Optimization and Simulation of Kidney Paired Donation Programs.

Abstract

An evolving strategy known as kidney paired donation (KPD) matches one donor-candidate pair to another pair with a complementary incompatibility, such that the donor of the first pair donates to the candidate of the second, and vice versa. In Chapter II, we propose novel organ allocation strategies to arrange kidney exchanges under uncertainties with advantages, including (i) allowance for a general utility-based evaluation of potential kidney transplants and an explicit consideration of stochastic features inherent in a KPD program; and (ii) exploitation of possible alternative exchanges when the originally planned allocation cannot be fully executed. This allocation strategy is implemented using an integer programming (IP) formulation, and its implication is assessed via a data-based simulation system by tracking an evolving KPD program over a series of match runs. Extensive simulation studies are provided to illustrate our proposed approach.

In recent years, KPD has also been extended to include living non-directed donors, or altruistic donors. In Chapter III, we propose a strategy to sequentially allocate the altruistic donor (or bridge donor) so as to maximize the expected utility over a certain given number of moves. Analogous to the way a computer plays chess, the idea is to evaluate different allocations for each altruistic donor (or bridge donor) by looking several moves ahead along a derived look-ahead search tree. Simulation studies are provided to illustrate our proposed method.

In Chapter IV, we examine in greater detail two important aspects in the management of a KPD program --- robust organ allocations and operational uncertainties. We first extend the idea of using exchange sets for planning organ allocations; the outcome of this extension is a more robust allocation strategy derived from the concept of strongly connected components (SCCs). We then study more carefully the operational uncertainties inherent in the management of KPD programs. We also develop a general mathematical framework based on Markov decision processes (MDPs), which can be use to rigorously and systematically formulate the problem of managing KPD programs in the presence of altruistic donors. Finally, we conclude with some discussion and future directions of this dissertation work.