A model for deceased-donor transplant queue waiting times

In many jurisdictions, organ allocation is done on the basis of the health status of the patient, either explicitly or implicitly. This paper presents a self-promoting priority queueing model for patient waiting times which takes into account changes in health status over time. In this model, most patients arrive as “regular” customers to the queue, but as the health of a patient degrades, their status is promoted to “priority” to reflect the increased urgency of the transplant. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the marginal delay distributions for each queue are computed via the use of matrix analytic techniques. The model is calibrated using liver transplantation wait-list data, provided by a regional health centre in Canada, which tracked approximately 1,100 patients over nearly 13 years. Blood-type-specific models are fit and performancemeasures, such as themean and distribution of the time until transplant, are obtained and compared to empirical estimates calculated using the raw data. S. Drekic (B) Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada e-mail: [email protected] D. A. Stanford Department of Statistical & Actuarial Sciences, Western University, London, ON N6A 5B7, Canada e-mail: [email protected] D. G. Woolford Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada e-mail: [email protected] V. C. McAlister Department of Surgery, Western University, London, ON N6A 5B7, Canada e-mail: [email protected]