Matching Kidneys with Priority in Kidney Exchange Programs

Kidney exchange programs (KEPs) allow the exchange of kidneys between incompatible donor-recipient pairs. Optimization approaches can help KEPs in defining which transplants should be made among all incompatible pairs according to some objective. The most common objective is to maximize the number of transplants. In this paper, we propose an integer programming model which addresses the objective of maximizing the expected number of transplants, given that there are equal probabilities of failure associated with vertices and arcs. The model is compact, i.e. has a polynomial number of decision variables and constraints, and therefore can be solved directly by a general purpose integer programming solver (e.g. Cplex).

ObjectivesLiving donor kidney transplantation (LTx) is the preferred treatment for patients with end-stage renal disease. Kidney exchange programs (KEPs) promote LTx by facilitating exchange of donors among patients who are not compatible with their donors. We analyze and maximize the efficacy and effectiveness of KEPS from a health value perspective and the health value of altruistic donation in KEPs. MethodsWe developed a Markov model for the health outcomes of patients, which was embedded in a discrete event simulation model to assess the effectiveness of allocation policies in KEPs. A new allocation policy to maximize health value was developed on the basis of integer programing techniques. The evidence-based transition probabilities in the Markov model were based on data from the Dutch KEP using a variety of econometric models. Scenarios analysis was presented to improve robustness. ResultsThe efficacy of the Dutch KEP without altruistic donation is reflected by the increase in expected discounted quality-adjusted life-years (QALYs) by 3.23 from 6.42 to 9.65. The present Dutch policy and the policy to maximize the number of transplants achieve 63% of the potential efficacy gain (2.11 discounted QALYs). The new policy achieves 69% of this gain (2.33 discounted QALYs). When systematically enrolling altruistic donors in the KEP, the new policy increased expected discounted QALYs by 4.05 to 10.27 and reduced inequities for patients with blood type O. ConclusionsThe Dutch KEP can increase health value for patients by more than half. An allocation policy that maximizes health outcomes and maximally allows altruistic donation can yield significant further improvements.

In kidney exchange programs, multiple patient-donor pairs each of whom are otherwise incompatible, exchange their donors to receive compatible kidneys. The Kidney Exchange problem is typically modelled as a directed graph where every vertex is either an altruistic donor or a pair of patient and donor; directed edges are added from a donor to its compatible patients. The computational task is to find if there exists a collection of disjoint cycles and paths starting from altruistic donor vertices of length at most $\ell_c$ and $\ell_p$ respectively that covers at least some specific number t of non-altruistic vertices (patients). We study parameterized algorithms for the kidney exchange problem in this paper. Specifically, we design FPT algorithms parameterized by each of the following parameters: (1) the number of patients who receive kidney, (2) treewidth of the input graph + $\max\\ell_p,\ell_c\ $, and (3) the number of vertex types in the input graph when $\ell_płeq \ell_c$. We also present interesting algorithmic and hardness results on the kernelization complexity of the problem. Finally, we present an approximation algorithm for an important special case of Kidney Exchange.

In kidney exchange programs, multiple patient-donor pairs each of whom are otherwise incompatible, exchange their donors to receive compatible kidneys. The Kidney Exchange problem is typically modelled as a directed graph where every vertex is either an altruistic donor or a pair of patient and donor; directed edges are added from a donor to its compatible patients. The computational task is to find if there exists a collection of disjoint cycles and paths starting from altruistic donor vertices of length at most l_c and l_p respectively that covers at least some specific number t of non-altruistic vertices (patients). We study parameterized algorithms for the kidney exchange problem in this paper. Specifically, we design FPT algorithms parameterized by each of the following parameters: (1) the number of patients who receive kidney, (2) treewidth of the input graph + max{l_p, l_c}, and (3) the number of vertex types in the input graph when l_p <= l_c. We also present interesting algorithmic and hardness results on the kernelization complexity of the problem. Finally, we present an approximation algorithm for an important special case of Kidney Exchange.

