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Comparing discharge rates
Here's a different way of addressing last week's question of whether hospitals are more inclined to discharge patients when it's busy
Last week's piece (Under Pressure: do we discharge inpatients from hospital when they are ready to be discharged? Or do we—instead—discharge them when we need their beds?) generated more feedback than usual.
The general gist of most of the comments was that if you want to describe the relationship between how busy a hospital is (measured by how many of its beds are occupied) and how likely it is to discharge patients (measured by how many discharges take place each day), then you should measure not the absolute number of discharges each day but—instead—the discharge rate.
Quite a few people of pointed out that my methodology had more than a whiff of tautology about it. As one person put it, there might be 60 inpatients on Day A and I discharge 12 that day. On Day B, I have 30 inpatients and I discharge 6. Does that not just tell me that I discharged 1 in 5 patients each day? I wasn't twice as likely to discharge on Day A—I just had twice as many patients in the first place.
So there was some scepticism about my hypothesis. And many of you were kind enough to suggest that the way to do it properly was to calculate a rate of discharge. For each day I should've worked out how many patients were discharged as a percentage of the number of patients in hospital on that particular day.
So yesterday I did just that. And I've looked at the resulting data in three different ways.
First, I re-drew the same scatterplots from last week's article, except that this time the vertical axis measures the discharge rate instead of the absolute numbers of discharges. And what we get in these three scatterplots are still positive relationships (the busier the hospital, the higher the discharge rate), but the correlations (for the medical specialties, r = 0.3; for Orthopaedics, r = 0.2; and for General Surgery, r = 0.6) are far less dramatic than the ones we obtained using absolute numbers of discharges:
Secondly, remembering that the objective of the exercise was to see if hospitals tend to discharge more inpatients when they are under pressure, the next thing I did was a crude hypothesis test. I wanted to answer the simple question: are discharge rates higher on busy days than on quiet days? And is the difference statistically significant?
To do this, I took the 1,000 days in my dataset (the days from 1 January 2009 to 27 September 2011) and divided them into two roughly equal chunks. 500 busy days. 500 quiet days. That meant that I could calculate a discharge rate for the quiet days, a discharge rate for the busy days and then see if the difference between the two rates was statistically significant.
The results of this were not brilliant. For the Medical specialties, the discharge rate on quiet days was 12.7% whilst on busy days it was 13.7%. As it happened, this difference of one percentage point was indeed statistically significant (P=0.02), but when I looked at Orthopaedics and General Surgery I got similar percentage-point-differences (both showed differences of 1.3 percentage points) but they weren't statistically significant (P= 0.11 and P=0.06 respectively) at the 95% level.
Thirdly, the previous P-value technique could be accused of being a bit too "binary" (i.e. just two categories: busy and quiet), so I decided to take a slightly less crude approach to see if there was a "dose-response" relationship. In other words, does the discharge rate increase with busy-ness and whereabouts on the "busy-ness" spectrum (if anywhere) are the results statistically significant? So: instead of splitting the data into just two chunks, I split it into ten chunks. Approximate deciles, if you will. The first chunk consists of the ten per cent of days that were the quietest. The second chunk (the second decile) consists of the next quietest days. And so on, until we get to the tenth decile which consists of the very busiest days.
I calculated discharge rates for each decile and drew 95% confidence intervals so that we could see which deciles (if any) were significantly different from the overall discharge rate.
Here are the results:
The top 30% busiest days seem to attract significantly higher discharge rates, but there is nothing really to report apart from that.
Secondly, General Surgery:
There is more of a gradient here. And the "dose-response" relationship looks a bit better. On the 20% quietest days: lower than average discharge rates; on the 20% busiest days: higher than average discharge rates.
Thirdly, the Medical specialties:
Again, the picture is a bit blurred but the difference is reasonably clear. It may not be massively clear-cut, but hospitals do appear to take discharges more seriously when the hospital is busier. And I'm not sure that this is an ideal state of affairs...
[9 January 2013]
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