Our Projects

Optimization and Simulation of Kidney Paired Donation Programs


KPD Network

The above is an illustration of a KPD network, with pairs represented by red nodes and altruistic donors represented by purple nodes.  Edges connecting nodes represent donor-candidate matches based on a virtual (computer based) cross match.  A selection with five subsets is highlighted and the possible transplants are indicated by purple edges.  These subsets are locally relevant subsets of size four or less and are chosen to present fall back opportunities should some transplants not be viable.  We proceed by evaluating all transplants for viability indicated by the purple arrows, then choosing the best possible disjoint set of cycles and chains for transplant.  (See Bray et al., 2015)


Kidney paired donation (KPD) provides an approach to overcome the barriers faced by many patients with kidney failure who present with willing, but immunologically or blood type incompatible living donors. KPD programs use a computerized algorithm to match one incompatible donor/recipient pair to another pair with a complementary incompatibility, such that the donor of the first pair gives to the recipient of the second, and vice versa. More complex exchanges of organs involving three or more pairs are also considered as are altruistic or non-directed donors (NDD) who donate a kidney voluntarily and thereby have the potential to create a chain of kidney transplants.  Such donors and chains have become increasingly important in KPD programs. Checking the viability of all potential transplants in a pool is not logistically possible, and so a fundamental problem in a KPD program is selecting an optimal subset of matches to consider among the many possibilities that exist.  We are developing methods of selecting  potential matches that take account of the uncertainty in the process; namely that potential transplants that are identified on a computer algorithm often fail when an attempt is made to put them into practice. Our approaches select subsets of patients with many options or fallbacks that could be implemented depending upon which potential transplants are found to be viable, and have been shown to have the potential to greatly increase the number and/or utility of transplants performed. We are also developing user friendly and efficient software to implement these approaches. In this work, we utilize data from the University of Michigan Paired Donation Program and the Alliance for Paired Donation.


Kidney Graft Survival Calculator:

Our calculator estimates the probability of graft survival given the characteristics of the candidate and potential donor, based on a Cox proportional hazards model fitted to SRTR data. This calculator has particular potential as a guide to candidates with a compatible living donor who may be able to improve their predicted graft or patient survival through participation in a KPD program.

Link to Calculator



KPD GUI: Software and Graphical Interface (download)

Our software platform can be used to manage and visualize exchanges suggested by optimization criteria in KPD, offering several advantages over other available software: 

  • Interactive visual display of the state of the KPD
  • Implementation of optimization methods from previous literature, accounting for probabilities of failure, as well as fallback options (uncertainties and contingencies)
  • Optimization extended to more general subsets of pairs and NDDs that facilitate fallback options. 


Related Publications:

Chen Y, Li Y, Kalbfleisch JD, Zhou Y, Leichtman A, Song PXK. Graph-based optimization algorithm and software on kidney exchanges. IEEE Transactions on Biomedical Engineering. 2012; 59:  1985-1991. doi: 10.1109/TBME.2012.2195663. Epub 2012 Apr 20.

Li Y, Song PXK, Leichtman AB, Rees MA, Kalbfleisch JD. Decision making in kidney paired donation programs with altruistic donors. SORT (Barcelona). 2014; 38(1): 53-72. PMID: 25309603 [PubMed]  PMCID: PMC4193813.

Li Y, Song PXK, Zhou Y, Leichtman A, Rees MA, Kalbfleisch JD. Optimal decisions for organ exchanges in a kidney paired donation program. Statistics in Biosciences. 2014; 6:  85-104. PMID:24795783 [PubMed]  PMCID: PMC4004760

Fumo D, Kapoor V, Reece IJ, Stepkowski SM, Kopke JE, Rees SE, Smith C, Roth AE, Leichtman AB, Rees MA. Historical matching strategies in kidney paired donation: The 7-year evolution of a web-based virtual matching system. American Journal of Transplantation. 2015; 15(10): 2646-2654. doi: 10.1111/ajt.13337. Epub 2015 May 26.

Bray M, Wang W, Song PK, Leichtman A, Rees M, Ashby V, Eikstadt R, Goulding A, Kalbfleisch J. Planning for uncertainty and fallbacks can increase the number of transplants in a kidney-paired donation program. American Journal of Transplantation. 2015; 15(10): 2636–2645. doi: 10.1111/ajt.13413. Epub 2015 Aug 4.

Melcher ML, Roberts JP, Leichtman AB, Roth AE, Rees MA. Utilization of deceased donor kidneys to initiate living donor chains. American Journal of Transplantation. 2016. doi: 10.1111/ajt.13740. Epub 2016 March.9

Ashby VA, Leichtman AB, Rees MA, Song PXK, Bray M, Wang W, and Kalbfleisch JD (2017).  A Kidney Graft Survival Calculator that Accounts for Mismatches in Age, Sex, HLA, and Body Size.  Clinical Journal of the American Society of Nephrology 12(7): 1148-60. doi: 10.2215/CJN.09330916 

Wang W, Bray M, Song PXK, Kalbflesich JD (2017).  A Look-Ahead Strategy for Non-Directed Donors in Kidney Paired-Donation. Statistics in Biosciences 9(2): 453-69. doi: 10.1007/s12561-016-9155-y

Bray M, Wang W, Song PXK, and Kalbfleishch JD (2018).  Valuing Sets of Potential Transplants in a Kidney Paired Donation Network.  Statistics in Biosciences (Published Online March 2018). doi: 10.1007/s12561-018-9214-7

Wang W, Bray M, Song PXK, Kalbfleisch JD (2018).  An Efficient Algorithm to Enumerate Sets with Fallbacks in a Kidney Paired Donation Program.  Operations Research for Health Care.  (Submitted)



Bray M, Wang W, Song PXK, Leichtman AB, Rees MA, Ashby VB, Eikstadt R, Kalbfleisch JD. Incorporating Uncertainties and Contingencies in a Paired Donation Program. ASN Kidney Week 2013. Atlanta, GA (November 7). American Society of Nephrology

Wang W, Bray M, Song PXK, Leichtman AB, Kalbfleisch JD. Multiple Decision Allocation Strategies in Kidney Paired Donation Program.  ASN Kidney Week 2013. Atlanta, GA (November 7). American Society of Nephrology.

Bray M, Wang W, Song PXK, Kalbfleisch JD. Incorporating Transplant Candidates with Multiple Associated Incompatible Donors in Kidney Paired-Donation. ENAR Spring Meeting 2016. Austin, TX (March 6). Eastern North American Region of the International Biometrics Society.

Wang W, Bray M, Song PXK, Kalbfleisch JD. Locally Relevant Subgraph Enumeration in Transplant Patient Network. ENAR Spring Meeting 2016. Austin, TX (March 6). Eastern North American Region of the International Biometrics Society.

Bray M, Wang W, Rees MA, Song PXK, Leichtman AB, Ashby VB, Kalbfleisch JD. A Visualization Software Platform for Managing a Kidney Paired-Donation Program.  American Transplant Congress 2016. Boston, MA (June14). American Society of Transplant Surgeons & American Society of Transplantation

Ashby VB, Leichtman AB, Rees MA, Song PXK, Bray M, Wang W, Kalbfleisch JD. Mismatch in Age, Sex, and Body Size Inform a Calculator for Kidney Graft Survival. American Transplant Congress 2016. Boston, MA (June 11). American Society of Transplant Surgeons & American Society of Transplantation