Utility, Equality, and the Tradeoff Between Quality of Graft and Waiting Time in KPD.

Abstract

Introduction: Virtual Matching for kidney paired donation (KPD) is dependent on both donor and patient ability to match others in a KPD database. Chains might impose fewer constraints than loops. We present a tool to assess the utility and fairness of KPD algorithms, and apply it to a large KPD program, the National Kidney Registry (NKR). We then show how the tool can be applied to tradeoffs between non-immunological characteristics of the match offer and the patient waiting time. Method: Using distribution of blood types and average PRA of 1151 pairs and 162 non-directed donors (NDD) in NKR pool, a Markov Chain model was built to estimate wait-time (WT)-to-match as a function of PMP, which equals the product of the probability of patient’s compatibility with arbitrary donor in the pool and the probability of the potential donor matching arbitrary recipient in the pool. Then the estimated WT-to-match was compared to actual WT-to-transplant of 690 consecutive NKR transplants. Finally a regression model was developed to investigate the correlation between PMP and average WT-to-transplant. Result: The figure illustrates that average WT-to-match correlates inversely with PMP. Low PMP (hard-to-match) pairs have the greatest reduction in estimated average WT-to-match when NDD are used to initiate chains compared to using cycles. Actual WT-to-transplant of patients in NKR also correlates inversely with PMP. The log of the pair’s pair match power (PMP) and the log of the average waiting time correlate negatively, with p = .00047.Figure: No Caption available.Conclusion: The tool can be used to compare the performances of different KPD match prioritization policies. As match offers are more “fairly” distributed, the slope of the WT-to-transplant line approaches zero. Relatively lower center location of the transplant data points in the figure suggests higher utility. Hard-to-match patients who impose restrictions on the potential donors have exponentially longer waiting times.