Valuing Sets of Potential Transplants in a Kidney Paired Donation Network

Abstract

In kidney paired donation (KPD), incompatible donor-candidate pairs and non-directed (also known as altruistic) donors are pooled together with the aim of maximizing the total utility of transplants realized via donor exchanges. We consider a setting in which disjoint sets of potential transplants are selected at regular intervals, with fallback options available within each proposed set in the case of individual donor, candidate or match failure. We develop methods for calculating the expected utility for such sets under a realistic probability model for the KPD. Exact expected utility calculations for these sets are compared to estimates based on Monte Carlo samples of the underlying network. Models and methods are extended to include transplant candidates who join KPD with more than one incompatible donor. Microsimulations demonstrate the superiority of accounting for failure probability and fallback options, as well as candidates joining with additional donors, in terms of realized transplants and waiting time for candidates.

An efficient algorithm to enumerate sets with fallbacks in a kidney paired donation program

“…Step (3b). In [16], we have investigated efficient methods to evaluate the expected utilities required in Step (2b). The IP problem that corresponds to Step (3b) becomes more complex as the number of potential sets to select increases.…”

“…Some additional work on the third type can be found in [16,13,14]. When failure probability is moderate, it has been demonstrated that such locally relevant subgraphs can lead to greatly improved selection processes that yield many more realized transplants, by as much as, 8% compared to fallbacks within cycles and chains [13].…”

KPDGUI: An interactive application for optimization and management of a virtual kidney paired donation program

“…In recent work we have shown considerable advantage of the approach based on LRSs as compared to the simple selection of cycles and chains. Over time, schemes that utilize LRSs, accounting for the uncertainty and the possibility to pursue fallback options within a failed exchange, yield higher numbers of realized transplants in KPD microsimulation models than schemes that only consider simple cycles and chains, with gains of roughly 40% when compared to the simplest settings [27,28].…”

“…Optimization can be further extended beyond selection of simple cycles or chains to encompass fallback options in case of non-viability [24][25][26]. We have previously investigated the incorporation of these considerations into KPD optimization through simulation, where formidable gains in realized utility were observed [27,28].…”

“…Note that while certain cycles, chains or LRSs may appear in more than one solution, the combination will be different for each unique solution produced. Estimation is based on Monte Carlo sampling procedures outlined in our previous studies [28]. If estimating, the user also specifies the number of sampling iterations to apply in the estimation procedure.…”