Dynamic Exception Points for Fair Liver Allocation

Problem Definition: There are disparities in access to livers based on transplant patients’ height - which disproportionately affects women across ethnicities, in addition to Hispanics and Asians broadly - as they can receive transplants from a smaller pool of available deceased donors for medical reasons. Reduced likelihood of transplantation leads to higher mortality rates and longer waiting times. Remedying this unfairness is a top priority for United Network for Organ Sharing (UNOS), the policy making entity in the US.

Academic/Practical Relevance: We analyze fairness within the current US liver allocation system where patients on the waiting list receive priority, dynamically, based on their Model for End-Stage Liver Disease (MELD) scores, which reflect the severity of liver disease. We propose a simple adjustment - providing additional (exception) points based on height and MELD score - that can be easily implemented in practice, which materially reduces the disparity without sacrificing overall efficiency.

Methodology: We model the liver allocation system as a multiclass fluid model of overloaded queues with multiple heterogeneous servers, which captures the disease evolution by allowing the patients to switch between classes over time, e.g. patients waiting for transplantation may get sicker/better, or may die. We impose explicit equity constraints based on height. We characterize the optimal solution to the fluid model under the objective of minimizing pre-transplant mortality using the duality framework for optimal control problems. The discretized version of the optimal policy is numerically solved using estimates from clinical data. A detailed simulation study demonstrates the effectiveness of the proposed policies.

Results: We show that the optimal policy, called the Equity Adjusted Mortality Risk Policy, is an intuitive dynamic index policy, where the indices depend on patients’ acceptance probabilities of the organ offers, mortality risks, and the shadow prices calculated from the dual dynamical system. This optimal policy advocates ranking patients based on their short-term mortality risk adjusted for equity among static (i.e., height) classes. The shadow prices of the equity constraints in the optimal control problem are novel in the organ transplant context, as is, even more importantly, their interpretation as MELD exception points, since they can be mapped seamlessly into the system already in practice. Providing these exception points to shorter patients dynamically increases their chances of receiving a transplant. Our simulations show that for women, the disparity can be almost completely eliminated. Hispanics and Asians greatly benefit from receiving these MELD exception points as well. These improved fairness can be achieved without decreasing the overall efficiency of the current liver allocation system.