Optimizing Liver Allocation System Incorporating Disease Evolution

We propose an efficient liver allocation system for allocating donated organs to patients waiting for transplantation, the only viable treatment for End-Stage Liver Disease. We optimize two metrics which are used to measure the efficiency: total quality adjusted life years and the number of organs wasted due to patients rejecting some organ offers. Our model incorporates the possibility that the patients may turn down the organ offers. Given the scarcity of available organs relative to the number patients waiting for transplantation, we model the system as a multiclass fluid model of overloaded queues. The fluid model we advance captures the disease evolution over time by allowing the patients to switch between classes over time, e.g. patients waiting for transplantation may get sicker/better, or may die. We characterize the optimal solution to the fluid model using the duality framework for optimal control problems developed by Rockafellar (1970a). The optimal solution for assigning livers to patients is an intuitive dynamic index policy, where the indices depend on patients' acceptance probabilities of the organ offer, immediate rewards, and the shadow prices calculated from the dual dynamical system. Finally, we perform a detailed simulation study to demonstrate the effectiveness of the proposed policy using data from the United Network for Organ Sharing System (UNOS).