Dual-Donor Organ Exchange

Abstract

APPENDIX B: DYNAMIC SIMULATIONSIN THE DYNAMIC SIMULATIONS, PATIENTS AND THEIR DONORS ARRIVE over time and remain in the population until they are matched through exchange. We run statically optimal exchange algorithms once in each period. 25 In each simulation, we generate S = 500 such populations and report the averages and sample standard errors of the simulation statistics. B.1. Dynamic Simulations for Lung ExchangeIn the dynamic lung-exchange simulations, we consider 200 triples arriving over 20 periods at a uniform rate of 10 triples per period. This time horizon roughly corresponds to more than 1 year of Japanese patient arrival, when exchanges are run once about every 3 weeks. We only consider the 2-way and 2&3-way exchange regimes.Based on the 2&3-way exchange simulation results reported in Table V, we can increase the number of living-donor transplants by 190%, thus nearly tripling them. This increase corresponds to 24% of all triples in the population. Even the logistically simpler 2-way exchange technology has a potential to increase the number of living-donor transplants by 125%. B.2. Dynamic Simulations for Dual-Graft Liver ExchangeFor dual-graft liver exchange, we consider 500 triples arriving over 20 periods at a uniform rate of 25 triples per period. In each period, we follow the same four-step transplantation scenario we used for the static simulations. The unmatched triples remain in the patient population waiting for the next period. 26Haluk Ergin: hie@berkeley.edu Tayfun Sönmez: sonmezt@bc.edu M. Utku Ünver: unver@bc.edu 25 Moreover, among the optimal matchings, we choose a random one rather than using a priority rule to choose whom to match now and whom to leave to future runs. The number of patients who can be matched dynamically can be further improved using dynamic optimization. For example, see Ünver (2010) for such an approach for kidney exchanges. 26 Roughly, a dynamic simulation corresponds to 3 5 months in real time and the exchange is run once every 5-6 days. This is a very crude mapping that relies on our specific patient and paired donor generation

Organizing Time Exchanges: Lessons from Matching Markets

“…The considered exchange market shares many features with some classical markets, previously considered in the matching literature, including, e.g., housing markets (Scarf and Shapley, 1974;Abdulkadiroglu and Sönmez, 1999;Aziz, 2018), organ markets (Roth et al, 2004;Biró et al, 2009;Ergin et al, 2017), one-to-one matching problems (Gale and Shapley, 1962), and markets for school seats (Abdulkadiroglu and Sönmez, 2003;Kesten and Ünver, 2015). There are, however, substantial differences between these problems and the one considered in this paper.…”

Adapting a Kidney Exchange Algorithm to Align With Human Values

“…A matching M is a set of disjoint cycles and chains in the compatibility graph G. There can be length limits on these cycles and chains, as discussed above, resulting in a smaller set of legal matchings. The cycles and chains must be disjoint because no donor can give more than one of her kidneys (some recent work explores multi-donor donation (Ergin, Sönmez, and Ünver 2017;Farina, Dickerson, and Sandholm 2017) but we do not consider this here). Given the set of all legal matchings M, the clearing house problem is to find a matching M * that maximizes utility function u : M → R. Formally:…”

Small Representations of Big Kidney Exchange Graphs

“…Better exact and approximate methods for computing (k, t)-representations of graphs would likely be a prerequisite for that research. Adaptation of the theoretical results to models of lung, liver, and multi-organ exchange would also be of practical use (Ergin, Sönmez, and Ünver 2014;Ergin, Sönmez, and Ünver 2015;Luo and Tang 2015;.…”