THE OPTIMAL TIMING OF PREDIALYSIS PREARRANGED PAIRED KIDNEY EXCHANGES

Purpose: Paired kidney exchange (PKE), a cross-exchange of organs among two incompatible patient-donor pairs, is a clinical strategy to overcome the difficulties in matching end-stage renal disease patients who are on dialysis with incompatible donors, but there has not been any emphasis on the timing of predialysis kidney exchanges and the effects of disease severity on the patients' decisions.

Method: We consider the transplant timing decisions of two autonomous patients  in a prearranged pre-dialysis PKE and develop a clinically realistic game-theoretic decision model to analyze the outcomes of the game resulting between the patient-donor pairs. We describe the state of the system as an ordered pair of the patients' individual glomerular filtration rates (GFR), each of which is assumed to evolve according to a discrete-time finite-state Markov process independent from the other.. The initiation of dialysis is an external probabilistic event. Given the patients are self-interested to maximize their own quality-adjusted life expectancies; we characterize socially efficient stationary equilibria of the game by a mixed-integer linear program. We also develop an easily implementable iterative best-response algorithm to characterize stable equilibria of the game.

Result: Using data from the University of Pittsburgh Medical Center we construct a discrete time Markov process to define a stochastic progression of predialysis GFR levels of a large-patient cohort involving more than 60000 patients. We also use publicly available data from the Scientific Registry of Transplant Recipients to estimate the patients' expected quality-adjusted post-transplant survival using proportional hazards. We find that patients’ maximum total life expectancies vary in between 26 and 35 quality-adjusted life years. Patients delay the exchange while their initial GFR levels are above 30 mL/min/1.73 m² whereas they immediately exchange the organs whenever their GFR levels fall below 20 mL/min/1.73 m². We evaluate the societal welfare loss due to patient autonomy, and estimate that patient autonomy may cost up to 2 quality-adjusted life years to the society.

Conclusion: The optimal time to exchange is highly sensitive to patient-donor characteristics and GFR-progression rates. Patients with a higher rate of decrease in GFR are more likely to offer to exchange than those with a lower rate of decrease. The quantitative estimates of the patients' expected lifetimes resulting from our model can provide a way to improve the matching mechanisms in current practice.