Model behaviour

Published: 17/10/2002, Volume II2, No.5827 Page 26 27

A more sophisticated method of predicting admissions than simply relying on previous years' figures has been shown to improve significantly the ability of acute trusts to plan ahead, as Stephen Moore explains NHS managers are keen to develop more sophisticated forms of modelling to help with decision-making.

1A model in use at Plymouth primary care trust for the three-year planning cycle is providing useful information.

Unplanned admissions to hospitals have always been the enemy of NHS service delivery and there seems to be a belief that the number of people who turn up at the hospital needing an emergency admission on any given day is dependant on such a huge array of complex interacting factors that it is impossible to plan on any other basis than the historic average number of admissions. This approach has been the staple fare of planning returns for many years. But a concentration on the average number of admissions misses the essential point for hospitals - the confounding effect that higher-than-average admissions can have on elective capacity and on public image. Cancellation of elective work never looks good in the newspapers and smacks of a service that has failed to modernise.

An alternative approach is to use the statistical properties inherent in the collective behaviour of non-elective admissions to build a model that can predict the daily number of admissions in the short to medium term, together with the quantified daily risk that the actual number of admissions will be higher (or lower) than this prediction.

Statistical properties of non-elective admissions The model was constructed using groups of specialties as a basic building block taking account of previous research.

2These groups were designed to reflect how beds were grouped within Plymouth Hospitals trust's Derriford Hospital. Data was then extracted from the hospital's patient administration system for each group detailing historic daily admissions and discharges from the hospital.With the exception of a few smaller specialty groups, which have few non-elective admissions and tend to be standalone services, analysis of this data revealed admissions closely followed a normal distribution.

This has obvious benefits for model building because the normal distribution has simple and 'well-behaved' characteristics that can be exploited in the simulation. A standard spreadsheet statistical package can easily create a stream of random numbers based on nothing more than the mean and standard deviation of the distribution. These random numbers represent the 'raw' number of admissions flowing into the hospital each day.

Essentially, the likelihood of a number being randomly selected by the software depends on how many standard deviations it is from the mean. The simulation therefore directly models for those unusual days when the hospital is inundated, as well as those days when it is unusually quiet.

By themselves, these numbers are not sufficient to allow for adequate planning. The next step is to adjust them according to how far in the future that particular day lies, which month the prediction is for and which day the prediction falls on. This information can be gleaned from the historic data using standard decomposition techniques.

Having 'processed' the raw numbers through each of the above steps, the model was run a number of times to give multiple predictions for each day in the prediction period. The local model had a prediction period of two years and was run around 500 times. This resulted in a predicted number of admissions for each day in the period coupled with its own probability distribution showing the degree of variation that might occur for that particular day (ie the degree of risk associated with planning for that level of non-elective admissions).

A simple calculation can convert admissions into occupied beds, using day-specific discharge rates for each specialty group, and actual numbers of beds can be plotted against this.

The graph opposite shows the output for the medical specialty group. A seven-day moving average has been plotted to make the graph clearer, though this is purely for presentational reasons.

The graph shows that the average number of occupied beds never crosses the actual available beds, though the rising trend is apparent. This is probably as far as most hospitals' planning would go for nonelective admissions.Of greater interest to the smooth running of the trust, however, is the growing risk of outliers shown by the dotted lines around the average. The 80 per cent line (green) shows the level of occupied beds that would be required if the trust wished to be certain of meeting daily non-elective demand 80 per cent of the time. The graph shows that in the winter of 2002-03, the trust will have insufficient beds to be this confident. The outer lines show how many occupied beds should be planned for if the trust wishes to be certain of having enough beds available almost 100 per cent of the time. To be this sure, the specialty group would need an extra 40 beds.

