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IMA Journal of Management Mathematics Advance Access published online on November 13, 2008
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpn032
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Modelling risk of readmission with phase-type distribution and transition models

Eren Demir{dagger}, Thierry Chaussalet{ddagger}, Haifeng Xie§ and Peter H. Millard

Health and Social Care Modelling Group, Department of Information Systems and Computing, School of Informatics, University of Westminster, London, W1W 6UW, UK

{dagger} Corresponding author. Email: demirer{at}wmin.ac.uk

{ddagger} Email: chausst{at}wmin.ac.uk

§ Email: xieh{at}wmin.ac.uk

Email: phmillard{at}tiscali.co.uk

Received on 1 May 2007. Accepted on 1 December 2007.

A patient with frequent past readmissions may have an increased risk of future readmission. The principal objective of this paper was to determine the risk of readmission, given individual patient's history of readmissions. First, we develop a modelling approach to systematically tackle the issue surrounding the appropriate choice of a time window which defines readmission. Discharged patients can be divided into two groups: a group at high risk of readmission and a group at low risk. Using national data (England), the estimated time window for chronic obstructive pulmonary disease is 38 days. Using this time window, we classify ‘high’ and ‘low’ risk of readmission groups. We use transition models to incorporate patients’ history of readmissions along with additional covariates. Solely using patients’ history of readmissions, the model has a receiver operating characteristic c statistic of 0.71, illustrating that such a simple model with no covariates has the potential of estimating risk of readmission.

Keywords: emergency readmission; time window; mixture distribution; transition model


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