There is a general assumption that an 85 per cent occupancy rate represents the optimum use of NHS beds. But, says Rodney Jones, this could be the source of many a winter beds crisis

Over recent years the NHS has had a series of winter bed crises. In the years leading up to them there was a widely held supposition in the NHS that 85 per cent average occupancy was the optimum for an efficient hospital and that this occupancy allowed a suitable margin for peaks and troughs in demand. Beds were then closed to meet this target.

But NHS guidance now suggests that no trust should exceed a target of 82 per cent average occupancy and that an extra 2,100 general and acute beds will be made available.

1The provision of extra beds appears to have arisen partly out of the analysis in the consultation document of the findings of the national beds inquiry, while the figure of 82 per cent may have arisen out of work sponsored by the NHS and the Department of Health. For example, one study looked at the effect of average occupancy on the percentage of 'crisis days' for emergency admissions.

2 ,3 How was this figure derived, is it adequate, does it equally apply to all sizes of hospital, and is there a simple method available to hospital and primary care managers to enable them to appraise current occupancy levels?

Efficient bed management It is often assumed that higher average occupancy is evidence of higher efficiency. This ignores the fact that for any given level of demand and bed provision there will be a resulting occupancy and an associated turn-away (or queuing) rate.

Turn-away is the proportion of patients who are unable to gain immediate access to the correct bed and therefore have to wait hours or days. The higher the average occupancy the higher the turnaway rate and hence the greater the demands on community health services.

The mathematical description of arrival events and turn-away was developed in 1909 by the Danish researcher, AK Erlang, who did pioneering work in telecommunications traffic. This has been widely applied to hospital beds.

4From Erlang's equation it is possible to predict accurately the turn-away associated with any level of average bed occupancy.

What is a bed pool?

A bed pool is any group of beds dedicated to a particular purpose such as orthopaedics or maternity. There are 22 NHS categories of overnight bed. For each trust and category of bed both the number of available beds and the annual average occupancy are available.

5Unfortunately the simple definition of a bed pool is obscured within the NHS in a number of ways:

Bed numbers are reported by trust total, hence a trust operating from multiple sites will add all beds from a similar category and report this as the bed pool. For example, the 1,851 general and acute beds for the Leeds Teaching Hospitals trust will be the summation of many wards over multiple locations.

The 22 categories of bed type are highly specific in some cases. But unfortunately there is only one category called 'general and acute' that is used to describe 50 per cent of all NHS beds - namely, the surgical and medical specialties of a large acute hospital.

There is no opportunity to differentiate mixed and single gender wards.

Occupancy The occupancy is the number of days' stay for all patients (occupied bed days) divided by the time the beds were available (available bed days). The percentage occupancy obviously depends on the way in which the available bed pool is reported.

Many trusts have beds that are only reported as 'available'when they are fully staffed. Beds closed over the weekend are not reported by some trusts.

This is partly because low percentage occupancy was regarded as a sign of inefficiency within the NHS and generally led to threats of bed closure.

The occupancy is also an annual average. The actual occupancy varies hourly, daily, weekly and monthly. It is for this reason that beds are used in a flexible way in most hospitals. However, it then becomes difficult to report bed numbers in a single, standard way.

Borrowed beds are another complication. In time of need a bed from another bed pool is used to house a patient. This bed is then added temporarily to the bed count and subtracted temporarily from the other bed count. The bed reverts back as soon as the patient is able to move to the correct bed pool.

This has the effect of increasing the apparent percentage occupancy of both bed pools.

Despite the limitations of NHS bed data, it is still useful as a starting point to compare apparent efficiency between trusts.

Model for percentage occupancy and turn-away The relationship between the turn-away associated with a given number of beds and their average occupancy is one of rapidly increasing turn-away as the bed pool's size diminishes. For example, at 85 per cent occupancy the turn-away is 0. 1 per cent for 300 beds, 1 per cent for 150 beds, 5 per cent for 50 beds and 20 per cent for 10 beds.

At 90 per cent occupancy the turn-away figures are 0. 1 per cent for 1,000 beds, 1 per cent for 300 beds, 5 per cent for 100 beds, 20 per cent for 30 beds and 50 per cent for 10 beds. Table 1 gives further details for a range of bed pool sizes.

