Time and again, as Ann suffered from setback after setback, it was suggested to us by the medical teams that Ann’s journey was just a series of episodes of plain bad luck. There were, we were told, no errors or failures. Just happenstance. I never believed that. Nobody, it seemed to me, could possibly be that unlucky.
Or could they?
Could the medical professionals be right and everything that happened be within the boundaries of ordinary misfortune? One day, with nothing better to do, I decided to delve a bit deeper and investigate just how unlikely Ann’s story was. Please walk with me on my stroll through the statistics. It is remarkably enlightening.
Prevalence is a term used widely in medicine and it tells us how many cases of a condition, disease or complication exist within a given population. So there might be, say, 10 cases of a particular condition in every thousand people. Prevalence converts easily into odds. So, in this example, 10 cases/1000 equates to odds of 100:1 of having that condition. Incidence is very similar but not quite the same. It refers to the number of new cases over a given period of time. So it provides odds of developing the condition in a given period. I cheated a little and used both prevalence and incidence in my little experiment but I wasn’t writing an academic paper, I was amusing myself. What I found is that there is data out there which tells us roughly how likely or unlikely all these events were so I didn’t have to make it up. (the sources I actually used are in the footnotes).
Now my maths skills are pretty basic so a statistician would probably be able to drive a coach and horses through the exercise I carried out but that really doesn’t matter. Hopefully, even though my amateur analysis is deeply flawed, the result still tells us something.
So, engaging what I call my tenacious streak (and Ann calls my obsessive personality), I started digging.
To begin her journey, Ann was taken ill with cardiac arrhythmia. I couldn’t find figures for the UK but in the USA (which should be broadly similar) the overall prevalence of cardiac arrhythmias is 53 cases per thousand people1 (or a surprising 1 in 18 – rather more common than I had guessed). Most of these are cases of AF which affects over 2 million Americans. In Ann’s case, she had a fast arrhythmia or tachycardia. Now the incidence falls to 16 per thousand (or 1 in 62).
There are up to ten types of tachycardia if you include the most obscure but most sources agree that there are four main types (supraventricular, sinus, ventricular and postural orthostatic) so we’ll ignore the others. Ann had VT (one of the main four) so we’ll approximate that the incidence has fallen again by a factor of four from 16 per thousand to to 4 per thousand (or 1 in 250).
So the approximate odds of Ann needing to go to the ED with ventricular tachycardia at any time in her life were about 250:1 against. That didn’t sound unreasonable. I was off and running.
Then the medics discovered (somewhat belatedly) a blocked coronary artery. Ann was one of 132,863 women who were admitted for in-patient treatment for coronary heart disease (CHD) in England in the year 2015/16.2
The population of England in 2015 was 54,786,300.3. We’ll assume half were women – so, 27,393,150.
So the incidence of female coronary heart disease admissions in 2015/16 was 132,863 out of 27,393,150 or roughly 4.8 admissions per thousand. The odds of Ann being one of them were therefore 208:1 – against.
So, we have:
Ventricular Tachycardia 250:1
Coronary heart disease admission 208:1
To calculate the probability or odds of having both, you multiply the two together. So, the odds of having ventricular tachycardia (VT) and then being admitted for treatment of coronary heart disease (CHD) in the same year are 52,083:1 (against).
So, around 50,000:1. That means that in a UK population of roughly 65 million people, around 1300 people might have had a similar experience. That too sounded plausible. Pretty long odds but well within the bounds of bad luck.
Of course, no-one is suggesting that the Trust had anything to do with Ann developing these conditions. The same isn’t true from this point forward.
Next, Ann had an avoidable out-of-hospital cardiac arrest. I decided to ignore the odds of that happening within hours of an inappropriate discharge from an ED. Keep it simple, I decided. So, there are around 30,000 out-of-hospital cardiac arrests in the UK each year4 among a population in 2015 of 65.13 million.5
So the odds of the out-of-hospital cardiac arrest were 2,171:1 against.
Our odds (VT plus CHD plus cardiac arrest) are up to 113 million:1 – against. There aren’t enough people in the UK to generate one such case.
But we aren’t even half way.
Then, Ann suffered the massive haematoma following the first implant. Sources related to ICD implantation are harder to find but one academic paper found that the incidence of pocket haematoma (less serious and more common than what happened to Ann but all I could find) is around 1.2% of all ICD implants6 – or 83:1 against.
So, VT, then a CHD admission, an out-of-hospital cardiac arrest then a post-implant haematoma gives us odds of 9.385 billion:1 against.
Then there was an ICD lead displacement. That is rather more common at 3.1%7 – or odds of 32:1 against.
So, now the odds of all 5 events has reached 300 billion:1 against.
That’s LESS likely than winning the National Lottery Jackpot twice in the same year.8
But we still haven’t quite finished.
Next we have the chronic post-operative neuropathic pain. I didn’t need to find a source for this as the specialist pain consultant Dr Q had told us that the incidence was 2% – or 50:1.
Now the odds of Ann’s journey are a staggering…
Or fifteen trillion to one against.
If I had continued and considered the odds of other issues such as the critical pages being missing from the medical notes, the numbers would get so big that I wouldn’t even know what they are called and my calculator would probably explode anyway.
So, I’ll stick at fifteen trillion to one.
According to those odds, you would need over 2,000 planet earths, each one with a full population of 7.3 billion people, to find just ONE person that unlucky.
But the NHS Trust asks us to believe that Ann was that person.
No, it wasn’t bad luck. There was another factor at play.
It is called human error.
US National Centre for Health Statistics, National Health Interview Survey on Disability ↩
British Heart Foundation – Cardiovascular Disease Statistics 2017 ↩
Office for National Statistics – mid-year population estimate 2015 ↩
British Medical Journal: Vol.5 Issue 10: The UK Out of Hospital Cardiac Arrest Outcome (OHCAO) project ↩
Office for National Statistics – mid-year population estimate 2015 ↩
British Medical Journal: A systematic review of ICD complications in randomised controlled trials versus registries: is our ‘real-world’ data an underestimation? ↩
Also from British Medical Journal: A systematic review of ICD complications in randomised controlled trials versus registries ↩
The chance of a jackpot win (since the extra balls were added) is 45 million to one against. There are 104 draws per year so the odds over a year are 1 in 432,000. Two wins in a year is that number squared which is 186 Billion to one. Almost twice as likely as what happened to Ann – so far! ↩