Matching Kidneys with Priority in Kidney Exchange Programs

Kidney exchanges were developed to match kidney failure patients with willing but incompatible donors to other donor-patient pairs. Finding a match in a large candidate pool can be modeled as an integer program. However, these exchanges accumulate participants with characteristics that increase the difficulty of finding a match and, therefore, increase patients’ waiting time. Therefore, we sought to fine-tune the formulation of the integer program by more accurately assigning priorities to patients based on their difficulty of matching. We provide a detailed formulation of prioritized kidney exchange and propose a novel prioritization algorithm. Our approach takes advantage of the global knowledge of the donor-patient compatibility within a pool of pairs and calculates an iterative, paired match power (iPMP) to represent the donor-patient pairs’ abilities to match. Monte Carlo simulation shows that an algorithm using the iPMP reduces the waiting time more than using paired match power (PMP) for the difficult-to-match pairs with hazard ratios of 1.3480 and 1.1100, respectively. Thus, the iPMP may be a more accurate assessment of the difficulty of matching a pair in a pool than PMP is, and its use may improve matching algorithms being used to match donors and recipients.