Statistics in Biosciences

, Volume 10, Issue 1, pp 255–279 | Cite as

Valuing Sets of Potential Transplants in a Kidney Paired Donation Network

  • Mathieu BrayEmail author
  • Wen Wang
  • Peter X.-K. Song
  • John D. Kalbfleisch


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.


Kidney paired donation Organ exchanges Expected utility Network analysis Fallback options Waiting time 



This research was supported by the National Institutes of Diabetes and Digestive and Kidney Diseases (NIDDK) through Grant Number R01-DK093513. We thank the editor and reviewer for their careful reading of the manuscript and their helpful comments and suggestions.


  1. 1.
    Adams PL, Cohen DJ, Danovitch GM, Edington RMD, Gaston RS, Jacobs CL, Luskin RS, Metzger RA, Peters TG, Siminoff LA, Veatch RM, Rothberg-Wegman L, Bartlett ST, Brigham L, Burdick J, Gunderson S, Harmon W, Matas AJ, Thistlethwaite JR, Delmonico FL (2002) The nondirected live-kidney donor: ethical considerations and practice guidelines: a national conference report. Transplantation 74(4):582–590CrossRefGoogle Scholar
  2. 2.
    Alvelos F, Klimentova X, Rais A, Viana A (2016) Maximizing expected number of transplants in kidney exchange programs. Electron Notes Discret Math 52:269–276. MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ashlagi I, Gilchrist DS, Roth AE, Rees MA (2011) Nonsimultaneous chains and dominos in kidney-paired donation—revisited. Am J Transpl 11(5):984–994. CrossRefGoogle Scholar
  4. 4.
    Bray M, Wang W, Song PXK, Leichtman AB, Rees MA, Ashby VB, Eikstadt R, Goulding A, Kalbfleisch JD (2015) Planning for uncertainty and fallbacks can increase the number of transplants in a kidney-paired donation program. Am J Transpl 15(10):2636–2645. CrossRefGoogle Scholar
  5. 5.
    Dickerson JP, Procaccia AD, Sandholm T (2013) Failure-aware kidney exchange. In: Proceedings of the 14th ACM conference on electronic commerce. ACM Press, pp 323–340.
  6. 6.
    Fumo DE, Kapoor V, Reece LJ, Stepkowski SM, Kopke JE, Rees SE, Smith C, Roth AE, Leichtman AB, Rees MA (2015) Historical matching strategies in kidney paired donation: the 7-year evolution of a web-based virtual matching system. Am J Transpl 15(10):2646–2654. CrossRefGoogle Scholar
  7. 7.
    Gentry SE, Montgomery RA, Swihart BJ, Segev DL (2009) The roles of dominos and nonsimultaneous chains in kidney paired donation. Am J Transpl 9(6):1330–1336. CrossRefGoogle Scholar
  8. 8.
    Gurobi Optimization Inc (2017) Gurobi optimizer reference manual.
  9. 9.
    Irwin FD, Bonagura AF, Crawford SW, Foote M (2012) Kidney paired donation: a payer perspective. Am J Transpl 12(6):1388–1391. CrossRefGoogle Scholar
  10. 10.
    Kher A (2016) Allocation based on virtual crossmatch alone: not yet ready for primetime. Am J Transpl 16(12):3577–3577. CrossRefGoogle Scholar
  11. 11.
    Klimentova X, Pedroso JP, Viana A (2016) Maximising expectation of the number of transplants in kidney exchange programmes. Comput Oper Res 73:1–11. MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Laupacis A, Keown P, Pus N, Krueger H, Ferguson B, Wong C, Muirhead N (1996) A study of the quality of life and cost-utility of renal transplantation. Kidney Int 50(1):235–242CrossRefGoogle Scholar
  13. 13.
