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IMA Journal of Management Mathematics Advance Access originally published online on April 12, 2005
IMA Journal of Management Mathematics 2005 16(4):369-381; doi:10.1093/imaman/dpi015
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Length of stay as a performance indicator: robust statistical methodology

Elena Kulinskaya1,**, Diana Kornbrot2 and Haiyan Gao3

1 Statistical Advisory Service, Room G06, Sir Alexander Fleming Building, South Kensington Campus, Imperial College, London SW7 2AZ, UK, 2 Faculty of Health and Human Sciences, University of Hertfordshire, Hatfield ALIO 9AB, UK, 3 Intensive Care National Audit and Research Centre, Tavistock House, Tavistock Square, London WC1H 9HR, UK

** Corresponding author. Email: E.Kulinskaya{at}imperial.ac.uk

Length of stay (LOS) is an important performance indicator for costing and hospital management and a key measure of efficiency of NHS. However, LOS is difficult to analyse because its statistical distribution is non-normal and LOS data habitually have many outliers. Furthermore, the usefulness of LOS for improving NHS performance is undermined because no adjustments are made for some key factors. This paper addresses both these problems. Health episodes statistics data from the UK NHS for 1997/98, and 1998/99 are analysed to investigate the effects of five key variables: admission method, discharge destination, provider (hospital) type, speciality and NHS region. All are found to influence LOS. The effects of some factors are substantial, and were not previously known, and so are not included in planned future NHS performance measures, e.g. LOS is at least 25% longer for patients transferred from other hospitals rather than admitted as an emergency; and LOS for patients discharged to private institutions is more than twice that for patients discharged to NHS institutions or their own home. The problem of finding the most appropriate statistical analysis for data of the LOS type is addressed by comparing standard general linear model methods with an advanced robust method called truncated maximum likelihood (TML). The TML methods are shown to have several advantages over standard methods, in terms of model fit and accuracy of parameter estimation. Implications of these findings for future use of LOS are considered.

Keywords: hospital performance indicators; adjustment; HRG classification; robust methods; general linear model; truncated maximum likelihood methods


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