Implications for short-term capacity planning An understanding of the degree of risk inherent in any planned level of non-elective capacity has obvious benefits for trusts constructing three-year capacity plans. Trusts have become increasingly sophisticated in the 'joining up' of elective capacity with waiting times, but have tended to be simplistic in their approach to predicting non-elective capacity requirement. In medical and child health specialties, it is not the average trend that poses the greatest threat to meeting waiting-time targets, it is the risk that the trust will have insufficient beds to accommodate the days demand surges. The model has demonstrated that as occupancy rates in medical beds rise, the risk of disruption to elective specialties rises exponentially. Indeed, running the model to 2005-06 has shown that, if the long-term trend in medical admissions continues, the number of occupied bed days consumed by outliers increases by almost 550 per cent from the level expected in 2002-03.

Achieving the waiting-time targets for 2005-06, including no-one waiting for more than six months for inpatient treatment, therefore involves more than finding ways to generate extra elective capacity, which is in itself a huge challenge to the local health economy.Without finding innovative solutions to non-elective medical admissions, there is a real risk that the extra elective capacity is simply consumed by increasing numbers of outliers languishing far from their 'home' department.

A modelling approach would also assist trust managers to explore 'what-if ' scenarios to see how the hospital may react to a system shock such as a flu crisis or a serious outbreak of Norwalk-like virus.

Diagnostic and treatment centres appear to be a central part of the modernisation of the NHS. In a follow-up paper to the NHS plan, Investment and Reform for NHS Hospitals, published in 2001, the following vision was put forward: '[DTCs] are a new way of delivering elective care, which moves almost all elective work out of acute hospitals and into dedicated units.Most of these units will be on the same site as emergency and complex or critical care services but their elective work will not be vulnerable to disruption by them.With its work insulated from emergency pressures, it can serve as a reliable and dedicated high volume service which can safely, quickly and conveniently provide routine diagnosis and elective surgery.'

3Clearly this vision points to a future where patients can rely on hospitals to agree firm dates for elective services and the NHS can look forward to creating services which are almost entirely 'plannable'. But what of the non-elective service left behind? Being stripped of its elective beds means it must have sufficient capacity to deal with its own peaks and troughs without recourse to elective beds.The model set out here has proved helpful in understanding what this would mean because it can focus on both the average bed occupancy and the possible peaks that may occur on any particular day.

Early work to simulate the impact that a DTC may have on the Plymouth health community indicates that average bed occupancy rates in the remaining nonelective service would fall to 63 per cent across all specialty groups. For some individual specialty groups, the average occupancy would be even lower - trauma and orthopaedics, for example, would fall to 48 per cent average occupancy.There were some simplifying assumptions in this work which may have resulted in these occupancy rates being 'worst case', but if elective work is viewed as sacrosanct the predictions are unlikely to be more than one or two percentage points below what may be required.

Given this prediction, the cost of creating DTCs as envisaged in the NHS plan could be far larger than merely the capital and running costs of new elective facilities.Could the NHS, either locally or nationally, preside over a non-elective service where almost 40 per cent of the capacity (beds, nurses, doctors etc) is not used up to half the time.While it is dangerous to predict how a complex system like the NHS might react, it seems likely that there will be pressure for non-elective lengths of stay to lengthen significantly, if only to maintain an illusion of 'busyness' around the hospital.

Simulations are a low risk way of testing innovative solutions.Other industries have done this for years, so perhaps it is time for the NHS to follow suit.

Key points

A model in use in a primary care trust enables the prediction of acute admissions to hospital over a two-year period.

The results show that the rise in emergency medical admissions threatens the local hospital's capacity to meet waitingtime targets for planned work.

The research also showed that the establishment of a local diagnostic and treatment centre would reduce levels of occupancy in the acute hospitals to a level that could threaten its survival.

REFERENCES

1Bensley D, Davidge M. Principles of Modelling Access to Elective Care Systems. NHS Modernisation Agency and the Department of Health's economics and operational research division joint paper.

June 2002.

2Bagust A, Place M, Posnbett JW. Dynamics of bed use in accommodating emergency admissions:

stochastic simulation model.BMJ 1999; 319(7203):155-8.

3Secretary of state for health. Investment and Reform for NHS hospitals.

Department of Health, 2001.

Stephen Moore is health economist, Plymouth primary care trust.