It really could happen to you…

01 May 2015, at 12:00am

GARETH CROSS has been contemplating probabilities and the likelihood of things occurring – in particular going wrong – in the normal course of events, with sometimes dreadful consequences

  • I had a one in 35 million chance happen today. I went to work and saw a car with the registration JK02JKO. There are 35 million cars registered in the UK so can you imagine how excited I was to see that one, out of the 35 million cars there was only one with that number and I saw it. As if that wasn’t enough I then saw RF11FPV. The chances of seeing those two are one in 1.23x10-15!
  • Work has been busy recently and going really well, apart from a few months ago we had a small run of unexplained anaesthetic deaths (this is true, we had about three in six months – probably half of all the similar deaths I remember in the 10 years I have worked there). We reviewed our systems and adjusted a pre-med dose and there has been no more, so that must have been it (we did, but a wrong conclusion). It reminded me of the recent case of a serial killer nurse. There was a cluster of unexplained deaths on a ward and they managed to link them all to one nurse. She got locked up…
  • Then my ankle was hurting the worst it has done for a long time; it waxes and wanes a bit. Some applied veterinary knowledge and Dr YouTube have diagnosed subcutaneous Achilles bursitis (true). The usual things hadn’t worked so I went to a homoeopath (false, I didn’t, I made that bit up for dramatic effect) and the next day it was loads better (true, it did get better the next day).

THOSE three paragraphs are based on real events with some deliberate misconceived conclusions based on misunderstanding of statistics and numbers.

They have a relevance to our daily working lives as vets, but most of the well-known examples used here refer to human medicine (we are all doctors now though).

The first two paragraphs deal with probabilities and random distribution, the last one with regression to the mean.

I have been inspired this month by two books: Alex’s Adventures in Numberland by Alex Bellos, and by rereading Bad Science by Ben Goldacre.

Regression to the mean is simply things returning to normal. Extreme events tend to normalise. Very tall people have slightly shorter children, mongrels all look similar and less like pugs or borzois, waxing and waning diseases tend to get better just after they peak (kind of by definition but often at the point that the client has lost faith in you and goes to the homoeopath).

There is a picture in Alex’s book which I have been pondering all month: I am reproducing a similar version here and will use it to help to explain the unexplained death episode at work.

The pattern on the left is truly random and has clear clusters; the pattern on the right (which is what many of us would draw as a random pattern) is not random.

No pattern in pi

Another way you can observe random patterns is to look at the number pi. Despite centuries of effort, no one has ever found a pattern to the numbers in pi. It is a true random sequence.

However, in the first 10 digits of pi the numeral “5” appears three times; which is more than you would think as each numeral has a one in 10 chance of appearing at any place.

After clusters of adverse events it is always good to look for a reason, but I think our cluster of GA deaths was like the run of fives in pi or the cluster of dots in the picture.

This can also be why certain villages may have an increased incidence of certain diseases. It can also be why hospitals have clusters of adverse events or deaths; and there have been several cases of these where an investigation has transformed into a witch-hunt for a cause.

Look up Lucia de Berk who was convicted of multiple murders in hospital after a cluster of deaths. The prosecutors also got the probabilities wrong and stated that “…the chance of a nurse working at the three hospitals being present at the scene of so many unexplained deaths and resuscitations is one in 342 million.”

So this is like seeing a random cluster as in the dot picture, then using the number plate analogy to calculate the chance of the clusters happening retrospectively. She was exonerated in 2010, partly due to correcting the maths used in her conviction.

I can confidently predict that one of you will experience an unexpected patient death within a month after reading this.

To the person that happens to it might feel a bit weird when it happens and you may be amazed by my prediction (please tell me on, and in hindsight it will seem highly improbable to all concerned that it was predicted in a magazine and you may be tempted to look for cause and effect.

Something went wrong

I always shiver when I hear nurses, doctors or parents convicted of a killing, or a vet disciplined for something that “went wrong”, when you hear prosecutors use probabilities like in the de Berk case, and even if they have got the probabilities right – if it’s a one in 50 million chance that someone died of x disease naturally, well in a country of 60 million people it is going to happen to someone.

But when it does happen and you start looking at it from the other end it all goes wrong. An example is rare endocrine diseases in children that have led to convictions of parents for murdering by salt poisoning, children with brittle bones, etc.

They are so rare that when a jury is presented with the likelihood of it being due to natural causes of being one in several million, they are inclined to convict. But in a country of 60 million it will happen and, occasionally, due to our clusters, more than once in the same family (e.g. multiple cot deaths).

The two books have helped me look at events, disease incidence and how things present in practice in a slightly different way. I would also highly recommend that, in the unfortunate event you are hauled up in front of the RCVS when something goes wrong, that as well as the VDS and the lawyer, you hire a very smart mathematician to defend you.