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Valuing Sets of Potential Transplants in a Kidney Paired Donation Network

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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.

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Notes

  1. Please refer to the Appendix for a complete list of notation used in this manuscript.

References

  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):582–590

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.endm.2016.03.036

    Article  MathSciNet  MATH  Google Scholar 

  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. https://doi.org/10.1111/j.1600-6143.2011.03481.x

    Article  Google Scholar 

  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. https://doi.org/10.1111/ajt.13413

    Article  Google Scholar 

  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. https://doi.org/10.1145/2482540.2482596

  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. https://doi.org/10.1111/ajt.13337

    Article  Google Scholar 

  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. https://doi.org/10.1111/j.1600-6143.2009.02622.x

    Article  Google Scholar 

  8. Gurobi Optimization Inc (2017) Gurobi optimizer reference manual. http://www.gurobi.com

  9. Irwin FD, Bonagura AF, Crawford SW, Foote M (2012) Kidney paired donation: a payer perspective. Am J Transpl 12(6):1388–1391. https://doi.org/10.1111/j.1600-6143.2012.03998.x

    Article  Google Scholar 

  10. Kher A (2016) Allocation based on virtual crossmatch alone: not yet ready for primetime. Am J Transpl 16(12):3577–3577. https://doi.org/10.1111/ajt.13992

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.cor.2016.03.004

    Article  MathSciNet  MATH  Google Scholar 

  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):235–242

    Article  Google Scholar 

  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. https://doi.org/10.1097/TP.0000000000000054

    Article  Google Scholar 

  14. Li Y (2012) Optimization and simulation of kidney paired donation programs. Doctoral dissertation, University of Michigan. https://deepblue.lib.umich.edu/handle/2027.42/96069

  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. https://doi.org/10.1007/s12561-013-9082-0 NIHMS150003

    Article  Google Scholar 

  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. https://doi.org/10.1016/j.humimm.2007.04.005

    Article  Google Scholar 

  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. https://doi.org/10.1001/2013.jamasurg.25

    Article  Google Scholar 

  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. https://doi.org/10.1016/S0140-6736(06)69115-0

    Article  Google Scholar 

  19. Organ Procurement and Transplantation Network (2017) Reports—national data. https://optn.transplant.hrsa.gov/data/view-data-reports/national-data/

  20. Park K, Moon JI, Kim SI, Kim YS (1999) Exchange donor program in kidney transplantation. Transplantation 67(2):336–338. https://doi.org/10.1097/00007890-199901270-00027

    Article  Google Scholar 

  21. Pedroso JP (2014) Maximizing size expectation on vertex-disjoint cycle packing. In: Computational Science and its Applications—ICCSA 2014, Springer, Berlin, pp 32–46

  22. Rapaport FT (1986) The case for a living emotionally related international kidney donor exchange registry. Transpl Proc 18:5–9

    Google Scholar 

  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. https://doi.org/10.1056/NEJMoa0803645

    Article  Google Scholar 

  24. Roth AE, Sonmez T, Unver MU (2004) Kidney exchange. Q J Econ 119(2):457–488. https://doi.org/10.1162/0033553041382157

    Article  MATH  Google Scholar 

  25. Roth AE, Sonmez T, Unver MU (2005) Pairwise kidney exchange. J Econ Theory 125(2):151–188. https://doi.org/10.1016/j.jet.2005.04.004

    Article  MathSciNet  MATH  Google Scholar 

  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. https://doi.org/10.1111/j.1600-6143.2006.01515.x

    Article  Google Scholar 

  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. https://doi.org/10.1257/aer.97.3.828

    Article  Google Scholar 

  28. Wang W, Bray M, Song, Peter X-K, Kalbfleisch JD (2017) Locally Relevant Subgraph Enumeration. Operations Research for Health Care (Submitted)

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Biostatistics, University of Michigan, Ann Arbor, MI, USA

    Mathieu Bray, Wen Wang, Peter X.-K. Song & John D. Kalbfleisch

  2. Kidney Epidemiology and Cost Center, University of Michigan, Ann Arbor, MI, USA

    John D. Kalbfleisch

Authors
  1. Mathieu Bray
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  2. Wen Wang
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  3. Peter X.-K. Song
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  4. John D. Kalbfleisch
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Corresponding author

Correspondence to Mathieu Bray.

Appendix: Glossary and Notation

Appendix: Glossary and Notation

We include a glossary of terms in Table 6, as well as a list of notation used in Table 7, in the order of appearance in the text.

Table 6 Glossary of terms
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Table 7 Notation
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Bray, M., Wang, W., Song, P.XK. et al. Valuing Sets of Potential Transplants in a Kidney Paired Donation Network. Stat Biosci 10, 255–279 (2018). https://doi.org/10.1007/s12561-018-9214-7

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  • DOI: https://doi.org/10.1007/s12561-018-9214-7

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