Allocation of Kidneys to Autonomous Transplant Candidates: A Sequential Stochastic Assignment Model

This paper considers the problem of allocating kidneys to autonomous transplant candidates who may refuse a kidney in anticipation of a superior future kidney. Starting with the first-best case where candidates are non-autonomous, we represent the kidney allocation problem using a sequential stochastic assignment model. In this model, there are n transplant candidates to be allocated n kidneys that will arrive sequentially. Each candidate and each kidney have their own type, kidney types are random and revealed upon arrival, and the reward from allocating a kidney to a particular candidate depends on both their types. The objective is to determine an organ allocation policy that maximizes total expected reward. We focus on partition policies in which the space of kidney types is divided into domains that correspond to the different transplant candidate types, and where each kidney is allocated to the candidate corresponding to its domain. Using large deviations we identify a partition policy that is asymptotically optimal as the number of transplant candidates becomes arbitrarily large. Next, we develop an incentive compatibility condition to characterize partition policies in which the autonomous candidates accept all allocated kidneys. This condition is then used to obtain an optimal incentive compatible partition policy. A numerical example shows that the first-best partition policy performs poorly when candidates are autonomous: In a scenario that resembles the current environment in the US, more than 10% of all kidneys are declined because transplant candidates consider them inferior to future offers they can expect. However, a modified policy that limits the variability in the type of kidneys each candidate expects to receive, recovers all the losses. A policy that maintains equity in access to transplantation across all patients is also tested, and the results show that almost 50% of all kidneys are declined by the transplant candidates in this policy. This demonstrates that candidate autonomy can severely compromise the performance of the organ allocation system, particularly if the allocation policy emphasizes an equitable distribution of organs.