  Currently in the United States, lung transplantations are allocated to
candidates according to the candidates' Lung Allocation Score (LAS). The LAS is
an ad-hoc ranking system for patients' priorities of transplantation. The goal
of this study is to develop a framework for improving patients' life expectancy
over the LAS based on a comprehensive modeling of the lung transplantation
waiting list. Patients and organs are modeled as arriving according to Poisson
processes, patients' health status evolving a waiting time inhomogeneous Markov
process until death or transplantation, with organ recipient's expected
post-transplant residual life depending on waiting time and health status at
transplantation. Under allocation rules satisfying minimal fairness
requirements, the long-term average expected life converges, and its limit is a
natural standard for comparing allocation strategies. Via the
Hamilton-Jacobi-Bellman equations, upper bounds for the limiting average
expected life are derived as a function of organ availability. Corresponding to
each upper bound is an allocable set of (time, state) pairs at which patients
would be optimally transplanted. The allocable set expands monotonically as
organ availability increases, which motivates the development of an allocation
strategy that leads to long-term expected life close to the upper bound.
Simulation studies are conducted with model parameters estimated from national
lung transplantation data. Results suggest that compared to the LAS, the
proposed allocation strategy could provide a 7.7% increase in average total
life. We further extended the results to the the allocation and matching of
multiple organ types.
