Pressure and Force or Space and Time

Then I read a 1784 translation of Aesop's fable about the Crow and the Pitcher and I cheered up:

'Faced with the problem of getting water out of a pitcher, the crow saw some pebbles lying by. One by one he cast them into the pitcher; and thus, by degrees, raised the water up to the very brim, and satisfied his thirst'. The moral being:

Then I remembered the warm welcome we received from everyone we met, at the ECCO 2004 conference in Beirut organised by Ibrahim Osman and prayed for peace.

Acute medical patients in orthopaedic wards, surgical operations cancelled; trolley waits; ambulance by passes, avoidable sickness and increased dependency. There has to be a better way:

In this issue John Preater, a mathematician, Keele University, UK explains queuing theory, illustrating the relationship between bed allocation, bed occupancy and queues. We also report collaborative research by Gary Harrison and Andrea Shafer in Charleston, South Carolina, USA and Mark Mackay in Adelaide, Australia, which has developed a model that accounts for daily, weekly and seasonal variability general medical bed occupancy and use. [2]

References:

Congratulations to Christos Vasilakis - SPARC grant.

Hospital Queue Networks

PUBLISHED PAPERS

Examines factors associated with 20,209 readmissions to a Manchester hospital. Male sex, heart failure and chronic pulmonary diseases significantly associated. Shorter length of stay is associated with higher readmissions. Concludes that performance analysis should take deprivation into account.

Mackay, M. and M. Lee (2005). "Choice of Models for the Analysis and Forecasting of Hospital Beds." Health Care Management Science 8(3): 221-230.

The authors investigated model selection and assessment in relation to hospital bed compartment flow models. Training and test data related to the 1998 and 1999 calendar years. Increasing model complexity resulted in overfitting. Seasonal models were best. Results of single day census type models were similar, but inferior, to models generated from a full year of training data. The additional data make the models better able to capture the variation across the year in activity.

Breakthrough in Modelling Acute Medical Services

Step by step, Gary Harrison has been developing explanatory flow models of bed occupancy and use. First a dynamic two compartment model, with a what-if component, which explained why mixed exponential equation with two components fitted midnight bed occupancy data in thirteen UK departments of geriatric medicine (short stay one month; long stay two years). Then a three compartmental model based on a midnight bed state in a large UK psychiatric hospital (short stay three months, medium stay two years and long stay twenty-five years.

Verification of a mixed exponential fit to midnight beds states in acute medical services (acute care seven days, longer stay two months) led to further exploration of bed occupancy patterns in other services. Early criticism of these tools in acute services focused on the use of midnight bed states and the variable, daily, weekly, seasonal demand for admissions to acute hospital care.

Now, in collaborative work with Mark Mackay from Adelaide, Gary has developed a model which follows the daily trajectories of acute patient care, thus creating a model of the average days bed use: i.e. Sunday, Monday, Tuesday, Wednesday etc admissions, revealing three stages:

1. First stage: new patients (7%) of all patients admitted are released on the first day,
2. Second stage: short stay leave within days; three in every hundred become longer stay, and
3. Third stage: longer stay leave within weeks.

Overall, upon admission the expected length of stay is 6.3 days, but for a patient who has been in the hospital 10 days the expected additional stay is 9.1 days. Moreover, though only 10.5% of the admitted patients are longer stay when they are discharged, they occupy 22.4% of the beds.

The model can simulate the resources needed as demand grows and shows the benefits to be gained by smoothing admission and discharge rates. It also explains the complex relationship between bed allocation, bed occupancy and emptiness. The model is both flexible and portable. The data used is already being collected. The work was done using Microsoft Excel and Visual Basic and sample spreadsheets are available from harrisong@cofc.edu

Darrab, A. A., J. Fan, et al. (2006). "How does fast track affect quality of care in the emergency department?" European Journal of Emergency Medicine 13(1): 32-35.

Fast tracking of non-urgent patients, between 13.00 and 19.00 hours, significantly shortened their length of stay without compromising urgent care. Used Canadian Triageand Acuity scale; data collection covered one week in August 2002 and 2003. Studies in other centres over longer periods are needed to confirm or refute this finding.

Kulinskraya, E., D. Kornbrot, et al. (2005). "Length of stay as a performance indicator: a robust statistical methodology." IMA Journal of Management Mathematics 16(4): 369-381.

NHS data. Compares standard general linear models with truncated maximum likelihood. Admission method, discharge destination, provider (hospital) type, specialty and NHS region all influence length of stay. Death occurs early and transfer occurs late. Since the new NHS case mix funding ignores transfers and destination at discharge, while encouraging shorter length of stay, trusts with higher mortality may be doing the best under the new system. Which is certainly not desirable from the patient's point of view.

MASH News

We are indebted to IMS MAXIMS plc's sponsorship for enabling the website version to be developed. IMS is a significant supplier to NHS and has an ongoing interest in enhancing the scope of IT support in the NHS, especially in the areas of clinical knowledge and decision support. Developers of systems looking for market opportunities are invited to contact IMS at their UK office, or by e-mail to Paul Cooper (pcooper at imsmaxims dot com). Accessing their web-site http://www.imsmaxims.com will give a feel for the scope of their work.

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Copyright (c)Roy Johnston, Ray Millard, 2005, for e-version; content is author's copyright,