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Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List

Department of Industrial and Systems Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706
Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106
Departments of Industrial Engineering and Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Section of Decision Sciences and Clinical Systems Modeling, Division of General Internal Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania 15213
alagoz{at}engr.wisc.edu
lisa.maillart{at}case.edu
schaefer{at}ie.pitt.edu
robertsm{at}upmc.edu

The only available therapy for patients with end-stage liver disease is organ transplantation. In the United States, patients with end-stage liver disease are placed on a waiting list and offered livers based on location and waiting time, as well as current and past health. Although there is a shortage of cadaveric livers, 45% of all cadaveric liver offers are declined by the first transplant surgeon and/or patient to whom they are offered. We consider the decision problem faced by these patients: Should an offered organ of a given quality be accepted or declined? We formulate a Markov decision process model in which the state of the process is described by patient state and organ quality. We use a detailed model of patient health to estimate the parameters of our decision model and implicitly consider the effects of the waiting list through our patient-state-dependent definition of the organ arrival probabilities. We derive structural properties of the model, including a set of intuitive conditions that ensure the existence of control-limit optimal policies. We use clinical data in our computational experiments, which confirm that the optimal policy is typically of control-limit type.

Subject classifications: dynamic programming/optimal control; applications and Markov; infinite horizon; health care; treatment.
History: Received September 2004; revision received May 2005; accepted December 2005.

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