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Ambex Ambulance Economics

Alstair Fischer
Senior Lecturer in Health Economics
St George's Hospital Medical School And
Lecturer in Economics, Trinity College, Cambridge

Paul O'Halloran
Statistician, St George's Hospital Medical School

Reporting on work done on ambulance response time data for the Surrey Ambulance Service

We have looked at the log of calls from April 1, 1997 to Jan 31, 1998.
* Emergency calls 59,000
* Of these, 55,000 were first ambulance
* Urgent calls 16,000
* Total calls 75,000
* Measure of responce time:

average responce time

* Easier to conduct analysis using the average responce time than the 75th percentile responce time.
* Close relationship between the two measures.

The centerpiece of the analysis:

ambulance responce curve

* Shows the relationship between responce time (r) and the number of ambulances available but not in use (n).


35 ambulances are available for use -

fully crewed,


waiting for a job

in the middle of a job.
Suppose that 12 ambulances are in the middle of a job.

Then 23 are waiting for a job.

This (23) is the value of n at the time the next job arrives.

Clearly, as n incereases, the response time (r) will fall, other things being equal.

**** For all 55,000 first-ambulance calls, we found the value of n and related it to r, the response time for that job.****

It resulted in a thick cloud of points.

Nothing happening there!

So then we took the average value of r for each value of n.

The fog lifted.

The ambulance response curve:

construction and properties

Allowance has been made for

Traffic - increases r during the day
The number of ambulances on duty
We have not taken into account who allocated ambulances in the control room . . . . . but we could have done
depends on activation time and travel time.
The slope of the ambulance response curve shows that each additional ambulance would save 9.7 seconds of response time.
An ambulance costs about £250,000 to run each year.
Each second of response time saved would cost about £250,000/9.7=£26,000, if achieved using additional resources
Let us be quite clear about what we have done:

We can now put a price on the benefit we get when we reduce response time by one second.

What does the ambulance response curve tell us?

It answers four questions:-

How many resources we will need to meet government response time targets? I.e. how many more ambulances do we need.
How should ambulances be rostered (at different times of the day and days of the week) to minimise average response time for a given budget?
Will an innovation with the same cost as an additional ambulance provide more or less benefit than the additional ambulance? That is, isi an innovation worth doing?
Other things being equal, how would an increase in demand of, say, 10% affect response times?
Let us look at these four things in turn.

Overall resources
75th percentile response time = 10 mins 26 seconds overall.

Average response time = 8 minutes 52 seconds

To reduce the 75th percentile response time to 8 minutes, the average response time would have to fall to 6 minutes 46 seconds, al fall of 126 seconds.

Each ambulance causes a 9.7 second fall, so

126/9.7 = 13.0

ambulances would be needed to achieve the target.

This represents about a 35% increase in the size of the ambulance fleet!!

(As we add additonal ambulances, it is unlikely that each new ambulance would maintain a 9.7 second saving. It the saving averaged around 8 seconds, for example, the number of new ambulances to achieve the target would rise to about 16, or over a 40% increase in the size of the fleet.)

How should the roster alter?

We compare 4 to 5 am Tuesday with 11 pm to midnight on Saturday.

From 4 am to 5 am om Tuesdays, there were 143 calls in the data period.

Average value of n, 4-5 am was 15.9.

From the slope of the ambulance response curve, each call would take 9.4 seconds longer on average if there were one less ambulance.

Thus the aggregate response time increase if there were one less ambulance at this time would be 9.4x143 = 1.344 seconds.

At 11 pm on Staurday evening, there were 535 calls.

Average value of n = 11.1.

If there were an additional ambulance at this time, it would save on average 14.4 secondsin response time for each call.

Therefore the aggregate saving would be 14.4 x 535 = 7,734 seconds.

This saving is more than the increase in time at 4am.

Add more ambulances at 11 pm Sat and take them from 4 am Tuesday.

As we continue to swap ambulances from 4 am Tues to 11 pm Sat, the time-reductions get smaller at 11 pm and the time-increases get larger at 4 am.

So there is an eventual natural halt to the transfer of resources.

For Surrey, the optimum is to split one of the 19 night shifts into two sixhour shifts for each day of the week. Put the 1.30 am to 7.30 am part of the shift to Saturday evening, giving 7 extra ambulances at that time.

However, when we do all the transfers that give us a net time saving, we gain only 4.6 seconds in overall response time!!

We consider three innovations:

Innovation 1: sit crew in ambulance

Crews already sitting in their vehicle answer calls some 35 to 40 seconds sooner than those who are at their base.

So this is like having 3.5 to 4 additional ambulances.

This response time saving would cost some £900,000 to £1m if it were done with additional resources.

Would it cost as much if crew had to be paid extra for sitting in their cab all day?

Innovation 2: faster job turnaround

The average time between emergency callas was 143 minutes, of which urgent calls took an average of 14 minutes.

So the "slack" time between jobs was 143 - 14 = 129 minutes.

If an emergency call could be reduced by one minute, to 44 minutes, slack time would increase to 130 minutes.

But "slack time" is our resource: the more the better! . . .because it is slack time that determines n

Innovation 3: triage

Surrey Ambulance Service crews were asked to note whether a call was life-threatening.

Overall, they said that 9.5% of calls were life-threatening.

Suppose that your ambulance service with its current fleet of ambulances only answered this 9.5% of calls, leaving the other 90.5% unanswered forever.

How much do you think your 75th percentile response time would be reduced

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