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Anna Karenina and the four-hour target

Can happy families help us make sense of Emergency Department delays?

The most famous first line in Russian literature occurs at the beginning of Leo Tolstoy's novel Anna Karenina:

Happy families are all alike; every unhappy family is unhappy in its own way.

Tolstoy's observation led Jared Diamond—in his book Guns, Germs and Steel—to coin the phrase "Anna Karenina principle". If I can just quote from Wikipedia for a minute, "the Anna Karenina principle describes an endeavour in which a deficiency in any one of a number of factors dooms it to failure. Consequently, a successful endeavour (subject to this principle) is one where every possible deficiency has been avoided."

And the Anna Karenina principle was what sprang to mind when—last Tuesday—I visited the ISD (Scotland) website to have a look at the latest A&E data from Scottish hospitals. I wanted to see whether the data could tell me if the best hospitals were all alike and if the others were all failing in their own ways.

I concentrated on the figures for March 2013, and I restricted myself to those hospitals with full-blown A&E departments (as opposed to just minor injuries units). I also disregarded those A&Es that saw fewer than 2,000 attendances in the month.

In the 26 hospitals I looked at, percentage compliance with the four-hour target ranged from 98.8% down to 80.2%. I identified three groups of three hospitals. The first three were hospitals at the top of the league table; the second three were mid-table; the final three were at the bottom. For each hospital I drew a histogram that showed the time spent in the department (in 15-minute intervals) along the horizontal axis and the percentage of patients who spent that amount of time in the department on the vertical axis. Note that the right-most column in each graph is a "catch-all" category that includes all of the patients who spent more than four hours in the department.

First of all, the three highest-achieving hospitals. Their compliance percentages in March 2013 were 98.8%, 97.7% and 97.4% respectively:


Hospital A:

3,730 attendances; 98.8%

Hospital B:

3,674 attendances; 97.7%

Hospital C:

2,493 attendances; 97.4%

If the Anna Karenina principle is to hold true, then we ought to find that these hospitals are alike. These three are, after all, the "happy family" of NHS Scotland. And their histogram shapes are indeed broadly similar. And what they have in common (from a measurement point of view, at any rate) is that their median times are comparable: for hospitals A and B it's around 105 minutes; for hospital C it's a bit shorter, closer to 90 minutes. And the upper quartile wait for all three is around 120-150 minutes. In other words, in the top-performing hospitals, three-quarters of the patients have left the department by the time two-and-a-half hours is up.

Secondly, the mid-table hospitals:


Hospital D:

4,200 attendances; 94.4%

Hospital E:

2,889 attendances; 93.0%

Hospital F:

5,666 attendances; 92.9%

By the time we get to 93-94% compliance, not only have the histogram shapes started to lose their definition, but we are starting to see significant numbers of patients in the penultimate 226-240 minute column as well as the final >240 minute column. The median wait for these three hospitals ranged from just over two hours at Hospital E to just less than three hours at Hospital F. And the upper quartiles also ranged quite a bit, from three hours at Hospital E to three-and-three-quarters of an hour at Hospital F. So: three hospitals with similar percentage compliance figures but quite different shapes. Unhappy in different ways.

Finally, the three worst-performing hospitals:


Hospital G:

3,685 attendances; 83.1%

Hospital H:

6,034 attendances; 82.0%

Hospital I:

9,218 attendances; 80.2%

Again, three different shapes, though of course they all share in common a large cohort of patients in the final column: between 15% and 20% of patients spending longer than four hours in the department. And it's interesting that the median waits and upper quartile waits are quite different for each of these three hospitals. Hospital G's numbers are surprisingly similar to the numbers generated by the Top Three - until we get to about three hours; whereas Hospitals H and I have much higher values. In Hospital I, for example, the median wait is three hours, with the upper quartile coming in at only a shade under four hours.

So: is the Anna Karenina principle something that can help us here? Well, yes, it would appear so. Because they are similar, it could be argued that the distribution shapes (and the associated vital statistics) of the top-performing hospitals provide us with a model of what every other shape ought to look like if it wants to achieve sustainable compliance with the four-hour target. If the top-performing hospitals have avoided all of the system deficiencies that get in the way of four-hour compliance then their shapes are a highly visual way of showing us what a functioning system looks like.

[5 June 2013]

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