Dynamic Exception Points for Fair Liver Allocation

There are disparities in access to livers based on transplant patients’ height, which disproportionately affects Hispanics, Asians, and women (across all ethnicities), because short patients 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. We analyze fairness within the current U.S. liver allocation system where patients 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. We model the liver allocation system as a multiclass fluid model of overloaded queues with heterogeneous servers. We impose explicit equity constraints for all static patient classes, that is, height. We characterize the optimal solution under the objective of minimizing pretransplant mortality. The discretized version of the optimal policy is numerically solved using estimates from clinical data and a detailed simulation study demonstrates its effectiveness. The optimal policy, called the equity adjusted mortality risk policy, advocates ranking patients based on their short-term mortality risk adjusted for equity among height classes. Interpretation of the shadow prices of equity constraints in the optimal control problem as MELD exception points is novel in the transplant context since they can be seamlessly mapped into the existing system. Our simulations show that for women, the disparity can be almost completely eliminated. Hispanics and Asians greatly benefit from receiving these MELD exception points also. Our work provides a remedy to reduce the disparities in access to liver transplantation within the MELD-based allocation. Our approach can help the on-going analysis of the continuous distribution model for livers because it also considers aspects of candidate biology, notably height and body surface area.