Paired and Altruistic Kidney Donation in the UK

Abstract

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 4-way exchanges would be likely to lead to a moderate number of additional transplants.

On Maximum Weight Clique Algorithms, and How They Are Evaluated

“…Kidney-exchange schemes exist in several countries to increase the number of transplants from living donors to patients with end-stage renal disease [24,35,47]. A patient enters the scheme along with a friend or family member who is willing to donate to that patient but unable to do so due to blood or tissue incompatibility.…”

“…The weighting scheme and exchange size cap we used are based on the system used in the UK's National Living Donor Kidney Sharing Scheme (NLDKSS) [35]. The NLDKSS has a maximum exchange size of three, and has five objectives, ranked hierarchically.…”

“…We use a simple transformation to convert the third objective from a minimisation to a maximisation. This method of combining scores in order to perform a single optimisation is not practical using IP solvers because, as Manlove and O'Malley [35] observe, the resulting weights would be too large for IP solvers. By contrast, all of our maximum-weight clique solvers can use 64-bit weights without loss of precision.…”

Kidney Procurement System in Colombia: A System Dynamics Approach

“…This program consists on contacting CKD patients that have a voluntary living kidney donor (a relative, spouse or a friend) with no histocompatibility and they are willing to participate in finding a couple in the same situation (no donor-recipient histocompatibility) and swap donors. The KEP has been implemented in countries such as South Korea (6), Switzerland (7), The United States (8)(9)(10), Turkey (11), Romania (12), Netherlands (13)(14)(15), United Kingdom (16)(17)(18), Portugal, Canada, New Zealand, and Australia (19).…”

Reformulation-Linearization Technique Approach for Kidney Exchange Program IT Healthcare Platforms

“…Furthermore, Constantino et al [18] proposed two compact formulations-that is, an edge-assignment (EA) formulation and an extended edge (EE) formulation. Manlove and O'Malley [19] presented how the cycle formulation by Roth et al [17] can be extended to find optimal solutions for the KEP in the United Kingdom, which are compatible with U.K. National Living Donor Kidney Sharing Schemes (NLDKSS).…”