Misleading Odds of Dying

There have been various claims in the media and research about the efficacy of cycle helmets lately.

One such article of note, was from 2012, Nonuse of bicycle helmets and risk of fatal head injury: a proportional mortality, case–control study, by Navindra Persaud et al., which claims that you're 2.5 times more likely to have a fatal head injury as a result of not wearing a helmet, with an odds-ratio increasing to 3.1 when "adjusted for age and sex".

Results: Not wearing a helmet while cycling was associated with an increased risk of dying as a result of sustaining a head injury (adjusted odds ratio [OR] 3.1, 95% confidence interval [CI] 1.3–7.3). We saw the same relationship when we excluded people younger than 18 years from the analysis (adjusted OR 3.5, 95% CI 1.4–8.5) and when we used a more stringent case definition (i.e., only a head injury with no other substantial injuries; adjusted OR 3.6, 95% CI 1.2–10.2).  

This study was note worthy as it was the first research into fatal head injuries that had any significant numbers and possibly proved the efficacy of helmets. And as always, when ever an article like this is published, within microseconds of the abstract being made public, the media were quick to promote it. So how was this reported by the papers?

Cyclists without helmets TRIPLE their chance of death by head injury ...

The suggestion by the abstract and the media is you're three times more likely to die without a helmet....

This Is Possibly Misleading...

But to be fair to the Star, the abstract is not easy to interpret, and most people would possibly come to (incorrect) conclusion that if you dont wear a helmet you'd be three times more likely to die, than if you did, when in fact the result pertains to fatality by head injury, not overall fatality,  i.e. where someone would have died regardless of whether they did or didnt suffer a head injury.

Is it possible to use their result to obtain the actual odds ratio for dying with and without a helmet? Yes.

There was 129 cycling deaths studied by coroners in Ontario from 2006-2010. Out of these deaths, 34 cyclists wear wearing helmets, and the rest, 95 cyclists were not wearing a helmet.

In studies like this, in order to estimate an odds ratio, a control group is required. Some of the fatalities need to be placed into a 'cases' group, and some need to be placed into a 'control' group. The control group effectively gives you the odds that someone was wearing a helmet. Autopsies were conducted to determine the cause of death, and as I understand it, the pertinent groups were

• death due entirely to other injuries, regardless of head injury
• death entirely and solely due to a fatal head injury, without other fatal injuries
• a fatal head injury with other injuries

The first of the above list comprised the control group for the first row of their results table (shown below). Helmet wearing for the controls was around 36%, which they claim to be consistent with a 2009 survey. In their second row, pertaining to pure head injury (no other injuries) they also claimed to have measured the same helmet wearing ratio of around 36%.

Their results are in table 3, and are thus:

Odds of death from a head injury when not wearing a helmet while cycling, with and without other substantial injuries

Case definition	Fraction not wearing a helmet		OR (95% CI)	Adjusted* OR (95% CI)
	Cases	Controls
Head injury as cause of death with other injuries	58/71	37/58	2.5 (1.2–5.7)	3.1 (1.3–7.3)
Head injury as cause of death with no other injuries	38/43	57/86	3.9 (1.4–10.9)	3.6 (1.2–10.2)

Note: CI = confidence interval, OR = odds ratio.

*Adjusted for age and sex.

As explained above these results are NOT THE odds ration for dying with and without a helmet, they pertain to fatal head injury.

Take row 2 for example, it means out of the group that died solely as a result of a fatal head injury, the odds-ratio was 3.6. But note the controls! 86 people out of the 129 died as a result of other injuries. They would have died anyway, helmet or no helmet.

How do calculate the actual odds of dying in without a helmet from the above data for the cyclists in this study group?

Simply as:

(95/34) x (0.36/ (1 - 0.36)) = 1.57

Where 0.36 was their measured helmet wearing rate in the controls, and as above, a total of 95 cyclists were not wearing a helmet, but 34 were.

Caveats, this odds ratio is pertinent to crashes of this severity, and is subject to the controls being correctly identified. A small bias in mis-classifying the controls, has a drastic effect on the supposed odds-ratio. This ratio also pertains to riding conditions in Ontario, where 78% of the victims were involved in a collision with a motorised vehicle.

Are Persaud's Results valid?

Many studies and researchers have found that drunk cyclists are very unlikely to be wearing a helmet. Out the 129 victim's in Persaud's study, 30 were drunk.
Just let that sink in....

Others have rightly criticised the study for not accounting for intoxicated cyclists.
http://www.cmaj.ca/content/early/2012/10/15/cmaj.120988/reply#cmaj_el_713394

If those drunk cyclists were removed, the confidence intervals for the study would no longer be significant! Equally, if all those drunk cyclists were in the 'cases' group and not distributed appropriately to the control group, then the reported odds ratio would decrease significantly.