Multiple Decision Allocation Strategies in Kidney Paired Donation Program
Wen
1
Wang ,
1 University
Mathieu
1
Bray ,
Peter XK Song
1,2
PhD ,
Alan Leichtman
2
MD ,
John D Kalbfleisch,
1,2
PhD
of Michigan Department of Biostatistics, Ann Arbor, MI, 2University of Michigan Kidney Epidemiology and Cost Center; Ann Arbor, MI
BACKGROUND
A kidney paired donation (KPD) program allows transplant candidates, who have
willing donors with blood type or HLA incompatibility [4], to exchange donors’
organs with other candidates [1].
Introducing an altruistic donor (AD) into a KPD pool results in a chain of organ
exchanges, in which AD is allocated to a candidate-donor pair whose candidate is
compatible with the AD and whose donor agrees to donate to another pair in the
pool, and so forth[2]. The donor of a pair at the end of a chain is called a bridge
donor (BD).
A virtual crossmatch can fail due to positive lab crossmatch, illness, and other
frictions [5].
Previous study [3] suggested that prioritizing chains with BD having larger
expected maximum number of a few subsequent transplants (BD utility with
looking a few steps ahead) results in larger realized number of transplants.
Previous study [2] showed that realized number of transplants benefits from
proceeding with longer chain.
The purpose of this study is to investigate whether proceeding with longer chains
improves number of transplants when prioritizing chains with BDs of larger BD
utilities with looking a few steps ahead.
METHODS
A simulation study using 585 candidate-donor pairs and 56 ADs from Alliance for
Paired Donation (APD) and 281 pairs and 7 altruistic donors from the University
of Michigan KPD program was conducted.
Multiple Decision allocation strategies with numbers of transplants within a
chain (chain lengths, denoted by D) and looking ahead steps (S) of BD utility
combinations (see Figure 1) were compared:
• Total depth (TD) is D+S. Given number of KPD pairs (n) and ADs (m), algorithm
complexity is 𝑂(𝑚 log 𝑛 𝑛𝑇𝐷 ). Due to computational limitation, set TD≤6 in
the following presentation.
1000 simulations for static KPD pools were performed for each strategy:
(1) Start the pool with 80 pairs and 1 AD.
(2) List all chains of length D initiated by ADs in a descending order by chain
utility with looking S steps ahead.
(3) Simulate failure incidences due to positive crossmatches or other frictions.
(4) Proceed with the top ranked chain without failure, and any remaining chains
overlapped with this chain would be removed from the list.
(5) Repeat step (4) until there were no chains without failure in the list and mark
BDs as ADs.
(6) Repeat steps (2)-(5) until AD could donate to none.
(7) Calculate number of transplants (NOT) in this simulation.
500 similar simulations for dynamic KPD pools were performed for each strategy.
For the dynamic pool, 30 pairs and 1 AD are added at random following each
round prior to step (2) and step (6) ends after 8 rounds are completed.
RESULTS
• Bridge donor 𝑣2 is evaluated by the Figure 1: An illustration of a chain of length 2
expected maximum number of
and BD utility with looking 2 steps ahead.
subsequent 2 transplants (BD utility
with looking 2 steps ahead).
• The chain starting from 𝑣0 to 𝑣2 is
evaluated by chain utility with
looking 2 steps ahead, which is a
D=2
sum of number of transplants in the
chain and BD utility with looking 2
steps ahead.
• Chain utility can be interpreted as a
composite benefit with both
present benefit (number of
S=2
transplants in a chain) and future
benefit (BD utility with looking S
steps ahead).
Figure 2: Mean realized number of transplants of static KPD pool simulations
• The optimum allocation strategy with fixed TD depends on
failure rate. When the rate decreases from 0.8 to 0, the optimum
allocation strategy moves from the strategy with the upper TD
and D=1 to the strategy with the upper TD and 𝐷 ≈ 𝑆.
Results from Dynamic Pool Simulations
• All results in static simulations are similar to those from
dynamic pool simulations.
CONCLUSIONS
With fixed TD, the allocation strategy with 𝑆 ≈ 𝐷 has the largest
realized number of transplants.
The proposed allocation strategy improving MRNOT leads to a
larger proportion of hard-to-match candidates transplanted.
Optimum allocation strategy depends on transplant failure rate.
DISCUSSIONS
In practice, both chains and cycles are involved in KPD matching.
Multiple decision allocation strategies can be utilized to evaluate
chains, exchange sets and exchange components [3].
Rather than number of transplants, an alternative utility reflecting
various values of transplants is of interest, such as 5 years or 10
years graft survival predicted by characteristics of candidates and
donors.
REFERENCES
Static Pool Simulation Results in Figure 2
• Fixed D, as S increases the mean realized number of transplants (MRNOT) first rises
and then reaches a plateau.
• Fixed S, as D increases MRNOT first rises and then reaches a plateau.
• With TD≤6 , in other words, limited TD, the strategy with the largest TD and 𝐷 ≈ 𝑆
had the largest MRNOT.
Additional Results from Static Pool Simulations
• Among transplanted patients, both proportions of blood type O candidates and
very high PRA (≥75) candidates increase as a result of increased MRNOT. Thus
the proposed allocation strategies are advantageous to have more hard-to-match
candidates transplanted.
[1] Gentry, S. E., Montgomery, R. A., & Segev, D. L. (2011). Kidney paired
donation: fundamentals, limitations, and expansions. American Journal of
Kidney Diseases, 57(1), 144-151.
[2] Ashlagi, I., Gilchrist, D. S., Roth, A. E., & Rees, M. A. (2011). Nonsimultaneous
Chains and Dominos in Kidney‐Paired Donation—Revisited. American Journal of
Transplantation, 11(5), 984-994.
[3] Li, Yijiang, Peter, X.-K., Alan B. A., Michael A. R. & John D. K. (2014). Decision
Making in Kidney Paired Donation Programs with Altruistic Donor. SORT, (to
appear).
[4] Koch, Matthew J., and Daniel C. Brennan. (2007) HLA and ABO sensitization
and desensitization in renal transplantation. Transplantation 1: 3.
[5] Patel, R., & Terasaki, P. I. (1969). Significance of the positive crossmatch test
in kidney transplantation. New England Journal of Medicine, 280(14), 735-739.
Funding for this project was provided by a research grant from the national
Institutes of Health (NIDDK) R01-DK093513 and from the Natural Sciences and
Engineering Research Council of Canada, in the form of a Post-Graduate
Scholarship (Master’s) PGS M award to Mathieu Bray.