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Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List

Graduate School of Business, Stanford University, Stanford, California 94305
Division of Nephrology, University of California San Francisco, San Francisco, California 94143
Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
stefzen{at}leland.stanford.edu
lwein{at}mit.edu

The crux of the kidney allocation problem is the trade-off between clinical efficiency and equity. We consider a dynamic resource allocation problem with the tri-criteria objective of maximizing the quality-adjusted life expectancy of transplant candidates (clinical efficiency) and minimizing two measures of inequity: a linear function of the likelihood of transplantation of the various types of patients, and a quadratic function that quantifies the differences in mean waiting times across patient types. The dynamic status of patients is modeled by a set of linear differential equations, and an approximate analysis of the optimal control problem yields a dynamic index policy. We construct a large-scale simulation model using data from over 30,000 transplants, and the simulation results demonstrate that, relative to the organ allocation policy currently employed in the United States, the dynamic index policy increases the quality-adjusted life expectancy and reduces the mean waiting time until transplantation for all six demographic groups (two sexes, races, and age groups) under consideration.

Subject classifications: Health care: Organ allocation; Queues: networks with reneging; Dynamic programming: applications.
History: Received July 1997; revision received April 1998; revision received December 1998; revision received March 1999; accepted March 1999.

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