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Do readmission rates say more about patients than they do about hospitals?

Readmission rates are commonly-used indicators in the NHS. Mostly, the idea behind their value is that if hospitals discharge patients too quicklybefore they are ready to be discharged—there’s a risk they’ll be re-admitted soon afterwards.

The traditional way of describing re-admissions is to compare the readmission rates of different consultants to see which ones are more likely than others to having their patients re-admitted. And one way of visualizing such a comparison would be to draw a funnel plot:


Funnel plot showing 7-day re-admission rates of 30 physicians

This funnel plot is telling us is that—as far as re-admissions are concerned—there really isn't much to choose between these 30 physicians. The overall, all-physician, 7-day re-admission rate is 4.4% (that's the solid black horizontal line running through the middle of the chart), and only one of the physicians has a value that is significantly different from this overall average when measured at the 99.7% significance level (the black dotted lines show the 99.7% control limits; the blue dashed lines show the 95% control limits).

But the problem with this "comparing-different-consultants" approach is that it fails to take account of another dynamic that might be affecting re-admission rates. This is a dynamic that we’re constantly being made aware of, and it is this: when hospitals are busy (i.e. when their beds are full), there is more pressure to discharge inpatients than there is when hospitals are quiet. It follows, therefore, that inpatients discharged on busy days might be more at risk of being re-admitted than those discharged at quieter times.

To test this hypothesis, let's see if we can analyze the data another way. Instead of comparing consultants, let’s compare days. Specifically, we'll compare "busy" days with "quiet" days (although we’ll refine this somewhat simplistic distinction in a minute).

In order to do this, we've taken a fairly large chunk of data. Two-and-three-quarter years' worth of data. 1,000 days in fact. And the reason for taking such a large chunk was that we wanted to give each of the 1,000 days a "busy-ness score". Days were scored on a scale of 1-10 depending on whether they were one of the least busy 10% of days (a score of 1) or one of the most busy 10% of days (a score of 10). And all of the points 2-9 in between. These scores on a scale of 1-10 represent approximate deciles. And "busy-ness" has been defined as the number of medical inpatient beds occupied at midday.

We then calculated the 7-day and 28-day readmission rates for each of the busy-ness scores. And we drew a league table-style caterpillar chart (with 95% confidence intervals calculated) to see if the readmission rates were related to busy-ness.


Re-admission rates and "busy-ness" scores based on today's "busy-ness"

But in neither of these charts can we see any significant difference (at the 95% level) from  the overall re-admission rates. It doesn't seem to matter whether inpatients are discharged on very quiet days (on the left-hand side of each graph) or very busy days (the right-hand side of the each graph): the re-admission rates are always indistinguishable from the overall re-admission rate.

Then we thought of another possibility.

Acute hospitals can sometimes be slow to respond to bed crises. A hospital that's full at midday may indeed prompt more patients than normal to be discharged. But those discharges may not actually happen until the following day.

So, to take account of this possibility, we re-drew the same charts as above, but this time allocating the re-admission rates to yesterday's busy-ness scores:


Re-admission rates and "busy-ness" scores based on yesterday's "busy-ness"

But there was no detectable pattern here, either.

So—for this hospital at leastthere's no evidence to support the notion that inpatients discharged in response to a hospital's "busy-ness" are more likely to be re-admitted than those inpatients who are discharged when there is no such pressure. There is no relationship.

Which leaves us wondering whether re-admission rates are an indicator that tells us more about the patients than it does about the hospitals or consultants that admit and discharge them.

But obviously there is more work to be done to prove that. So far, it's just a hunch.


[28 November 2012]


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