Gerrymandering for Justice: Redistricting U.S. Liver Allocation

Abstract

U.S. organ allocation policy sequesters livers from deceased donors within arbitrary geographic boundaries, frustrating the intent of those who wish to offer the livers to transplant candidates based on medical urgency. We used a zero-one integer program to partition 58 donor service areas into between four and eight sharing districts that minimize the disparity in liver availability among districts. Because the integer program necessarily suppressed clinically significant differences among patients and organs, we tested the optimized district maps with a discrete-event simulation tool that represents liver allocation at a per-person, per-organ level of detail. In April 2014, the liver committee of the Organ Procurement and Transplantation Network (OPTN) decided in a unanimous vote of 22-0-0 to write a policy proposal based on our eight-district and four-district maps. The OPTN board of directors could implement the policy after the proposal and public-comment period.Redistricting liver allocation would save hundreds of lives over the next five years and would attenuate the serious geographic inequity in liver transplant offers.

Keywords: healthcare; liver; location allocation; redistricting; set partitioning; transplantation; zero-one integer programming.

Figure 1:

The current liver allocation system includes 11 regions, as the shadings represent. The regions reflect historical relationships among early transplant centers and were not designed to achieve any allocation goal(s). Alaska, Hawaii, and Puerto Rico are shown in separate frames in this map and in the maps in Figures 2–5 and Figures 7 and 8.

Figure 2:

Of the 58 local DSAs in the United States, several are defined as unions of noncontiguous geographic blocks.

Figure 3:

Minimizing disparity in liver allocation using four organ-sharing districts yields these districts.

Figure 4:

Minimizing disparity in liver allocation using eight organ-sharing districts yields these districts.

Figure 5:

Policy makers use the LSAM to compare alternative organ allocation schemes.

Figure 6:

For district plans with varying numbers of districts and varying upper bounds on transport time, the range of values over 10 simulations of the sample standard deviation of median MELD score at transplant overlaps to a significant extent for redistricted plans. The exceptions are the district plans with a 2.5-hour transport limit, which appears to be too short to provide equitable allocation. Note. Abbreviation: dct represents number of districts. These infeasible combinations are not shown: four, five, and six districts with 2.5-hour transport-time limit.

Figure 7:

Compared to current local allocation (left), a redistricting plan with four districts (right) markedly reduces geographic disparity in the median MELD score at which candidates are offered transplants.

Figure 8:

Compared to current local allocation (left), a redistricting plan with eight districts (right) markedly reduces geographic disparity in the median MELD score at which candidates are offered transplants.