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September 2020 Efficiency in lung transplant allocation strategies
Jingjing Zou, David J. Lederer, Daniel Rabinowitz
Ann. Appl. Stat. 14(3): 1088-1121 (September 2020). DOI: 10.1214/20-AOAS1350

Abstract

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.

Citation

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Jingjing Zou. David J. Lederer. Daniel Rabinowitz. "Efficiency in lung transplant allocation strategies." Ann. Appl. Stat. 14 (3) 1088 - 1121, September 2020. https://doi.org/10.1214/20-AOAS1350

Information

Received: 1 December 2018; Revised: 1 April 2020; Published: September 2020
First available in Project Euclid: 18 September 2020

MathSciNet: MR4152125
Digital Object Identifier: 10.1214/20-AOAS1350

Keywords: allocation rules , Hamilton–Jacobi–Bellman equations , lung allocation score (LAS) , Lung transplantation , Markov decision models , simulation studies

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September 2020
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