    Li H, Stegall MD, Dean PG, Casey ET, Reddy KS, Khamash HA, Heilman RL, Mai ML, Taner CB, Kosberg CL, Bakken LL, Wozniak EJ, Giles KL, Veal LA, Gandhi MJ, Cosio FG, Prieto M (2014a) Assessing the efficacy of kidney paired donationperformance of an integrated three-site program. Transplantation 98(3):300–305. CrossRefGoogle Scholar
  14. 14.
    Li Y (2012) Optimization and simulation of kidney paired donation programs. Doctoral dissertation, University of Michigan.
  15. 15.
    Li Y, Song PXK, Zhou Y, Leichtman AB, Rees MA, Kalbfleisch JD (2014b) Optimal decisions for organ exchanges in a kidney paired donation program. Stat Biosci 6(1):85–104. NIHMS150003CrossRefGoogle Scholar
  16. 16.
    Maiers M, Gragert L, Klitz W (2007) High-resolution HLA alleles and haplotypes in the United States population. Hum Immunol 68(9):779–88. CrossRefGoogle Scholar
  17. 17.
    Melcher ML, Veale JL, Javaid B, Leeser DB, Davis CL, Hil G, Milner JE (2013) Kidney transplant chains amplify benefit of nondirected donors. JAMA Surg 148(2):165. CrossRefGoogle Scholar
  18. 18.
    Montgomery RA, Gentry SE, Marks WH, Warren DS, Hiller JM, Houp J, Zachary AA, Melancon JK, Maley WR, Rabb H, Simpkins CE, Segev DL (2006) Domino paired kidney donation: a strategy to make best use of live non-directed donation. The Lancet 368(9533):419–421. CrossRefGoogle Scholar
  19. 19.
    Organ Procurement and Transplantation Network (2017) Reports—national data.
  20. 20.
    Park K, Moon JI, Kim SI, Kim YS (1999) Exchange donor program in kidney transplantation. Transplantation 67(2):336–338. CrossRefGoogle Scholar
  21. 21.
    Pedroso JP (2014) Maximizing size expectation on vertex-disjoint cycle packing. In: Computational Science and its Applications—ICCSA 2014, Springer, Berlin, pp 32–46Google Scholar
  22. 22.
    Rapaport FT (1986) The case for a living emotionally related international kidney donor exchange registry. Transpl Proc 18:5–9Google Scholar
  23. 23.
    Rees MA, Kopke JE, Pelletier RP, Segev DL, Rutter ME, Fabrega AJ, Rogers J, Pankewycz OG, Hiller JM, Roth AE, Sandholm T, Unver MU, Montgomery RA (2009) A nonsimultaneous, extended, altruistic-donor chain. N Engl J Med 360(11):1096–1101. CrossRefGoogle Scholar
  24. 24.
    Roth AE, Sonmez T, Unver MU (2004) Kidney exchange. Q J Econ 119(2):457–488. CrossRefzbMATHGoogle Scholar
  25. 25.
    Roth AE, Sonmez T, Unver MU (2005) Pairwise kidney exchange. J Econ Theory 125(2):151–188. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Roth AE, Sonmez T, Unver MU, Delmonico FL, Saidman SL (2006) Utilizing list exchange and nondirected donation through ’chain’ paired kidney donations. Am J Transpl 6(11):2694–2705. CrossRefGoogle Scholar
  27. 27.
    Roth AE, Sonmez T, Unver MU (2007) Efficient kidney exchange: coincidence of wants in markets with compatibility-based preferences. Am Econ Rev 97(3):828–851. CrossRefGoogle Scholar
  28. 28.
    Wang W, Bray M, Song, Peter X-K, Kalbfleisch JD (2017) Locally Relevant Subgraph Enumeration. Operations Research for Health Care (Submitted)Google Scholar

Copyright information

© International Chinese Statistical Association 2018

Authors and Affiliations

  1. 1.Department of BiostatisticsUniversity of MichiganAnn ArborUSA
  2. 2.Kidney Epidemiology and Cost CenterUniversity of MichiganAnn ArborUSA

Personalised recommendations