The Fantasy Maths of Redirection

Here’s why the potentially risky and unpopular redirection of patients away from A&E is a distracting side show from the real cause of service failure. A long thread with sums. Take a medium sized average A&E seeing 200 patients per day.

50% patients are very unwell or have high risk presentations and need a full history, examination, ECG, X-ray, scans, blood tests, and treatment. This takes approx 120 mins in total of clinical time in a cubicle. Total time = 120 x 100 = 12,000 mins per day.

50% patients need a more focused quicker assessment for less complex, lower risk problems. This takes 20 mins for those that need a test, treatment or X-ray and 10 mins for those that don’t. Assuming 50:50 split: Total time = 50 x 20 + 50 x 10 = 1,500 mins per day.

30% of the all patients (60) need admitted to hospital and wait in A&E for a ward bed occupying a cubicle space. This wait is 60 X B where B is the bed wait in minutes. This is normally 60 mins when beds are available: Total time = 3,600 mins per day.

So in our average department, we need 12,000 + 1,500 + 3,600 mins = 17,100 mins of cubicle space per day with a 1 hour bed wait and no redirection. This works out at 17,100/1440 = 12 staffed cubicles.

If all the patients (25% = 50) who need neither a full assessment nor tests are redirected at the door, we save 10 mins per patient = 500 mins (assuming redirection takes negligible time). This reduces the staffed cubicles needed to 16,600/1440 = 11.5 staffed cubicles.

If instead the average wait for a bed increases due to a doubling of admission delays to 120 mins, the bed wait becomes 60x120= 7,200 mins. We now need 20,700/1440 = 14 cubicles to avoid corridor waits or queues for assessment.

And if those bed delays further increase to average out at 4 hours, we need 60x240 extra cubicle mins which means a requirement for the ED to have 27,900/1440 = 19 staffed cubicles.

So increasing bed delays (which btw add no clinical value and put patients at real risk of harm) from 1 hr to 4 hrs means the necessary ED footprint to avoid crowding and queues increases by 7 cubicles.

Whereas, redirection of every patient not likely to require the services of an ED reduces the necessary ED footprint by less than half a cubicle. 

Currently, bed waits can exceed 10 hours. But hey, let’s look over there at a few unfortunate patients who have for a multitude of reasons ended up seeking help from an overcrowded A&E rendered too small by the maths of poor hospital flow.