Renal patients who have a willing but incompatible donor can decide to participate in a kidney exchange program (KEP). The goal of a KEP is to identify sets of incompatible pairs that can exchange donors, leading to compatible transplants for each recipient. Significant uncertainty is involved in this process, as planned transplants may be canceled for many reasons. It is therefore crucial to take into account failures while planning exchanges. In this paper, we consider a robust variant of this problem with recourse studied in the literature that takes into account failures of donors or recipients. This problem belongs to the class of defender–attacker–defender (DAD) models. We propose a cutting plane method for solving the attacker–defender subproblem based on two commonly used mixed-integer programming formulations for kidney exchange problems. Our results imply a running time improvement of one order of magnitude compared to the state-of-the-art. Moreover, our cutting plane methods can solve many previously unsolved instances. Furthermore, we propose a new practical policy for recourse in KEPs and show that the robust optimization problem concerning this policy is tractable for small to mid-size KEPs in practice.

In kidney transplantation, immunosuppressants are being used to relax all immunological constraints, allowing patients to receive transplants from biologically incompatible donors. We propose an efficient way of using immunosuppressants in combination with a kidney exchange program. We introduce the top‐trading cycles and chains solution, a modification of the top‐trading cycles rule for the standard kidney exchange problem, and investigate its properties.

Living donor kidney transplantation is the preferred treatment for patients suffering from end-stage renal disease. To alleviate the shortage of kidney donors, many advances have been made to improve the utilization of living donors deemed incompatible with their intended recipient. The most prominent of these advances is kidney paired donation (KPD), which matches incompatible patient-donor pairs to facilitate a kidney exchange. This review discusses the various approaches to matching and allocation in KPD. In particular, it focuses on the underlying principles of matching and allocation approaches, the combination of KPD with other strategies such as ABO incompatible transplantation, the organization of KPD, and important future challenges. As the transplant community strives to balance quantity and equity of transplants to achieve the best possible outcomes, determining the right long-term allocation strategy becomes increasingly important. In this light, challenges include making full use of the various modalities that are now available through integrated and optimized matching software, encouragement of transplant centers to fully participate, improving transplant rates by focusing on the expected long-run number of transplants, and selecting uniform allocation criteria to facilitate international pools.

A Possible System for Optimal Donor Kidney Exchange in Turkey

Branch-and-cut-and-price for the cardinality-constrained multi-cycle problem in kidney exchange

Efficient Kidney Exchange with Dichotomous Preferences

A kidney exchange is an organized barter market where patients in need of a kidney swap willing but incompatible donors. Determining an optimal set of exchanges is theoretically and empirically hard. Traditionally, exchanges took place in cycles, with each participating patient-donor pair both giving and receiving a kidney. The recent introduction of chains, where a donor without a paired patient triggers a sequence of donations without requiring a kidney in return, increased the efficacy of fielded kidney exchanges---while also dramatically raising the empirical computational hardness of clearing the market in practice. While chains can be quite long, unbounded-length chains are not desirable: planned donations can fail before transplant for a variety of reasons, and the failure of a single donation causes the rest of that chain to fail, so parallel shorter chains are better in practice. In this paper, we address the tractable clearing of kidney exchanges with short cycles and chains that are long but bounded. This corresponds to the practice at most modern fielded kidney exchanges. We introduce three new integer programming formulations, two of which are compact. Furthermore, one of these models has a linear programming relaxation that is exactly as tight as the previous tightest formulation (which was not compact) for instances in which each donor has a paired patient. On real data from the UNOS nationwide exchange in the United States and the NLDKSS nationwide exchange in the United Kingdom, as well as on generated realistic large-scale data, we show that our new models are competitive with all existing solvers---in many cases outperforming all other solvers by orders of magnitude. Finally, we note that our position-indexed chain-edge formulation can be modified in a straightforward way to take post-match edge failure into account, under the restriction that edges have equal probabilities of failure. Post-match edge failure is a primary source of inefficiency in presently-fielded kidney exchanges. We show how to implement such failure-aware matching in our model, and also extend the state-of-the-art general branch-and-price-based non-compact formulation for the failure-aware problem to run its pricing problem in polynomial time.

