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Valuing Sets of Potential Transplants in a Kidney Paired Donation Network

Author

Listed:
  • Mathieu Bray

    (University of Michigan)

  • Wen Wang

    (University of Michigan)

  • Peter X.-K. Song

    (University of Michigan)

  • John D. Kalbfleisch

    (University of Michigan
    University of Michigan)

Abstract

In kidney paired donation (KPD), incompatible donor–candidate pairs and non-directed (also known as altruistic) donors are pooled together with the aim of maximizing the total utility of transplants realized via donor exchanges. We consider a setting in which disjoint sets of potential transplants are selected at regular intervals, with fallback options available within each proposed set in the case of individual donor, candidate, or match failure. We develop methods for calculating the expected utility for such sets under a realistic probability model for the KPD. Exact expected utility calculations for these sets are compared to estimates based on Monte Carlo samples of the underlying network. Models and methods are extended to include transplant candidates who join KPD with more than one incompatible donor. Microsimulations demonstrate the superiority of accounting for failure probability and fallback options, as well as candidates joining with additional donors, in terms of realized transplants and waiting time for candidates.

Suggested Citation

  • Mathieu Bray & Wen Wang & Peter X.-K. Song & John D. Kalbfleisch, 2018. "Valuing Sets of Potential Transplants in a Kidney Paired Donation Network," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 255-279, April.
    • Handle: RePEc:spr:stabio:v:10:y:2018:i:1:d:10.1007_s12561-018-9214-7
    DOI: 10.1007/s12561-018-9214-7
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    References listed on IDEAS

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    1. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    4. Rees, Michael Kenneth & Kopke, Jonathan E. & Pelletier, Ronald P. & Segev, Dorry L. & Rutter, Matthew E. & Fabrega, Alfredo J. & Rogers, Jeffrey David & Pankewycz, Oleh G. & Hiller, Janet & Roth, Alvi, 2009. "A Nonsimultaneous, Extended, Altruistic-Donor Chain," Scholarly Articles 29408291, Harvard University Department of Economics.
    5. Roth, Alvin E. & Sonmez, Tayfun & Unver, Utku & Delmonico, Francis & Saidman, Susan L., 2014. "Utilizing List Exchange and Non-directed Donation through “Chain” Paired Kidney Donations," MPRA Paper 58246, University Library of Munich, Germany.
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