An Operations Management Framework to Improve Geographic Equity in Liver Transplantation

Abstract

In the United States (U.S.), on average three people die every day awaiting a liver transplant for a total of 1,133 lives lost in 2021. While 13,439 patients were added to the waiting list in 2021, only 9,236 patients received liver transplantation. To make matters worse, there is significant geographic disparity across the U.S. in transplant candidate access to deceased donor organs. The U.S. Department of Health and Human Services (HHS) is keen to improve transplant policy to mitigate these disparities. The deceased donor liver allocation policy has been through three major implementations in the last nine years, but yet the issue persists. This dissertation seeks to apply operations management models to (i) understand transplant candidate behavior, and (ii) suggest improvements to transplant policy that mitigate geographic disparity. In the first essay, we focus on reducing disparities in the organ supply to candidate demand (s/d) ratios across transplant centers. We develop a nonlinear integer programming model that allocates organ supply to maximize the minimum s/d ratios across all transplant centers. We focus on circular donation regions that address legal issues raised with earlier organ distribution frameworks. This enables reformulating our model as a set-partitioning problem and our proposal can be viewed as a heterogeneous donor circle policy. Compared to the current Acuity Circles policy that has fixed radius circles around donation locations, the heterogeneous donor circle policy greatly improves both the worst s/d ratio, and the range of s/d ratios. With the fixed radius policy of 500 nautical miles (NM) the s/d ratio ranges from 0.37 to 0.84 at transplant centers, while with the heterogeneous circle policy capped at a maximum radius of 500NM the s/d ratio ranges from 0.55 to 0.60, closely matching the national s/d ratio of 0.5983. Broader sharing of organs is believed to mitigate geographic disparity. Recent policies are moving towards broader sharing in principle. In the second essay, we develop a patient's dynamic choice model to analyze her strategic response to a policy change. First, we study the impact of the Share 35 policy, a variant of broader sharing introduced in 2013, on the behavioral change of patients at the transplant centers (i.e., change in their organ acceptance probability), geographic equity, and efficiency (transplant quality, offer refusals, survival benefit from a transplant, and organ travel distance). We find that sicker patients became more selective in accepting organs (acceptance probability decreased) under the Share 35 policy. Second, we study the current Acuity Circles policy and conclude that it would result in lower efficiency (more offer refusals and a lower transplant benefit) than the previous Share 35 policy. Finally, we show that broader sharing in its current form may not be the best strategy to balance geographic equity and efficiency. The intuition is that by indiscriminately enlarging the pool of supply locations from where patients can receive offers, they tend to become more selective, resulting in more offer rejections and less efficiency. We illustrate that the heterogeneous donor circles policy that equalizes the s/d ratios across geographies is better than Acuity Circles in achieving geographic equity at the lowest trade-off on efficiency metrics. The previous two essays demonstrate the benefit of equalizing the s/d ratios across geographies. In December 2018 the Organ Procurement and Transplantation Network (OPTN) Board of Directors approved the continuous distribution framework as the desired policy goal for all the organ allocation systems. In this framework, the waiting list candidates will be prioritized based on several factors, each contributing some points towards the total score of a candidate. The factors in consideration are medical severity, expected post-transplant outcome, the efficient management of organ placement, and equity. However, the respective weights for each of these potential factors are not yet decided. In the third essay, we consider two factors, medical severity and the efficient management of organ placement (captured using the distance between the donor hospital and transplant center), and we design an allocation policy that maximizes the geographic equity. We develop a mathematical model to calculate the s/d ratio of deceased-donor organs at a transplant center in a continuous scoring framework of organ allocation policy. We then formulate a set-partitioning optimization problem and test our proposals using simulation. Our experiments suggest that reducing inherent differences in s/d ratios at the transplant centers result in saving lives and reduced geographic disparity.