Transplant Disparities and Kidney Exchanges: Estimating Quantity and Quality Effects by Patient Blood Type and Sensitization

We study the stochastic matching problem with the goal of finding a maximum matching in a graph whose edges are unknown but can be accessed via queries. This is a special case of stochastic k-cycle packing, in which the problem is to find a maximum packing of cycles, each of which exists with some probability. We provide polynomial-time adaptive and nonadaptive algorithms that provably yield a near-optimal solution, using a number of edge queries that is linear in the number of vertices. We are especially interested in kidney exchange, with which pairs of patients with end-stage renal failure and their willing but incompatible donors participate in a mechanism that performs compatibility tests between patients and donors and swaps the donors of some patients so that a large number of patients receive compatible kidneys. Because of the significant cost of performing compatibility tests, currently, kidney exchange programs perform at most one compatibility test per patient. Our theoretical results applied to kidney exchange show that, by increasing the number of compatibility tests performed per patient from one to a larger constant, we effectively get the full benefit of exhaustive testing at a fraction of the cost. We show, on both generated and real data from the UNOS nationwide kidney exchange, that even a small number of nonadaptive edge queries per vertex results in large gains in expected successful matches.

To this day, there are still some countries where the exchange of kidneys between multiple incompatible patient-donor pairs is restricted by law. Typically, legal regulations in this context are put in place to prohibit coercion and manipulation in order to prevent a market for organ trade. Yet, in countries where kidney exchange is practiced, existing platforms to facilitate such exchanges generally lack sufficient privacy mechanisms. In this paper, we propose a privacy-preserving protocol for kidney exchange that not only addresses the privacy problem of existing platforms but also is geared to lead the way in overcoming legal issues in those countries where kidney exchange is still not practiced. In our approach, we use the concept of secret sharing to distribute the medical data of patients and donors among a set of computing peers in a privacy-preserving fashion. These computing peers then execute our new Secure Multi-Party Computation (SMPC) protocol among each other to determine an optimal set of kidney exchanges. As part of our new protocol, we devise a privacy-preserving solution to the maximum matching problem on general graphs. We have implemented the protocol in the SMPC benchmarking framework MP-SPDZ and provide a comprehensive performance evaluation. Furthermore, we analyze the practicality of our protocol when used in a dynamic setting (where patients and donors arrive and depart over time) based on a data set from the United Network for Organ Sharing.

This article studies multicenter coordination of unspecified living kidney donation and transplantation across the blood-type barrier in kidney exchange. Important questions are whether such coordination should use domino paired donation or non simultaneous extended altruistic donor chains, what the length of the segments in such chains should be, when they should be terminated, and how much time should be allowed between matching rounds. Furthermore, it is controversial whether the different modalities should be coordinated centrally or locally and independently. Kidney exchange policies are simulated using actual data from the Dutch national kidney exchange program. Sensitivity analysis is performed on the composition of the population, the time unspecified and bridge donors wait before donating to the wait list, the time between matching rounds, and donor renege rates. Central coordination of unspecified donation and transplantation across the blood-type barrier can increase transplants by 10% (PG0.001). Especially highly sensitized and blood type O patients benefit. Sufficient time between matching rounds is essential: three-monthly exchanges result in 31% more transplants than weekly exchanges. Benefits of non simultaneous extended altruistic donor chains are limited in case of low numbers of highly sensitized patients and sufficient unspecified donors. Chains are best terminated when no further segment is part of an optimal exchange within 3 months. There is clear synergy in the central coordination of both unspecified donation and transplantation across the blood-type barrier in kidney exchange. The best configuration of a national program depends on the composition of the patient Y donor population.