In the United States, patients with end-stage liver disease must join a waiting list to be eligible for cadaveric liver transplantation. However, the details of the composition of this waiting list are only partially available to the patients. Patients currently have the prerogative to reject any offered livers without any penalty. We study the problem of optimally deciding which offers to accept and which to reject. This decision is significantly affected by the patient's health status and progression as well as the composition of the waiting list, as it determines the chances a patient receives offers. We evaluate the value of obtaining the waiting list information through explicitly incorporating this information into the decision making process faced by these patients. We define the concept of the patient's price of privacy, namely the number of expected life days lost due to a lack of perfect waiting list information.

We develop Markov decision process models that examine this question. Our first model assumes perfect waiting list information and, when compared to an existing model from the literature, yields upper bounds on the true price of privacy. Our second model relaxes the perfect information assumption and, hence, provides an accurate representation of the partially observable waiting list as in current practice. Comparing the optimal policies associated with these two models provides more accurate estimates for the price of privacy. We derive structural properties of both models, including conditions that guarantee monotone value functions and control-limit policies, and solve both models using clinical data.

We also provide an extensive empirical study to test whether patients are actually making their accept/reject decisions so as to maximize their life expectancy, as this is assumed in our previous models. For this purpose, we consider patients transplanted with living-donor livers only, as considering other patients implies a model with enormous data requirements, and compare their actual decisions to the decisions suggested by a nonstationary MDP model that extends an existing model from the literature.

Keywords: Markov decision processes, partially observable Markov decision processes, structured optimal policies, value of information, price of privacy, organ transplantation, medical decision making, health care treatment.