How Risky Is A Risk?

 

[I was contemplating risk the other day, when someone forwarded me an article I wrote a couple of years ago on risk. I think it is still highly relevant to what is happening today with the mangling of medical statistics]

I have only just recovered from the idea that everyone in the whole world over the age of fifty-five should spend the rest of their lives on six different medications, all stuck together in one great big pill. The following was headline from a study in the BMJ.

‘Polypill—A Statin plus 3 Blood Pressure Drugs plus Folic Acid plus Aspirin. Authors claim Polypill would reduce risk of dying from coronary heart disease by 80%. The authors of the polypill article in the BMJ made the claim that taking their polypill would reduce the risk of dying of coronary heart disease (CHD) by 80%.’

You may have seen the non-story about the, yet to be marketed polypill, peddled in the British Medical Journal (BMJ). I was stimulated to look again at the concept of risk.

Whether or not you believe their figures—and I don’t—I sense that this figure of 80% would be taken by most people to mean that eighty out of one hundred people would be saved from death if they took this magic tablet. But this figure, if true, could only possibly be a relative risk reduction. And a relative risk reduction means almost nothing, by itself.

However, because everyone’s eyes glaze over whenever you start talking about statistics, most researchers manage to get away with using relative risk reduction figures when, in reality, they should be shot for doing so. Now, here’s a challenge. The challenge to make a short article about statistics interesting. Okay, that’s not possible. But maybe a little bit interesting?

You must know the time period, and the absolute risk, for the relative risk to have any meaning

When you talk about a risk, you need to know the absolute risk of a thing happening. For example, the risk of getting struck by lightning. I don’t actually know what this risk is, but I would imagine it is about one in five million. But again, that figure means little unless you put a time scale on it. Is this a one in five million risk over a hundred years, or one year, or a day? If you don’t put a time scale in, you can claim pretty much anything you like.

For example an astronomer could attempt to shock you by stating that ‘The Earth will be hit by a big Asteroid. This is one hundred per-cent certain.’ – stunning announcement from A.N. Astronomer. Read all about it.  And of course, this is true. The Earth will be hit by a big Asteroid, sometime in the next three billion years or so. The odds ratio for this event is 1 = 100% certain. I am even willing to take a bet on it. What you probably want to know is however, is, what is the likelihood of this happening in my lifetime. Sorry, no idea.

Anyway, I hope this makes it clear that you must define risk in two ways, the possibility of the nasty thing happening, and the time period during which it is likely that the thing will happen. With lightening strikes, I would guess this is about a one in five million risk, over a five year period. Not high.

However, whilst the time factor is important, people don’t just bend statistics by ignoring the time factor. What also happens is that people inflate the risk by using relative instead of absolute risks.

For example, the chances of dying of lung cancer, for a non-smoker, are about 0.1% (lifetime risk). If, however, you live with a heavy smoker, your chances will increase to about 0.15%. (These figures are for illustration only, and are not completely accurate).

Now, you can report this in two ways. You can state that passive smoking can increase the risk of lung cancer by 0.05% – one in two thousand. Or, you can state that passive smoking increases the risk of lung cancer by fifty per cent (0.15% vs 0.1%). Both figures are correct. One is increase in absolute risk, the second the increase in relative risk.

If you are an anti-smoking zealot, then I would imagine you would prefer to highlight the second figure. The relative risk figure. And when it comes to reducing cardiovascular risk, exactly the same procedure is used (in reverse).

Let’s say that the chance of dying of CHD over the next five years, in a healthy fifty-five year-old, is 1%. By reducing this risk to 0.2%, you can claim to have reduced the relative risk of dying of CHD by 80%. The absolute risk reduction is 0.8%. Mangling statistics is easy when you know how. It’s even fun.

Anyway, now you know the difference between a relative risk and an absolute risk, and I hope this makes it easier for you to hack your way through the misinformation that spews forth from the great medical research machine.

By the way, I believe the Polypill will achieve a 0.00% absolute and relative risk reduction. But we shall see.

 

 

8 thoughts on “How Risky Is A Risk?

  1. John Wright

    But a healthy return for investors. So important for absolute returns, in these times of significant relative (market) risks!

    Reply
  2. Dillinger

    It seems in general that the relative risk reduction for statins and cardiovascular death sits at about 30% (i.e. the same as the West Of Scotland Coronary Prevention Study give or take) and the absolute is still under 1%. Surely, that means that the slight benefit cannot be coming from reducing cholesterol? Statins reduce cholesterol; undeniably, and as that is the case the cardiovascular risk reduction must logically be down to something else they do? These levels of risk reduction therefore prove that cholesterol is not the villain.

    I just cannot understand how that pretty simple point is so widely ignored. I’m know I’m preaching to the choir master and all, but there we are…

    Reply
  3. Ed Terry

    When a doctor recommends a treatment option for me or my wife and they provide a relative risk reduction, I always ask what the absolute risk reduction is. Most of the time, the doctor’s response is simply a confused look, followed by a remark that the suggested treatment is established policy according to (fill in the blank). I’m no longer allowed to accompany my wife to her gastroenterologist because of the silly remarks her doctor makes. She once suggested my wife reduce her consumption of processed foods and suggested that my wife switch to soy burgers. I not no calmly explained to her doctor that a soy burger is one of the most heavily processed foods on the face of the earth and that her two statements were contradictory.

    Reply

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