Can chance make you a killer?

Surgeon (stock picture)

Can chance make you a killer? In his regular column, Michael Blastland invites you to try the deadly Go Figure Chance Calculator.

Imagine you are a hospital doctor. Some patients die. But how many is too many before you or your hospital are labelled killers?

We've devised a chance calculator to simulate this scenario. It is set up so that you are innocent of any failing. But bad luck might convict you all the same.

In the real world all kinds of factors make a difference, like surgical skill. But in the calculator, every patient in every hospital has exactly the same chance of dying and every surgeon is equally good. This is to show what chance alone can do, even when the odds are the same all round.

  • The calculator (below) shows 100 hospitals each performing 100 operations
  • The probability that a patient dies is initially fixed at five in 100
  • The government, meanwhile, says death rates 60% worse than the norm are unacceptable (in red)
  • So any hospital which has eight deaths or more out of 100 ops - when the expected average is only five - is in trouble.
  • We've assigned one hospital to you, with a box around it - it could come out green or red.

Start the calculator by clicking on the slider itself and see whether your hospital - the boxed one - is safe or deadly. Click "recalculate", in the lower right-hand corner of the module, a few times to see how you and others do.

image showing Micahel Blastland's chance calculator

Here's what happened when I ran the calculator a few times.

Chance calculator 1

First, some hospitals look dodgy, others brilliant. In this example (see image, right), one surgeon or hospital had 14 deaths (that's the red H out on its own beneath the big cluster), 1,300 per cent higher mortality than some others, who had only one, a huge disparity. Mine - boxed - was one of the unacceptables. So sack me.

But remember, these results are pure chance, computer-generated, based on exactly the same risk for every patient. So hospitals are not really good or bad, it's just chance, lucky or unlucky.

That sounds odd. The calculator seems to show fatal incompetence or maybe even - let's speculate what goes through the public mind - murder at one, medical genius at another.

Keep recalculating and sometimes only a few are unacceptable.

Chance calculator 2 and 3

The example above left has five "bad" surgeons. Roll the dice again and it comes up with a shocking 20 that failed to meet the standard.

Chance calculator 4 and 5

Next, move the slider up to, say, a 12% death rate. This imagines a more dangerous operation. But now there are fewer unacceptables as there tends to be relatively less variation around bigger numbers.

Finally, move the slider right down to a 1% death rate. Now, still using the 60% threshold, a huge number of hospitals are often unacceptable. That's because there tends to be relatively more variation around smaller numbers.

The same applies to the number of ops performed. Do more, and the variation tends to be relatively smaller. Do only a few and the results are more likely to be - relatively - all over the shop. The government says it would like to publish results right down to the level of the individual surgeon.

Chance v skill

Note that chance does not mean without cause. Every death has a cause, but sometimes these come together more often in certain places at certain times in ways that have nothing to do with anything we know or that can currently be known about the patient or the surgeon.

Think of it like this...

Think of a bag of 100 balls, five of them red. Pull a red ball from the bag and it means a death. What if you pull 100 balls from the bag, each time putting the ball back?

Your chance - and it is only chance - of pulling a deadly ball is 5 in 100, or one in 20, or 5%. But it's easy now to imagine that you might draw 14 red balls or more in 100 attempts, or none, purely by chance.

This is the same as the simulation in our calculator; every time you run it, it is like imagining that 100 hospitals dip into the bag 100 times each.

Does all this mean that every hospital mortality rate is pure chance? Of course not. There can be what's called special-cause variation - in contrast to the common-cause variation in our calculator. Special-cause variation is when something like surgical skill is the real reason for 15 deaths. The big problem - bigger than many people think - is how to tell the difference.

So what about a hospital like Mid Staffs, where hundreds are thought to have died unnecessarily? That's an example - probably - of special-cause variation, not chance. There's to be more of this kind of measurement as the government says the effort must shift from setting targets for how much work is done to judging how well it's done. That probably means more emphasis on counting bodies.

In practice, regulators who make calls about standards perform many hard judgments and calculations to work out what's chance and what's not.

