Statistics in Biosciences

, Volume 6, Issue 1, pp 85–104 | Cite as

Optimal Decisions for Organ Exchanges in a Kidney Paired Donation Program

  • Yijiang LiEmail author
  • Peter X.-K. Song
  • Yan Zhou
  • Alan B. Leichtman
  • Michael A. Rees
  • John D. Kalbfleisch


The traditional concept of barter exchange in economics has been extended in the modern era to the area of living-donor kidney transplantation, where one incompatible donor-candidate pair is matched to another pair with a complementary incompatibility, such that the donor from one pair gives an organ to a compatible candidate in the other pair and vice versa. Kidney paired donation (KPD) programs provide a unique and important platform for living incompatible donor-candidate pairs to exchange organs in order to achieve mutual benefit. In this paper, we propose novel organ allocation strategies to arrange kidney exchanges under uncertainties with advantages, including (i) allowance for a general utility-based evaluation of potential kidney transplants and an explicit consideration of stochastic features inherent in a KPD program; and (ii) exploitation of possible alternative exchanges when the originally planned allocation cannot be fully executed. This allocation strategy is implemented using an integer programming (IP) formulation, and its implication is assessed via a data-based simulation system by tracking an evolving KPD program over a series of match runs. Extensive simulation studies are provided to illustrate our proposed approach.


Decision under uncertainty Expected utility Integer programming Probabilistic modeling Organ exchanges 



The authors thank the support from the Michigan Institute for Clinical and Health Research (MICHR), Michigan School of Public Health, Scientific Registry of Transplant Recipients, and National Institute of General Medical Sciences (NIGMS). The authors are also grateful for invaluable suggestions and comments from Drs. Yanhua Chen, David Abraham and Tuomas Sandholm. The authors would like to thank an anonymous referee whose comments helped to improve this manuscript. This work was supported in part by a grant from the National Institutes of Health (NIH) CTSA at the University of Michigan 2UL1TR000433-06 and by the NIH grant 1R01-DK093513.


