Funding for this research project is provided under the Exploratory Research on Engineering the Service Sector (ESS) program announcement. The United Network for Organ Sharing (UNOS) manages the national organ donation and allocation system. When UNOS offers an organ to a transplant patient, the patient decides to either accept it or to continue waiting. The research question at hand is therefore: if offered an organ, when should a patient decide to accept it? This question is of great practical importance, as it is a life-or-death decision faced by thousands of people per year, and growing. This research will focus only on livers, however the methodology used is applicable to other organs. The key issue in modeling this decision process is the assumption made regarding the information available to the patient. In all cases, the pertinent characteristics of the liver are known at the time an offer is made, as is the patient's health. What is uncertain is the ranking of the patient relative to the other patients on the waiting list, and the timing of future offers. The simplest version of this problem is the case in which a living donor exists. Typically, however, donors are cadaveric. In the latter situation, liver offerings occur randomly and patients "compete" with each other for livers without knowing their relative position on the waiting list.
This research project will formulate mathematical models for the living-donor as well as the cadaveric-donor situation, in which the objective is to maximize, for instance, "quality-adjusted life expectancy" or some other objective. A model will be developed for the hypothetical situation in which the composition of the waiting list is public information. Specifically, the reach team will formulate these situations as Markov decision processes and engage in numerical and analytical study of the resulting optimal policies. Numerical study will make use of extensive clinical data, identify patterns that will guide the analytical study, and allow the researchers to explore the potential value in publishing the waiting list. Analytical study will determine conditions under which the optimal policies have appealing, consistent structure. It is interesting to note that most of the existing literature focuses on modeling the organ transplant problem from UNOS's perspective, rather than from the patient's perspective as considered here. Note, however, that the research may have an impact on this policy-perspective line of research, since one of the objectives is to study the policy change that involves the publication of the waiting list.