But because chance has such a variable effect, they will often be unsure, even about the kind of huge differences we see in the calculator. Anyone thinking raw data is all we need, beware.

Before naming the good or bad, we need to understand the extent to which chance can make the innocent appear dangerous and make heroes of the ordinary.

Note: For a great but techie illustration of how hard it can be to determine whether a pattern of results tells us anything, there is a fascinating exchange on Ben Goldacre's other blog.

A selection of your comments appears below

I've always thought these sorts of claims based on statistics are fairly dubious for the reasons above. The "unacceptable" category should only apply to hospitals where fault on behalf of the staff can be proved or where frequent complaints e.g. about cleanliness are made. The statistics should simply serve as a guide as to where to concentrate your search for this poor practice rather than a proof of their existence

David, Durham

From a personal anecdotal perspective may I add this; in 1990 (20 years ago) I underwent a cardiac quadruple bypass and today, in my 80th year, I am in remarkably good health and not on prescription medication. About 3 years ago on seeing the track-record of the cardiac surgeons still practicing it revealed that the surgeon who did my operation had the worst track-record. Okay, so I am lucky but could there exist unluck on the surgeon's side due principally to the health of the patients allocated to him (and the management of their own after care)? While there remains an unnecessarily high level of deaths due to mistake or carelessness could it also be that successful surgery more of a roulette game?

Robert , Kirriemuir, Scotland

It is not only the surgeons who are variable in quality-- the clinical state of the individual patients and the difficulty of the individual operations also throw in variables.

JD, Birmingham

Death rates can be very misleading. Hospitals which take on riskier cases where surgery is the final and only option may have a higher rate of deaths than another which does not have clinicians with the right level of skill to perform these often tricky operations. Does this make it a worse hospital? Of course it doesn't.

Andy, London

A good statistical evaluation WILL point out the laggards. This is because a good statistical evaluation will recognize the effects of what you are showing. It will not base the analysis on a single year's data, but on multiple years, and will take into account the danger of a particular operation. When those factors are considered, a good statistical analysis will accurately identify "outliers"--those hospitals or doctors whose performance lies outside of chance.

John Wendt, Kampala, Uganda

Suppose you're one of the failing hospitals above, and you're told to improve. You do nothing at all. Next year, you roll the dice again and, by chance, you're now in the pass category. You are praised. However, the results are nothing more than chance. This is regression to the mean - the tendency for extreme results to become mean results over time. The same would apply to any random "corrective" action you take - if next year's results are better, that corrective action is likely to be praised as effective even if it was totally useless, and your original problem was solely down to chance.

Dan Talmage, Cambridge

For anyone who thinks that this is just a bit of harmless fun, go searching for the similar case of Lucia de Berk, also highlighted by Ben Goldacre. She is a Dutch nurse who spent six year in prison convicted of the murders of child patients which were, in all probability, natural deaths. But because she happened to have been in the wrong place at the wrong time several times, by chance, helped by a witch-hunt which used some heavily-criticised statistics, she got the blame. Even the statistics used to condemn Mid Staffs hospital, and to allow credulous journalists to claim hundreds of excess deaths there, were strongly criticised by an article in the British Medical Journal at the time, but which seems to have been largely ignored by both the media and by the relevant politicians.

Dr JG, West Yorkshire

It would be equally fascinating to see such an experiment applied to investment firms and banks. Since the 1920s experiments have contsantly shown that their performance is no more than a random distribution. In fact random selection (literally throwing darts at the Wall Street Journal in the Harvard Economics staff room) gave better results. Yet The City continues to behave, and charge fees, as though they have some special insight. In reality they depend on the fact that most of us do not understand the sort of statistics Michale has just shown.

Des, London, UK

It's amazing how many situations this can be applied to. A good one (although slightly worrying) is the application in the financial world. After five years, an original pool of 1,000 individuals (could be traders, budding entrepreneurs etc) will diminish to 31 assuming they have a 50:50 chance of success each year and are fired if loss-making. We forget about the 969 individuals who lost and heap praise on the remaining 31 - not realising their success is pure luck and a result of basic probability.

RH, Manchester

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