Efficiency in Lung Transplant Allocation Strategies

Currently in the United States, lungs are allocated to transplant candidates based on the Lung Allocation Score (LAS). The LAS is an empirically derived score aimed at increasing total life span pre- and post-transplantation, for patients on lung transplant waiting lists. The goal here is to develop efficient allocation strategies in the context of lung transplantation. In this study, patient and organ arrivals to the waiting list are modeled as independent homogeneous Poisson processes. Patients' health status prior to allocations are modeled as evolving according to independent and identically distributed finite-state inhomogeneous Markov processes, in which death is treated as an absorbing state. The expected post-transplantation residual life is modeled as depending on time on the waiting list and on current health status. For allocation strategies satisfying certain minimal fairness requirements, the long-term limit of expected average total life exists, and is used as the standard for comparing allocation strategies. Via the Hamilton-Jacobi-Bellman equations, upper bounds as a function of the ratio of organ arrival rate to the patient arrival rate for the long-term expected average total life are derived, and corresponding to each upper bound is an allocable set of (state, time) pairs at which patients would be optimally transplanted. As availability of organs increases, the allocable set expands monotonically, and ranking members of the waiting list according to the availability at which they enter the allocable set provides an allocation strategy that leads to long-term expected average total life close to the upper bound. Simulation studies are conducted with model parameters estimated from national lung transplantation data from United Network for Organ Sharing (UNOS). Results suggest that compared to the LAS, the proposed allocation strategy could provide a 7% increase in average total life.