Age-Based Preferences in Paired Kidney Exchange

We consider a model of Paired Kidney Exchange (PKE) with feasibility constraints on the number of patient-donor pairs involved in exchanges. Patients' preferences are restricted so that patients prefer kidneys from compatible younger donors to kidneys from older donors. In this framework, patients with compatible donors may enroll on PKE programs to receive an organ with higher expected graft survival than that of their intended donor. PKE rules that satisfy individual rationality, eciency, and strategy-proofness necessarily select pairwise exchanges. Such rules maximize the number of transplantations among pairs with the youngest donors, and sequentially among pairs with donors of dierent age group

Paired and altruistic kidney donation in the UK: Algorithms and experimentation

We study the computational problem of identifying optimal sets of kidney exchanges in the UK. We show how to expand an integer programming-based formulation due to Roth et al. [2007] in order to model the criteria that constitute the UK definition of optimality. The software arising from this work has been used by the National Health Service Blood and Transplant to find optimal sets of kidney exchanges for their National Living Donor Kidney Sharing Schemes since July 2008. We report on the characteristics of the solutions that have been obtained in matching runs of the scheme since this time. We then present empirical results arising from experiments on the real datasets that stem from these matching runs, with the aim of establishing the extent to which the particular optimality criteria that are present in the UK influence the structure of the solutions that are ultimately computed. A key observation is that allowing four-way exchanges would be likely to lead to a moderate number of additional transplants

Scalable Robust Kidney Exchange

In barter exchanges, participants directly trade their endowed goods in a constrained economic setting without money. Transactions in barter exchanges are often facilitated via a central clearinghouse that must match participants even in the face of uncertainty---over participants, existence and quality of potential trades, and so on. Leveraging robust combinatorial optimization techniques, we address uncertainty in kidney exchange, a real-world barter market where patients swap (in)compatible paired donors. We provide two scalable robust methods to handle two distinct types of uncertainty in kidney exchange---over the quality and the existence of a potential match. The latter case directly addresses a weakness in all stochastic-optimization-based methods to the kidney exchange clearing problem, which all necessarily require explicit estimates of the probability of a transaction existing---a still-unsolved problem in this nascent market. We also propose a novel, scalable kidney exchange formulation that eliminates the need for an exponential-time constraint generation process in competing formulations, maintains provable optimality, and serves as a subsolver for our robust approach. For each type of uncertainty we demonstrate the benefits of robustness on real data from a large, fielded kidney exchange in the United States. We conclude by drawing parallels between robustness and notions of fairness in the kidney exchange setting.Comment: Presented at AAAI1

Planning for Uncertainty and Fallbacks Can Increase the Number of Transplants in a Kidney‐Paired Donation Program

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/113739/1/ajt13413.pd

Using deceased-donor kidneys to initiate chains of living donor kidney paired donations: algorithms and experimentation

We design a flexible algorithm that exploits deceased donor kidneys to initiate chains of living donor kidney paired donations, combining deceased and living donor allocation mechanisms to improve the quantity and quality of kidney transplants. The advantages of this approach have been measured using retrospective data on the pool of donor/recipient incompatible and desensitized pairs at the Padua University Hospital, the largest center for living donor kidney transplants in Italy. The experiments show a remarkable improvement on the number of patients with incompatible donor who could be transplanted, a decrease in the number of desensitization procedures, and an increase in the number of UT patients (that is, patients unlikely to be transplanted for immunological reasons) in the waiting list who could receive an organ.Comment: To be published in AIES 201