One can describe all NHS bed demand in terms of randomness in the arrival of patients, using Poisson statistics. These also describe the formation of queues and, hence, the turn-away or queuing rate.

These dynamics are encapsulated in the Erlang equation.

In an NHS context, elective surgery may be seen to be a non-random event. But its fundamental origin lies in GP referral which is subject to Poisson randomness. Hence even elective demand can be approximated by a Poisson-based approach.

6This allows us to calculate an approximate turnaway rate that will include cancelled operations and will not be too far distant from real life for even an acute hospital with a mixture of emergency and elective admissions.

The model works as follows. If the average rate of arrival is one per day, then Poisson statistics tell us that we can receive anywhere between 0 and seven patients per day (where an arrival rate of seven occurs on 0. 01 per cent of occasions). If we are resourced to receive the average of one, then on 26 per cent of occasions we will be faced with more patients than we are able to immediately handle - ie 26 per cent is the frequency of receiving two or more patients. To maintain an average of one the high occurrences are counterbalanced by a 37 per cent likelihood of not receiving any patients on a particular day.

A Poisson distribution is a skewed distribution with a higher proportion of events occuring less than the average - but counterbalanced by a long tail of lower-probability, higher-than-average events. It is this tail that creates the problems in a healthcare context.

A modified Erlang equation can be used to describe bed occupancy where there is an associated average length of stay.

4It is a fortunate feature of the Erlang equation that a line of constant turn-away, which is independent of average length of stay, can be drawn on a graph where percentage occupancy is the Y-axis and bed pool size is the X-axis. Poisson randomness also explains why bed occupancy decreases in an approximately exponential manner as the bed pool size decreases. It is far easier for a large bed pool to achieve high occupancy and it is a meaningless measure to take average bed occupancies from different-sized bed pools.

As can be seen from table 2, the average position can be very misleading. Only 1. 8 per cent of English trusts have adequate intensive care unit beds to avoid turn-away (with 40 per cent having higher than 20 per cent turn-away) while 65 per cent of maternity and paediatric units have sufficient beds to avoid turn-away. For general and acute beds some 10 per cent of English trusts are operating above 5 per cent turn-away. While the bulk of these trusts have fewer than 100 beds (some of which will be small community hospitals operating as an extended overflow bed pool to a nearby larger acute trust) there are still 12 larger acute trusts in this category. These trusts will have almost no hope of achieving national inpatient waiting-list targets because of a severe shortage of beds relative to the local demand.

Range in occupancy The occupancy for general and acute beds ranges from 40 per cent to 100 per cent, depending on size and mismatch between the supply of beds and the demand for them.

The previously assumed optimum occupancy for NHS beds of 85 per cent can be seen to be inappropriate and has probably been a significant contributory factor to the winter bed crisis.

For example, if 1 per cent turn-away is a desirable objective, then average occupancy around 70 per cent is appropriate to a 50-bed hospital, while 83 per cent is appropriate for 100 beds. A figure of 85 per cent is only appropriate above 150 beds.

In general, larger bed pools have higher average occupancy at the same turn-away rate. These are the benefits of scale.

The comments regarding the lumping of many bed pools into a single figure for general and acute must be seen in this context. The effect of this would be to reduce the percentage occupancy for some trusts at any given reported bed pool size.

General and acute Beds designated 'general and acute' form the bulk of what the public regards as 'hospital' beds. These are the beds that are the source of the winter bed crisis.

First perceptions can be misleading and a more detailed analysis shows that the winter bed crisis will be restricted to particular hospitals. For example, some 35 per cent of trusts with fewer than 100 general and acute beds are operating at an average turn-away of higher than 5 per cent.

Across all sizes, some 92 trusts are operating with higher than a 1 per cent turn-away rate - obvious first candidates for the extra 2,100 beds promised to the NHS.

The final statement needs to be qualified by reference to overall efficiency. For example, neither high average length of stay (relative to best practice for that particular condition) nor low day case rates are valid reasons for requiring additional overnight beds.

2But sub-division of the total bed pool into individual specialties will mean additional beds are required. This is because the effective bed pool size is thus reduced.

