Alleviating the Patient's Price of Privacy Through a Partially Observable Waiting List

In the United States, end-stage liver disease patients join a waiting list and then make accept/reject decisions for transplantation as deceased-donor organs are offered to them over time. These decisions are largely influenced by the patient's prospect for future offers, which can be ascertained most accurately by knowing the entire composition of the waiting list. Under the current transplantation system, however, the United Network for Organ Sharing (UNOS), in an effort to strike a balance between privacy and transparency, only publishes an aggregated version of the waiting list. However, it is not clear whether the published information is good enough (compared with perfect information) to help patients make optimal decisions that maximize their individual life expectancies. We provide a novel model of this accept/reject problem from an individual patient's perspective using a partially observed Markov decision process (POMDP) framework, which incorporates the imperfect waiting list information as published currently into the patient's decision making. We analyze structural properties of this model. In particular, we establish conditions that guarantee a monotone value function and a threshold-type optimal policy with respect to the partially observable rank state that captures the imperfect waiting list information. Furthermore, we develop an improved solution methodology to solve a generic POMDP model. This solution method guarantees, for any fixed grid, the best possible approximation to the optimal value function by solving linear programs to compute the optimal weights used for the approximation. Finally, we compare, in a clinically driven numerical study, the results of this model with those of an existing Markov decision process model that differs from our model in assuming the availability of perfect waiting list information. This comparison allows us to assess the quality of the published imperfect information as measured by a patient's so-called price of privacy (i.e., the opportunity loss in expected life days due to a lack of perfect waiting list information). Previous work estimates a significant loss in a patient's life expectancy, on average, when the patient has no waiting list information compared with full information. In this paper, we find that the currently published partial information is nearly sufficient to eliminate this loss, resulting in a negligible price of privacy and supporting current UNOS practice.