Optimal Control of a Paired-Kidney Exchange Program

Professor Stefanos Zenios

Graduate School of Business

Stanford University

Organ exchanges are expected to increase the utilization of living donors and to alleviate the critical shortage of organs for transplantation. The typical arrangement is a direct exchange between two pairs of blood-type incompatible donors-recipients. An alternate possibility is an indirect exchange between one such pair and the highest-priority candidate on the regular waiting list for cadaveric organs. This paper is concerned with the mix of direct and indirect exchanges that maximizes the expected total discounted quality-adjusted life years of the recipients in the participating pairs. Direct exchanges are preferable because the recipient in the participating pair receives an organ from a living donor as opposed to an inferior cadaveric organ she would have received in an indirect exchange. However, the latter involve a shorter wait. To capture this trade-off, we develop a double-ended queueing model for an exchange system with two types of donor-recipient pairs, and obtain an optimal dynamic exchange policy by invoking a Brownian approximation. The policy takes the form of a two-sided regulator in which new pairs will join the exchange pool to wait for a direct exchange if and only if the process modeling the exchange system is within the regulator's two barriers. In all other circumstances, new pairs will participate in an indirect exchange. Expressions for the optimal barriers are obtained under different complementary assumptions about the objective function. These expressions depend on the exchange system's physical and behavioral parameters. The physical parameters are the pair arrival rates and the quality of life scores associated with living and cadaveric organs. The behavioral parameters include the weights assigned to the preferences of the different parties participating in the exchange system and the discount rate for future health outcomes.