### Why you should ignore median waiting times

##### 03/05/2011

by Rob Findlay

The median wait will also continue to be monitored

with a view to improvement.## The Operating Framework

“Targets” have been abolished, of course. But the Department of Health nevertheless makes sure that the NHS is aware of the standards that are expected, and currently for median referral-to-treatment (RTT) waits these are:

- Admitted (inpatients and daycases): <= 11.1 weeks
- Non admitted (outpatients): <= 6.6 weeks
- Incomplete (still waiting for treatment): <= 7.2 weeks

Who could possibly object to this? The median is a kind of average, and everybody wants average waits to come down. If the waiting list backlog is being cleared, then the median will fall. So it’s an indicator of success. Isn’t it?

Before criticising the median, let’s start with its good points. Sometimes the median is a better way of describing the average, especially when large variations are involved. For instance, let’s say we are looking at how much money people earn. The mean is skewed by a small minority of millionaires: so skewed that two-thirds of people in the UK earn less than the mean. So the median is a more interesting measure of income, as it shows the income level that half the population are above and half below. (You’ll find a better discussion of this here.)

When you’re talking about income, the median tells you how you are doing relative to everyone else. But when it comes to waiting times it doesn’t work so well. Why? Because there are two kinds of patients on elective waiting lists: urgents and routines. And it matters which group you fall into.

If you are an urgent patient, you can expect to be treated as quickly as your condition requires; the long-wait statistics won’t apply to you. But all these urgent patients do affect the median: across all specialties they make up a big chunk of the 50% of patients who fall below the median waiting time, and virtually none of those above it. So if you happen to be a routine patient, then the overall median is a poor guide to the waiting time you should expect. If you are an urgent patient then it is no guide at all.

If we narrow our focus to medical specialties then the situation is reversed, because more than 50% of patients are likely to be urgent. Then the median patient is an urgent patient, and so the median tells us nothing at all about routine waiting times.

It gets worse for the poor old median. Imagine you work in a Trust where (across all specialties) 25% of elective patients are urgent. Imagine that the other 75% of patients – the routines – are being admitted in a fairly random order. Where is the median? The 50% of patients who wait less than the median comprise the 25% who are urgent, plus a further 25% who are routine. The median waiting time is at the top of these shorter routine waits.

These lucky short-waiting routine patients are jumping the queue on those less-fortunate routines who wait longer than the median. That isn’t very fair, and so you decide to sort it out. In practice it isn’t possible to admit routine patients exactly on a first-come-first-served basis, but to keep this example simple we will assume that you can. So you eliminate queue-jumping by routine patients, and make those short-waiting routines wait their turn instead. In return, the long-waiters aren’t being delayed by queue-jumping any more, so their waiting times (and the maximum waiting time) come down.

What happens to median waiting times when we achieve this perfection?

The 25% of patients who are urgent are still being treated quickly, below the median waiting time. Then the remaining 75% who are routine all wait their turn in the queue, so they all experience the same waiting time. Where is the median now? The median is now equal to the new routine waiting time, which is equal to the maximum waiting time. You have improved the management of your waiting list, everything is better and fairer, and yet (because the shortest-waiting routine patients are waiting longer) the median wait has gone up.

This is the killer argument against the median waiting time. If it goes up, it might mean that things are getting better (e.g. better scheduling), or it might mean they are getting worse (e.g. longer waiting lists). Likewise if it goes down. The position of the median does not tell us clearly whether things are good, bad, or indifferent. We always need to look at other measures, because the median on its own doesn’t help us.

That is why Trusts, Commissioners, the Department of Health, Monitor, the CQC, and everybody else should ignore the median. Instead, they should focus on the 90th or 95th centile, because that really is a guide to routine waiting times. And, as argued elsewhere, incomplete pathways are a better guide than admitted pathways (or non-admitted ones, for that matter). The statistic to watch is the 90th (or 95th) centile waiting time for incomplete pathways. The other seven measures in common usage can safely fall by the wayside.

Is there no measure of the average that could help us? Unfortunately there isn’t an easy one. The mean waiting time of patients who are still waiting is affected by the order in which patients are admitted. And the mean waiting time of admitted patients, while unaffected by the order in which patients are admitted, is only a guide to the underlying pressures in a steady-state situation (which isn’t the case here).

Having said that, we could get a reasonable indicator by dividing the number waiting by the average referral rate over some recent period, in order to back-calculate the mean sustainable admitted waiting time. And if we’re going to go to those lengths, then we may as well do the job properly and calculate the achievable waiting time, taking account of clinical priorities, removals, etc. But that is a topic for another post.

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