# Efficiency in Lung Transplant Allocation Strategies

## TL;DR

This paper develops a new framework for lung transplant allocation that models patient and organ dynamics to optimize long-term patient survival, outperforming the current LAS system.

## Contribution

It introduces a comprehensive stochastic model and an optimal allocation strategy that significantly improves patient life expectancy over existing methods.

## Key findings

- Proposed strategy increases average total life by 7.7% compared to LAS.
- Model accurately predicts optimal transplant timing based on patient health and organ availability.
- Simulation results validate the effectiveness of the new allocation approach.

## Abstract

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.