Proportionally fair organ transplantation allocation rules

We introduce a new fairness measure for designing organ allocation rules for transplantation. In particular, we apply the proportional fairness measure for organ transplantation whose solution can be interpreted as the solution to the Nash bargaining problem for sharing limited donor organs among patients who seek to maximize their Quality-Adjusted Life-Years (QALYs). The motivation arises from several observations that current measures of fairness induce significant inefficiencies in terms of total QALYs of the patient population. We use the asymptotic results for the fluid approximation of a transplant queuing system to estimate the expected utility of patients and formulate an optimization problem where the decision maker partitions the set of organ types to achieve a proportionally fair objective. We use an achievable region approach to transform our formulation to an alternative optimization problem and show that the optimal allocation policy under the proportional fairness measure is assortative, which has the following insight: higher quality organs are allocated to patients who will have higher expected QALYs. We compare the performance of allocation rules developed for fairness purposes in organ allocation along with our proposed policy via a validated simulation model for heart transplantation in the US.