Optimising paired and pooled kidney exchanges
Recent changes in legislation in the UK have allowed a patient who requires a kidney transplant, and who has a willing but incompatible donor, to be involved in a 'pairwise kidney exchange' (i.e., to 'swap' their donor) with another patient-donor pair in a similar position.
'Pooled donations' extend this concept to three or more couples in a cyclic manner. NHS Blood and Transplant (NHSBT) run the National Matching Scheme for Paired Donation (NMSPD), which finds pairwise and 3-way exchanges (the latter being pooled exchanges involving three
couples) at regular intervals. This matching scheme is based on finding an optimal solution, where the optimality definition involves a number of criteria including the need to maximise the number of transplants, and subject to this, maximise the total weight of the transplants, based on a scoring system that incorporates a number of factors including sensitivity, HLA compatibility, donor age and patient waiting time. In this talk we describe the computational technique that we have used in order to construct optimal exchanges for matching runs of the NMSPD
between July 2008 and January 2011. This involves integer programming using the COIN solver, in conjunction with graph matching using the LEMON library. We will also present some statistical results regarding the numbers of pairwise and 3-way exchanges from these matching runs.
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