorrecipient distance and maintaining the allocation circle of 600 NM radius as a geographic boundary for prioritizing status 1 patients.…”

“…Our CAS for liver allocation was designed using simulation with optimization to be minimally disruptive to all other priorities in the existing system while eliminating geographic boundaries. Previously, optimization methods were used to redesign district boundaries 10‐12 for liver distribution and design geographically heterogeneous circular distribution 13 . Stewart et al.…”

Geographic disparities in transplantation

“…It is paramount that changes to allocation policy should enhance transparency and allow for re-evaluation of models and rules used. In this regard, a positive aspect of this new system is the flexibility for future adjustments [40,56]. A recent study has already suggested a refinement, by using heterogeneous instead of fixed circles to further reduce geographic disparity [56].…”