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Optimal Control of a Paired-Kidney Exchange Program

Author

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  • Stefanos A. Zenios

    (Graduate School of Business, Stanford University, Stanford, California 94305)

Abstract

Organ exchanges are expected to increase the utilization of living donors and to alleviate the critical shortage of organs for transplantation. The typical arrangement involves a direct exchange between two blood-type incompatible donor-candidate pairs. 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 focuses on the mix of direct and indirect exchanges that maximizes the expected total discounted quality-adjusted life years (QALY) of the candidates in the participating pairs. Direct exchanges are preferable because the candidate receives a living-donor organ instead of the inferior cadaveric organ an indirect exchange provides. However, the latter involves a shorter wait. To capture this tradeoff, we develop a double-ended queueing model for an exchange system with two types of donorcandidate 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 system 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 a variety of assumptions about the objective function, including one of complete candidate autonomy. The analysis identifies three design principles that will amplify the likelihood of an exchange program's success. First, exchange programs must involve the coordinated activities of multiple local transplant centers to enjoy the substantial benefits of resource pooling. Second, participant wait must be controlled through indirect exchanges. Third, the program must respect participants' autonomy and weigh that autonomy against the broader goal of maximizing their overall welfare.

Suggested Citation

  • Stefanos A. Zenios, 2002. "Optimal Control of a Paired-Kidney Exchange Program," Management Science, INFORMS, vol. 48(3), pages 328-342, March.
    • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:3:p:328-342
    DOI: 10.1287/mnsc.48.3.328.7732
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    References listed on IDEAS

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    1. J. Michael Harrison & Michael I. Taksar, 1983. "Instantaneous Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 439-453, August.
    2. Stefanos A. Zenios & Glenn M. Chertow & Lawrence M. Wein, 2000. "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," Operations Research, INFORMS, vol. 48(4), pages 549-569, August.
    3. Zenios, Stefanos & Woodle, E. Steve & Ross, Lainie Friedman, 2001. "Primum Non Nocere: Avoiding Harm to Vulnerable Wait List Candidates in an Indirect Kidney Exchange," Research Papers 1684, Stanford University, Graduate School of Business.
    4. Lode Li, 1988. "A Stochastic Theory of the Firm," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 447-466, August.
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    4. Alireza Sabouri & Woonghee Tim Huh & Steven M. Shechter, 2017. "Screening Strategies for Patients on the Kidney Transplant Waiting List," Operations Research, INFORMS, vol. 65(5), pages 1131-1146, October.
    5. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    6. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Choosing Among Living-Donor and Cadaveric Livers," Management Science, INFORMS, vol. 53(11), pages 1702-1715, November.
    7. Panayotis Mertikopoulos & Heinrich H. Nax & Bary S. R. Pradelski, 2019. "Quick or cheap? Breaking points in dynamic markets," ECON - Working Papers 338, Department of Economics - University of Zurich.
    8. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
    9. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    10. Yılmaz, Özgür, 2014. "Kidney exchange: Further utilization of donors via listed exchange," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 178-186.
    11. Zahra Gharibi & Michael Hahsler, 2021. "A Simulation-Based Optimization Model to Study the Impact of Multiple-Region Listing and Information Sharing on Kidney Transplant Outcomes," IJERPH, MDPI, vol. 18(3), pages 1-20, January.
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    13. Katarína Cechlárová & Martina Hančová & Diana Plačková & Tatiana Baltesová, 2021. "Stochastic modelling and simulation of a kidney transplant waiting list," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 909-931, September.
    14. Burhaneddin Sandıkçı & Lisa M. Maillart & Andrew J. Schaefer & Oguzhan Alagoz & Mark S. Roberts, 2008. "Estimating the Patient's Price of Privacy in Liver Transplantation," Operations Research, INFORMS, vol. 56(6), pages 1393-1410, December.
    15. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2013. "Fairness, Efficiency, and Flexibility in Organ Allocation for Kidney Transplantation," Operations Research, INFORMS, vol. 61(1), pages 73-87, February.
    16. Barış Ata & Anton Skaro & Sridhar Tayur, 2017. "OrganJet: Overcoming Geographical Disparities in Access to Deceased Donor Kidneys in the United States," Management Science, INFORMS, vol. 63(9), pages 2776-2794, September.
    17. Murat Kurt & Mark S. Roberts & Andrew J. Schaefer & M. Utku Ünver, 2011. "Valuing Prearranged Paired Kidney Exchanges: A Stochastic Game Approach," Boston College Working Papers in Economics 785, Boston College Department of Economics, revised 14 Oct 2011.
    18. Marc Bollecker & Wilfrid Azan, 2008. "Les frontières de la recherche en contrôle de gestion : une analyse des cadres théoriques mobilisés," Post-Print halshs-00522395, HAL.
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