Redesigning liver allocation regions through optimization

Abstract

End-stage liver disease is one of the leading causes of death in the United States, and the only viable treatment is liver transplantation. Since the quality of a donor liver decreases with transportation time, United States organ policy prioritizes transplants within geographic regions. However, the boundaries of these regions were defined mostly by informal relationships between transplant centers many decades ago, which has created local imbalances in supply and demand. As a result, candidates on the waiting list for donor livers face drastically different odds of receiving a transplant. Policy makers have noticed this geographic inequity and are considering proposals for alternative liver allocation approaches. This thesis uses mathematical optimization to redesign liver allocation regions by modeling and including several key elements of the allocation process directly in the optimization formulation. Specifically, we use a fluid approximation to model the dynamics of the wait-list progression and liver allocation. The model is fit using historical data of wait-list candidates and donors. Then, we propose two optimization formulations to reduce geographic inequality. The first directly minimizes the variation in median level of illness at the time of transplant across geographical areas, which is a key metric used by policy makers in addressing geographic inequality. The second approach minimizes the liver transport distance, subject to a certain allowable level of geographic variation. We discuss how these models can flexibly incorporate additional policy constraints to create more realistic models to reduce geographic variation. The region configurations are evaluated on key metrics relating to fairness and system efficiency using a standardized, validated, simulation approach widely accepted by policymakers. Finally, we propose a region design that significantly reduces geographic inequality without any substantial impact on the system's efficiency.