With between 100 and 400 beds, the 'average' occupancy corresponds to around 0. 1 per cent turn-away. Both common sense and 'average' practice therefore suggest that this is probably the 'optimum' turn-away rate for an acute hospital. It is turn-away rather than occupancy that should be used as the basis for comparison within the context of the other whole system factors identified in the national beds inquiry.

2In many ways occupancy has very little to do with efficiency. Occupancy is the outcome of demand and bed pool size.

The bed needs of each acute trust would need to be evaluated in more depth before categorically declaring that there were insufficient beds.

Particular emphasis would need to be placed on the degree of exclusivity between specialties and the need to provide separate bed pools for women, men and children. Other whole-system factors will also be important.

The fact that most bed pools experience seasonal peaks in demand is one reason why it is not wise to calculate the bed requirement of a new hospital based on annual averages.

Benefits from process redesign Benefits can be achieved by redesign of processes leading to a reduction in length of stay. For instance, a 10 per cent reduction in length of stay leads to a 10 per cent increase in throughput at the same level of occupancy and turn-away. At the same throughput a 10 per cent reduction in length of stay leads to a slightly less absolute reduction in turn-away - that is, from 20 per cent down to 12 per cent and so on.

Beds are expensive One may suspect that the 85 per cent occupancy 'rule' arose from the assumption that beds are expensive - hence, minimise the number of beds to minimise the expense. But this does not take account of the considerable demands on the community-based healthcare services.

There is another argument that an open bed is an occupied bed. The data from trusts does not support this theory and neither does the observation that the average US hospital operates at 65 per cent occupancy.

6The availability of 'excess beds' is therefore a key factor to the efficient operation of a large hospital.

It must be emphasised that the number of beds - and hence the resulting occupancy and turn-away - are the choice of a healthcare system. Hence while 85 per cent average occupancy may be technically too high, it may well be appropriate to certain (but not all) types of bed pool within the overall context of the surrounding healthcare system. This would also include the number of beds in nursing homes - a lack of which leads to bed blocking and high apparent length of stay in some acute trusts.

The impact of one more / less bed The ability to size small bed pools correctly is governed by the effect of randomness. For instance, a hospital with 20 beds and 42 per cent occupancy (no turn-away) may have been advised to close beds to 'save money'. Our imaginary hospital dutifully closes five beds, thus planning to increase average occupancy to 56 per cent. This takes it from 0 per cent to nearly 5 per cent turn-away. The local GPs go on strike, refusing to visit the extra patients now waiting at home for admission. The five closed beds do not save any money, since the number of patients per year does not change - and hence the nursing workload is not affected. The hospital may, however, have to employ a full-time bed manager to 'manage' the problems thus created, and the GPs will be consuming hours and petrol 'managing' those patients who have to queue for admission.

This is precisely the reason that some bed pools appear to have more beds than are required to achieve no turn-away. Allowance for seasonal variation (winter emergency pressures, etc) and the avoidance of widespread disruption elsewhere in the healthcare system explains what at first appears to be 'inefficient' (low) occupancy.

Turn-away does imply additional expense and hence it can be useful to consider the impact of one additional bed. One additional bed reduces occupancy by the proportion of the incremental change. Hence to go from nine to 10 beds reduces occupancy by 10 per cent and from 10 to 11 beds reduces occupancy by 9. 1 per cent. The Erlang equation can be used to estimate the effect of occupancy on turn-away and the associated costs then estimated for the entire healthcare system.

Economies of scale Since large acute hospitals are made up of many smaller bed pools, how do many hospitals achieve higher than 85 per cent average occupancy? By blurring the boundaries of all the bed pools they actually operate as a single large bed pool. This suggests that smaller community hospitals need to have almost no boundaries between bed pools in order to maximise throughput for a set number of beds.

Incremental changes to bed pool size have an enormous impact on the overall efficiency of the healthcare system surrounding smaller community hospitals. Given that the total bed pool of such hospitals is often less than 100 beds, then the only way to gain the benefits of size is to designate one ward as a general 'overflow'ward which acts as the buffer between supply and demand.

It is probably even likely that many primary care trusts will be debating whether to increase the size of their newly inherited community hospitals. The methods given here will allow them to make rational decisions and to forecast the likely total cost of turn-away.

