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 performance measures, such as the mean and distribution of the time until transplant, are obtained and compared to empirical estimates calculated using the raw data.
KeywordsAbandonments Competing risks Estimation Liver transplantation Phase-type distribution Quasi-birth-and-death process Reneging
Mathematics Subject Classification60K25 90B22
The authors thank the Associate Editor and the referees for their useful comments and valuable suggestions that helped improve this paper. The authors also wish to thank D. Bellhouse who suggested we consider a competing risks framework for calibrating our model. This research was supported by the Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program.
- 3.Bazarah, S.M., Peltekian, K.M., McAlister, V.C., Bitter-Suermann, H., MacDonald, A.S.: Utility of MELD and Child–Turcotte–Pugh scores and the Canadian waitlisting algorithm in predicting short-term survival after liver transplant. Clin. Investig. Med. 27, 162–167 (2004)Google Scholar
- 5.Canadian Blood Services. Blood Type Facts. http://www.blood.ca/CentreApps/Internet/UW_V502_MainEngine.nsf/page/Blood+Type+Facts?OpenDocument&CloseMenu. Accessed 27 April 2013
- 11.Krishnamoorthy, A., Narayanan, V.C.: On a queueing system with self generation of priorities. In: Srinivasan, S.K., Vijayakumar, A. (eds.) Stochastic Point Processes, pp. 212–217. Narosa Publishing House, Chennai (2003)Google Scholar
- 12.Krishnamoorthy, A., Narayanan, V.C., Deepak, T.G.: On a queueing system with self generation of priorities. Neural Parallel Sci. Comput. 13, 119–130 (2005)Google Scholar
- 15.Krishnamoorthy, A., Narayanan, V. C., Chakravarthy, S. R.: The impact of priority generations in a multi-priority queueing system: a simulation approach. In: Proceedings of the 2009 Winter Simulation Conference (Eds. M.D. Rossetti, R.R. Hill, B. Johansson, A. Dunkin & R.G. Ingalls), IEEE Computer Society, New York, USA, pp. 1622-1633 (2009)Google Scholar
- 17.Lawless, J.F.: Statistical Models and Methods for Lifetime Data, 2nd edn. Wiley, Hoboken (2003)Google Scholar
- 20.Pinsky, M.A., Karlin, S.: An Introduction to Stochastic Modeling, 4th edn. Academic Press, Boston (2011)Google Scholar
- 22.Stanford, D.A., Lee, J.M., Chandok, N., McAlister, V.C.: A queueing model to address wait time inconsistency in solid-organ transplantation. Oper. Res. Health Care 3, 40–45 (2014)Google Scholar
- 23.Su, X., Zenios, S.: Patient choice in kidney allocation: the role of the queueing discipline. Manuf. Serv. Oper. Manag. 6, 280–301 (2004)Google Scholar
- 24.Syski, R.: Passage Times for Markov Chains. IOS Press, Amsterdam (1992)Google Scholar