A scoring-based ranking system and its application in cadaver kidney allocation [electronic resource]
Keywords: Management Science and Engineering

This dissertation presents a modeling-based analysis of scoring-based policies for allocating cadaver kidneys to recipient patients. The policies are categorized into two major groups: donor-dependent and donor-independent, depending on whether or not the quality of a kidney plays a role in calculating the candidate's score. I develop three different models for evaluating different types of scoring-based policies with respect to three major criteria: 1) whether or not patients and kidneys are matched according to expected survival times; 2) whether or not most kidneys will be accepted by the patients; and 3) the amount of freedom patients have in choosing their kidneys. All of the models assume that patients and kidneys are classified into different groups according to their estimated survival time, and that the patients leave the waitlist system either by transplantation or by death. The first model assumes that patients always accept the first-offered kidney, and then investigates the allocation outcome under different types of scoring policies. To capture the scoring-based nature of the allocation scheme, I study the asymptotic behavior of an overloaded queuing system when the abandon rate is much smaller than the traffic throughput. I prove that the waiting time at steady-state converges in probability to a point limit in the asymptotic regime. This limit can be solved through a system of equations. The analysis based on this limit reveals that, under a donor-independent scoring scheme, the quality of kidneys offered to a patient is independent of the patient's estimated survival years. In contrast, a supermodular, donor-dependent scoring scheme increases the chance of a higher-quality kidney being allocated to a higher-longevity patient. The second model considers the possibility that a patient may reject a kidney being offered to receive a better kidney in the future. It has been reported that, in the current system, a high number of rejections occur, which results in delays in transplantation and a decrease in organ quality. To address this issue, I propose a policy called "partitioning and scoring, " where patients must specify the class of kidneys they are waiting for, and cannot change their choice later. Because a low-quality kidney usually corresponds to a less crowded queue and a shorter waiting time, patients must choose between a better kidney or a shorter waiting time. By modeling the waitlist as a multi-queue system, I show that the queue-length process converges to a diffusion process in the heavy traffic limit regime, and therefore the allocation outcome can be approximately predicted. In particular, the allocation outcome shows that a partitioning and scoring policy can improve the survival matching between a recipient and a donor and reduce the kidney rejection rate. This result supports the idea of keeping a separated waitlist for kidneys from Expanded Criterion Donors (ECD), which has been implemented since 1992. The third model is motivated by the fact that a partitioning-based policy gives patients less freedom in choosing kidneys. An alternative is considered that merges the candidates into a single waitlist; each candidate is under consideration for all kidney offers and can accept or reject a kidney based on individual preference. I propose a model that approximately predicts the outcome of using such a policy, and use simulation to verify the approximation. My analysis shows that a donor-dependent scoring scheme (DDSS) constitutes a good compromise between the two conflicting objectives of reducing kidney rejections and allowing patients more freedom in choosing their kidneys. That is, a carefully calibrated donor-dependent scoring policy reduces kidney rejections to an affordable level and meanwhile gives patients adequate freedom to choose between a shorter waiting time or a higher-quality organ. I compared the performance of four representative scoring-based allocation policies by a simulation test using kidney-pancreas simulated allocation model (KPSAM), a software developed by the Scientific Registration of Transplant Research (SRTR). The results shows that a DDSS reduces the number of discarded kidneys by about 7% compared with a DISS, although the difference could be even larger if the KPSAM could capture the impact of different policies on patient behavior.