Headline figures

If you haven’t done so already, start from this post and work your way forward.

In rare events like bicyclist injuries, odds ratios can be used as an approximation of relative risk: that is, how much a medical intervention changes the risk of a specific outcome.  An odds ratio of 0.3 is interpreted as a 70% reduction in risk of head injury when wearing a bicycle helmet.

The Cochrane Review looked at five studies, which contained a number of sub-analyses.  There was actually a range of odds ratios found when looking at different types of injury in different groups of cyclists.  In one, an odds ratio of 0.15 was reported.

So now the headline figure is that bicycle helmets protect against a whopping 85% of injuries.  Imagine the lives that could be saved.  Won’t somebody think of the children?  The 85% figure is constantly repeated by “Road Safety” spokesmen, and reported without context by journalists.  It’s cited by the British Medical Association in support for banning people from riding bicycles except when wearing helmets.  The 85% figure matters.

Leaving aside questions over whether the 85% figure represents the real efficacy of helmets, how useful is it as a guide for how to live our lives?  Well, as Ben Goldacre puts it: “you are 80% less likely to die from a meteor landing on your head if you wear a bicycle helmet all day.”  Nobody has ever died from a meteor falling on their head*.

What Ben is saying is that relative risk is only a useful number to communicate to the public if you also communicate the absolute risk.  If you want to know whether it’s worth acting to reduce the risk of something bad happening, you need to know how likely it is to happen in the first place.

In the UK, 104 cyclists died on the roads in 2009, according to DfT stats.  It was 115 in 2008, but the trend has been downwards for a long time.  For simplicity, lets say that in future years we could expect on average 100 cyclist deaths per year.  It’s really difficult to say how many cyclists there are in the UK, because you can define it in several different ways, and even then the data that we have is crap.  You can estimate how many bicycles there are, but these estimates vary, many bicycles might be out of use, and many of us own more than one.  You can take daily commuter modal share — which would give us 1 million cyclists — but there’s more to using a bicycle than commuting, and most people mix and match their modes.  According to the latest National Travel Survey, 14% of people use a bicycle for transport at least once per week.  An additional 4% cycle several times a month, and 4% again cycle at least once a month.  Cumulatively, 32% of the British people cycle at least sometimes, but some of those are too infrequent to be worth counting.  To be generous, and to keep the numbers simple, I’ll round it down to 16%, giving us 10 million on-road cyclists in the UK.  That means one in 100,000 cyclists is killed in cycling incident each year.

To put it another way, there’s a good chance you’ll get killed if you carry on cycling right up to your 100,000th birthday.  (If you do not first die in the inferno caused by the candles on the cake.)  Or, if when Adam and Eve first left Africa 200,000 years ago they had done so on bicycles, there is a good chance that at least one of them would be dead by now.  Alternatively, if you accept that life expectancy is around 80-90, make the unlikely assumption that all cyclists remain cyclists pretty much from cradle to grave, you might die cycling once in over a thousand lifetimes.  Nine-hundred and ninety-nine lifetimes in a thousand, you will die of something much more probable.  Like heart disease, or cancer.

But not everybody who dies on a bicycle dies of head injuries, and not everybody who dies of head injuries sustained while riding a bicycle would be helped by wearing a helmet.  The DfT/Transport Research Laboratory have done their own extensive review of the medical literature on helmets and say: “A forensic case by case review of over 100 British police cyclist fatality reports highlighted that between 10 and 16% of the fatalities reviewed  could have been prevented if they had worn an appropriate cycle helmet.”  This is because, while some form of head injury was involved in over half of cyclist fatalities, the head injury was usually in combination with one or more serious injury elsewhere on the body; and even in those where only the head sustained a serious injury, as often than not, it was of a type or severity that a helmet could not prevent.  There are, of course, many caveats and limitations of such an estimation, which relied on many assumptions, some amount of subjective judgement, and a limited dataset which was biased to the sort of cyclist fatalities that the police are interested in.  So we could be generous and round it up to 20% — that helps keep our numbers simple.

So we’re talking about about 20 lives saved per year, or in terms that matter to you, your life saved if you cycled for half a million years. Of course, a third of British cyclists already wear helmets, so we can add the number of cyclists whose lives are already being saved.  We could be generous again and say 40 lives per year.

That would give you a chance of less than 1 in 2,500 that, as a cradle-to-grave bicycle user, bicycling from nursery school to nursing home, you will die in a crash that a helmet would have protected against.  The chances are 2,499 in 2,500 that you will die of something else.  Like the 4 in 2,500 chances of being killed in a cycling incident where a helmet would not have helped.

Or the 6 in 2,500 chances of death by falling down stairs.  Or the 3 in 2,500 of being run over by a drunk driver.  Or the whopping 30 in 2,500 chances of dying of an air pollution related respiratory disease.**  Unfortunately I couldn’t find the British Medical Association’s policy on legal compulsion for users of stairs to wear appropriate personal protective equipment.

Of course, in addition to the 100 cyclists killed on British roads each year, another 1,000 suffer serious but non-fatal head injury, sometimes involving permanent and life-changing brain damage (as do users of stairs).  The Cochrane Review says that up to 850 of those injuries would be avoided or less severe if a helmet were worn; the more pessimistic TRL review says that perhaps 200 of them might be prevented or mitigated by an appropriate helmet.  Either way, we’re still in the area of many thousands of years spent cycling.

Whether you think those numbers make helmets worthwhile  it is up to you — I don’t think these numbers alone objectively prove that helmets are or are not worth using.  Just don’t be fooled by the stark headline-grabbing figure of 85% risk reduction.  When the absolute risk to begin with is smaller than that for fatally falling down the stairs, and a fraction of one percent of that for cancer and heart disease, consider whether risk reduction matters.

Of course, that might all change once we’ve looked at the next part of the story…

* I have not checked this fact, which I just made up, but I would be surprised to hear that it is not true.

** Hastily googled and calculated headline figures for illustrative purposes only; again, I have not thoroughly assessed these.

Final disclaimer: this is a hastily scribbled blog post, not an academic paper.  I’ve checked my zeroes and decimal places, but if I’ve overlooked something or accidentally written something to the wrong order of magnitude, please do point it out.

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8 responses to “Headline figures

  1. Excellent article. It’s a shame journalists ignore writings like this, and continue to cite the same old 1990s fact from a dodgy scientific journal over and over.

  2. Good post. Incidentally:

    In 1860, in Ohio, a horse reportedly died after being struck by a meteor. In 1911 a dog was killed in Egypt.

    No mention of whether they were hit on the head. I love Yahoo answers.

  3. Pingback: What is a bicyclist? | At War With The Motorist

  4. Pingback: Would a helmet help if hit by a car? | At War With The Motorist

  5. Pingback: Risk compensation and bicycle helmets | At War With The Motorist

  6. –An odds ratio of 0.3 is interpreted as a 70% reduction in risk of head injury when wearing a bicycle helmet.–

    Actually, I think a relative risk of 0.3 might be interpreted that way. Odds ratios end up higher than relative risks (slight difference in the way they’re calculated). The paper that put forward the 85% claim used the wrong statistic — I suspect because it sounded more impressive.

    The paper has several other shortcomings, which are dealt with here:
    http://cyclehelmets.org/1068.html

  7. Pingback: Appendix: Bad Science Bingo in the BMA’s “safe cycling” pages | At War With The Motorist

  8. Pingback: All those helmets posts in one place | At War With The Motorist

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