Diseconomies of scale For the larger acute hospitals (more than 100 beds) there are significant numbers of trusts in the region, with 90 per cent to 100 per cent average occupancy. Above 300 beds this appears to drop off rapidly, and at 1,000 beds the range is between 7090 per cent occupancy - roughly the occupancy expected of bed pools with only 100 beds.

Hospitals in the range 100-300 beds seem able to make greatest use of the flexible boundary between bed pools. Above 300 beds organisational complexity and sheer size prevents economy of scale and leads to blockages to overall throughput. Super-trusts behave as if they were made up of a series of 100 bed pools each with a closed boundary.

Another reason that large hospitals may show lower occupancy is that they tend to see far more elective patients.

Many of the hospitals with around 100 beds and operating in the range 90-100 per cent occupancy are community hospitals. Some of the community hospitals are probably acting as an extended overflow bed pool for any nearby large acute hospitals.

High percentage turn-away is crippling to the operation of a waiting list and will result in very high levels of cancelled operations. An occupancy level of around 80 per cent would therefore tend to be a suitable balance between throughput and turnaway for a large acute hospital.

Limitations of the national beds inquiry One outcome of the national beds inquiry was a capitation-based approach to forecasting bed needs. This national approach is then scaled down to local level to forecast the bed requirements of individual hospitals. The Erlang equation shows that this approach is fundamentally flawed because it makes no allowance for the effect of size. Smaller populations require more beds due to the higher turn-away associated with smaller size bed pools.

For example, two hospitals serve need-weighted populations of 1 million and 100,000 respectively.

Assuming the bed requirement is 0. 5 beds per 1,000 head of population, then the two hospitals would have 500 and 50 beds respectively - that is, equal allocation in terms of population size. Both hospitals would have 82 per cent average occupancy. However, the smaller hospital would have 5 per cent turn-away while the larger would have less than 0. 1 per cent turn-away - highly inequitable bed provision.

To achieve a similar level of turn-away to the larger hospital the smaller hospital would need to operate at only 65 per cent average occupancy and would require 63 beds - a 25 per cent increase in its bed allocation. The 'one-size-fits-all' approach simply does not work and generates yet another set of healthcare inequalities. In this instance the community-based services surrounding the smaller hospital would be working far harder than those surrounding the larger hospital. Yet everyone would be telling them that they have got the 'correct' number of beds based on their population.

Any combination of beds and occupancy has an associated turn-away rate. An adequate bed requirement therefore depends on the size of the bed pool, the category of beds and the supporting structures in the community-based part of the healthcare system.

The previously assumed figure of 85 per cent occupancy will lead to unacceptable turn-away in all but the largest bed pools (assuming that there are no boundaries between adjacent sub-pools).

The more recent figure of 82 per cent is likewise only appropriate to greater than 100 beds (1 per cent turn-away) and assumes that there are no boundaries between bed pools.

Large acute hospitals handling a high volume of elective surgery via a number of specialtyspecific bed pools should probably have an average annual occupancy of around 80 per cent.

Other types of bed need to be evaluated with reference to the entire healthcare system. High turn-away will imply a high level of supporting community-based services. The extent of the required community services can be calculated with some precision using the Erlang equation.

Capitation formulas fail to take the important effect of relative size into account. Smaller community hospitals will therefore need up to 25 per cent more beds in order to achieve equity in terms of equal turn-away.

REFERENCES

1 HSC 2001/03 LAC(2001) 4.

2 Department of Health. Shaping the future NHS: long-term planning for hospitals and related services. Consultation document on the Findings of the National Bed Inquiry - Supporting Analysis, 2000.

3 Baghurst A, Place M, Posnett JW. Dynamics of bed use in accommodating emergency admissions: stochastic simulation model. Br Med J 1999; 319, 155-158.

4 Lamiell, JM. Modeling Intensive Care Unit Census. Military Medicine, 1995; 160, 227-232.

5 Data was obtained from the Department of Health and is for 1999-00 for 335 trusts (acute, community, maternity, mental health, elderly and learning disabilities).

6 Jones R. How many beds do we need? Healthcare Analysis & Forecasting. UK: Reading, 1997.