Introduction

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Hospital provision for accommodating increasing numbers of emergency admissions is a matter of considerable public and political concern and has been the subject of widespread debate. ^{1 2} For several years hospital managers have been under pressure to reduce bed capacity and increase occupancy rates in the name of operational efficiency. More recently, public disquiet has arisen in cases where patients could not gain ready access to a local hospital or were subjected to extended delays while vacant beds were identified. An appreciation of the dynamics of the hospital system in its ability to respond to fluctuating demand is important in framing policy, determining appropriate levels of service provision, and establishing realistic performance monitoring criteria.

Systematic analysis of long term trends in emergency admissions has been most fully developed in Scotland by Kendrick et al, ^{3 4} but no comparable series has been published for England. A detailed analysis of hospital episode statistics for all diagnoses (excluding mental health) in England for the period 1989-90 to 1995-6, undertaken as part of the project reported here, showed a trend line for emergency admissions rising at 1.9% a year, of which only a quarter was attributable to changes in the size and composition of the population.⁵ Elective admissions over the same period declined at a rate of 1.9% a year, while day cases rose by 16.3% a year. Occupied bed days declined by 4.6% a year for emergencies and by 5.4% a year for elective admissions.

Thus the balance between emergency and elective admissions has shifted in six years from 56%:44% to 61%:39%, with emergency patients now occupying 65% of the staffed beds available. Hospitals are thus faced with an increasing proportion of their inpatient work coming from the fluctuating and unpredictable demands of emergency admissions, and less coming from planned elective patients.

Analysis of hospital episode statistics shows that emergency admissions will continue to rise, probably at a similar rate in the future to that experienced in the past. Equally, the proportion of emergency admissions is also likely to increase, so that the proportion of bed capacity required for emergency work will continue to grow.

Lane et al have examined the impact of hour by hour demand on an accident and emergency department, with particular emphasis on long waiting times for admission,⁶ but there is also a need to study the implications of the random nature of demand for emergency admission on a daily basis as it affects use of the bed stock. We are not aware of any recent published research with this emphasis.

Day to day fluctuations in emergency demand affect the quality of care and hospital efficiency, and an understanding of these effects is required to help in planning services and choosing operational interventions to alleviate problems and avoid crises.

	Methods

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Discrete-event stochastic simulation modelling is a well established management technique for investigating the behaviour of complex systems subject to random effects.⁷ Such a model was developed, using a Microsoft Excel 5 spreadsheet, to explore the relation between randomly fluctuating demand for patient admission and available inpatient bed capacity. The model generates new arrivals for each day of a 1000 day period as random variations around a long term trend line, using an empirically derived normal distribution adjusted for seasonal and day of week variations. These patients are then accommodated as long as the hospital has a vacant bed. The model is designed to allow complex interactions to be explored (for example, random shocks such as flu epidemics, or feedback between discharge and admission rates), but these features are not reported in this paper.

The model has been further extended to encompass elective admissions sharing a common bed pool (including some designated elective beds), and an additional performance measure has been introduced to indicate the proportion of elective admissions cancelled each day. However, the effect of this change proved limitedsome emergencies are admitted at the expense of cancelled electives but with no increase in the occupancy rates for the emergency bed pool. The simplicity of the emergencies-only model is preferred here as it serves to focus attention on the primary problem of rising emergency admissions for acute hospitals.

The model was calibrated to a notional baseline position by using data obtained from detailed analysis of admissions records and length of stay distributions at two NHS trusts (one city centre teaching hospital and one non-teaching hospital in a semirural post-industrial town) and was adjusted to represent a situation where the hospital is just beginning to experience significant operational risks in relation to accommodating emergency arrivals. The baseline values are shown in table 1.

A wide range of statistics can be derived from the model; the key output measures of system performance are the proportion of new arrivals for emergency admission who cannot be accommodated owing to lack of available beds; the proportion of days in a year when at least one patient requiring immediate admission cannot be accommodated (termed a crisis day); and the bed occupancy rates achieved. The level of risk to both patients and hospital is a function of the rate at which new emergency patients arrive at the hospital, the rate at which emergency patients are subsequently discharged, and the daily available bed capacity.

It was determined by experiment that a stable result was achieved when 100 repetitions of the model were carried out with different random numbers and the results aggregated. Eleven separate experiments were undertaken, in each of which a different factor was varied within a range of realistic values (table 2).

	Results

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Experiments 1-5 and experiment 10 were equivalent in terms of system dynamics; the figure shows the combined results. The level of risk for a hospital bed shortage is about four times that for an individual patient. Risks are minimal so long as the mean bed occupancy remains below about 85%. Above this level the risks become substantial (at 85%, a hospital can expect to be short of beds for admissions on four days in a year), and above a mean bed occupancy of 90% the system is regularly subject to bed crises.

View larger version (20K): [in this window] [in a new window]   Relation of performance risks to average bed occupancy

Experiment 6 indicated that from very different initial bed occupancy positions all simulations converge to a relatively stable band within 14-16 days. Thus a hospital that experiences a day on which no further admissions can be accommodated can expect to recover its long term demand-capacity balance in a period approximately equal to twice the mean length of stay. This implies that even a relatively low risk of failure can disrupt the operation of the hospital for a considerable time: at 85% mean occupancy, a hospital that runs out of beds for four days in a year may be disrupted for up to eight weeks in total.

The results of experiments 7-9 show that risk increases as variability rises, seasonality being the most influential factor. Varying the size of the bed pool over a wide range (experiment 11) affects risk only for capacities below about 150 beds, and even then produces only modest increases in risk.

	Discussion

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Management scientists have long been aware of the implications of queuing theory in systems with fixed or limited capacity. Thus our principal finding of a rapid increase in risk to patients and to the system at high occupancy levels is not unexpected.

Any model can capture only a limited range of the many contributory factors in real life, and models include various simplifying assumptions (such as the admission and discharge rate functions). Moreover we have intentionally reported only univariate experiments to show the relative importance of individual factors in the performance of the system. In reality these would all be operating together interactively, and additional complex organisational and psychological behaviours are likely to come into play as a hospital approaches maximum capacity. None the less, the results show how such responses may affect the system: if consultants seek to protect beds against mounting demand by delaying discharges, this will probably hasten the onset of a crisis, whereas action to discharge patients early may allow a crisis to be temporarily delayed.

Demand and capacity
The relation between demand, capacity, and the risk of failure is reflected in the average occupancy rate. At rates above 85% risks become discernible, and above 90% the hospital system is subject to regular bed crises. The average occupancy rate in acute hospitals in England was 78.9% in 1996-7,⁸ and this is probably typical of the whole NHS. At a projected rate of growth in emergency bed days of 2.5% a year, this suggests that the NHS as a whole may be operating at 85% occupancy currently, and could exceed 90% by 2002-3. 

Effect of interventions
It is important to distinguish between one-off interventions with only a short term impact and interventions that alter underlying trends. For example, the introduction of a rapid response team will not have a long term effect unless the capacity of the team is increased annually in line with the increase in demand.

Difficulties in evaluation
The stochastic nature of emergency admissions has an important implication for attempts to evaluate management interventions. The performance of an acute hospital can vary considerably from one year to another solely as a result of the large fluctuations in demand, swamping the effects of policy or operational initiatives. Hence the meaningful evaluation of any measures taken to improve the performance of a single acute hospital in relation to emergency admissions is not possible unless effects are monitored over a long period (typically 5-10 years) or across a very large sample of hospitals; year on year comparisons for one hospital are meaningless. The difficulty of carrying out such evaluations is an important justification for a modelling approach.