Currently in the United States, lung transplantations are allocated to candidates according to each candidate’s 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 expectancies 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 (state, time) 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 extend the results to the allocation and matching of multiple organ types.

中文翻译：

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肺移植分配策略的效率

当前在美国，根据每个候选人的肺分配分数（LAS）将肺移植分配给候选人。LAS是针对患者移植优先级的特设排名系统。这项研究的目的是在肺移植等待名单的综合模型的基础上，为改善患者的预期寿命建立一个框架。将患者和器官建模为根据Poisson过程到达的状态，患者的健康状况会演变成不均匀的马尔可夫过程的等待时间，直到死亡或移植为止，器官接受者的预期移植后剩余寿命取决于移植时的等待时间和健康状况。在满足最低公平要求的分配规则下，长期平均预期寿命会收敛，其极限是比较分配策略的自然标准。通过汉密尔顿-雅各比-贝尔曼方程，可以得出器官平均预期寿命的上限。与每个上限相对应的是一组（状态，时间）对的可分配集合，可以在该集合上对患者进行最佳移植。可分配的集合随着器官可用性的增加而单调扩展，这刺激了分配策略的发展，从而导致长期预期寿命接近上限。使用根据国家肺移植数据估算的模型参数进行模拟研究。结果表明，与LAS相比，拟议的分配策略可以使平均总寿命增加7.7％。我们进一步将结果扩展到多种器官类型的分配和匹配。