  1. 1.
    Abraham DJ, Blum A, Sandholm T (2007) Clearing algorithms for barter exchange markets: enabling nationwide kidney exchanges. In: Ec’07: proceedings of the eighth annual conference on electronic commerce, pp 295–304 CrossRefGoogle Scholar
  2. 2.
    Edmonds J (1965) Paths, trees, and flowers. Can J Math 17:449–467 CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Evans RW, Manninen DL, Garrison LP, Hart LG, Blagg CR, Gutman RA, Hull AR, Lowrie EG (1985) The quality of life of patients with end-stage renal disease. N Engl J Med 312(9):553–559 CrossRefGoogle Scholar
  4. 4.
    Hariharan S, Johnson CP, Bresnahan BA, Taranto SE, McIntosh MJ, Stablein D (2000) Improved graft survival after renal transplantation in the United States, 1988 to 1996. N Engl J Med 342(9):605–612 CrossRefGoogle Scholar
  5. 5.
    Keizer KM, de Klerk M, Haase-Kromwijk BJJM, Weimar W (2005) The Dutch algorithm for allocation in living donor kidney exchange. Transplant Proc 37(2):589–591 CrossRefGoogle Scholar
  6. 6.
    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):235–242 CrossRefGoogle Scholar
  7. 7.
    Maiers M, Gragert L, Klitz W (2007) High-resolution hla alleles and haplotypes in the United States population. Hum Immunol 68(9):779–788 CrossRefGoogle Scholar
  8. 8.
    Park K, Moon JI, Kim SI, Kim YS (1999) Exchange donor program in kidney transplantation. Transplantation 67(2):336–338 CrossRefGoogle Scholar
  9. 9.
    Rapaport FT (1986) The case for a living emotionally related international kidney donor exchange registry. Transplant Proc 18:5–9 Google Scholar
  10. 10.
    Rees MA, Kopke JE, Pelletier RP, Segev DL, Rutter ME, Fabrega AJ, Rogers J, Pankewycz OG, Hiller J, Roth AE, Sandholm T, Ünver MU, Montgomery RA (2009) A nonsimultaneous, extended, altruistic-donor chain. N Engl J Med 360(11):1096–1101 CrossRefGoogle Scholar
  11. 11.
    Ross LF, Rubin DT, Siegler M, Josephson MA, Thistlethwaite JR, Woodle ES (1997) Ethics of a paired-kidney-exchange program. N Engl J Med 336(24):1752–1755 CrossRefGoogle Scholar
  12. 12.
    Roth AE, Sönmez T, Ünver MU (2004) Kidney exchange. Q J Econ 119(2):457–488 CrossRefzbMATHGoogle Scholar
  13. 13.
    Roth AE, Sönmez T, Ünver MU (2005) A kidney exchange clearinghouse in new England. Am Econ Rev 95(2):376–380 CrossRefGoogle Scholar
  14. 14.
    Roth AE, Sönmez T, Ünver MU (2007) Efficient kidney exchange: coincidence of wants in markets with compatibility-based preferences. Am Econ Rev 97(3):828–851 CrossRefGoogle Scholar
  15. 15.
    Russell JD, Beecroft ML, Ludwin D, Churchill DN (1992) The quality of life in renal transplantation—a prospective study. Transplantation 54(4):656–660 CrossRefGoogle Scholar
  16. 16.
    Schaubel DE, Wolfe RA, Port FK (2006) A sequential stratification method for estimating the effect of a time-dependent experimental treatment in observational studies. Biometrics 62(3):910–917 CrossRefMathSciNetGoogle Scholar
  17. 17.
    Schaubel DE, Wolfe RA, Sima CS, Merion RM (2009) Estimating the effect of a time-dependent treatment by levels of an internal time-dependent covariate: application to the contrast between liver wait-list and posttransplant mortality. J Am Stat Assoc 104(485):49–59 CrossRefMathSciNetGoogle Scholar
  18. 18.
    Segev DL, Gentry SE, Warren DS, Reel B, Montgomery RA (2005) Kidney paired donation and optimizing the use of live donor organs. J Am Med Assoc 293(15):1883–1890 CrossRefGoogle Scholar
  19. 19.
    Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1(1):23–37 CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Terasaki PI, Cecka JM, Gjertson DW, Takemoto S (1995) High survival rates of kidney-transplants from spousal and living unrelated donors. N Engl J Med 333(6):333–336 CrossRefGoogle Scholar
  21. 21.
    Wolfe RA, Ashby VB, Milford EL, Ojo AO, Ettenger RE, Agodoa LYC, Held PJ, Port FK (1999) Comparison of mortality in all patients on dialysis, patients on dialysis awaiting transplantation, and recipients of a first cadaveric transplant. N Engl J Med 341(23):1725–1730 CrossRefGoogle Scholar
  22. 22.
    Wolfe RA, McCullough KP, Schaubel DE, Kalbfleisch JD, Murray S, Stegall MD, Leichtman AB (2008) Calculating life years from transplant (lyft): methods for kidney and kidney-pancreas candidates. Am J Transplant 8(4p2):997–1011 CrossRefGoogle Scholar

Copyright information

© International Chinese Statistical Association 2013

Authors and Affiliations

  • Yijiang Li
    • 1
    Email author
  • Peter X.-K. Song
    • 2
  • Yan Zhou
    • 2
  • Alan B. Leichtman
    • 3
  • Michael A. Rees
    • 4
  • John D. Kalbfleisch
    • 2
  1. 1.Google Inc.Mountain ViewUSA
  2. 2.Department of BiostatisticsUniversity of MichiganAnn ArborUSA
  3. 3.Department of Internal MedicineUniversity of MichiganAnn ArborUSA
  4. 4.Department of UrologyUniversity of Toledo Medical CenterToledoUSA

Personalised recommendations