Towards fairness in Kidney Exchange Programs

Le traitement médical de choix pour la maladie rénale chronique est la transplantation d'organe. Cependant, plusieurs patients ne sont en mesure que de trouver un donneur direct avec lequel ils ne sont pas compatibles. Les Programmes de Don Croisé de Reins peuvent aider plusieurs paires donneur-patient incompatibles à échanger leur donneur entre elles. Typiquement, l'objectif principal d'un tel programme est de maximiser le nombre total de transplantations qui seront effectuées grâce à un plan d'échange. Plusieurs solutions optimales peuvent co-exister et comme la plupart correspondent à différents ensembles de patients obtenant un donneur compatible, il devient important de considérer quels individus seront sélectionnés. Fréquemment, ce problème n'est pas abordé et la première solution fournie par un solveur est choisie comme plan d'échange. Ceci peut mener à des parti-pris en faveur ou défaveur de certains patients, ce qui n'est pas considéré une approche juste. De plus, il est de la responsabilité des informaticiens de s'assurer du contrôle des résultats fournis par leurs algorithmes. Pour répondre à ce besoin, nous explorons l'emploi de multiples solutions optimales ainsi que la manière dont il est possible de sélectionner un plan d'échange parmi celles-ci. Nous proposons l'emploi de politiques aléatoires pour la sélection de solutions optimales suite à leur enumération. Cette tâche est accomplie grâce à la programmation en nombres entiers et à la programmation par contraintes. Nous introduisons aussi un nouveau concept intitulé équité individuelle. Ceci a pour but de trouver une politique juste pouvant être utilisée en collaboration avec les solutions énumerées. La mise à disposition de plusieurs métriques fait partie intégrante de la méthode. En faisant usage de la génération de colonnes en combinaison au métrique $L_1$, nous parvenons à applique la méthode à de plus larges graphes. Lors de l'évaluation de l'équité individuelle, nous analysons de façon systématique d'autres schémas d'équité tels que le principle d'Aristote, la justice Rawlsienne, le principe d'équité de Nash et les valeurs de Shapley. Nous étudions leur description mathématiques ainsi que leurs avantages et désavantages. Finalement, nous soulignons le besoin de considérer de multiples solutions, incluant des solutions non optimales en ce qui concerne le nombre de transplantations d'un plan d'échange. Pour la sélection d'une politique équitable ayant comme domaine un tel ensemble de solutions, nous notons l'importance de trouver un équilibre entre les mesures d'utilité et d'équité d'une solution. Nous utilisons le Programme de Bien-être Social de Nash afin de satisfaire à un tel objectif. Nous proposons aussi une méthodologie de décomposition qui permet d'étendre le système sous-jacent et de faciliter l'énumeration de solutions.The preferred treatment for chronic kidney disease is transplantation. However, many patients can only find direct donors that are not fully compatible with them. Kidney Exchange Programs (KEPs) can help these patients by swapping the donors of multiple patient-donor pairs in order to accommodate them. Usually, the objective is to maximize the total number of transplants that can be realized as part of an exchange plan. Many optimal solutions can co-exist and since a large part of them features different subsets of patients that obtain a compatible donor, the question of who is selected becomes relevant. Often, this problem is not even addressed and the first solution returned by a solver is chosen as the exchange plan to be performed. This can lead to bias against some patients and thus is not considered a fair approach. Moreover, it is of the responsibility of computer scientists to have control of the output of the algorithms they design. To resolve this issue, we explore the use of multiple optimal solutions and how to pick an exchange plan among them. We propose the use of randomized policies for selecting an optimal solution, first by enumerating them. This task is achieved through both integer programming and constraint programming methods. We also introduce a new concept called individual fairness in a bid to find a fair policy over the enumerated solutions by making use of multiple metrics. We scale the method to larger instances by adding column generation as part of the enumeration with the $L_1$ metric. When evaluating individual fairness, we systematically review other fairness schemes such as Aristotle's principle, Rawlsian justice, Nash's principle of fairness, and Shapley values. We analyze their mathematical descriptions and their pros and cons. Finally, we motivate the need to consider solutions that are not optimal in the number of transplants. For the selection of a good policy over this larger set of solutions, we motivate the need to balance utility and our individual fairness measure. We use the Nash Social Welfare Program in order to achieve this, and we also propose a decomposition methodology to extend the machinery for an efficient enumeration of solutions