Raise the Hammer

The tricky point is that the control cases are "[cyclist] fatalities for which the cause of death was not a head injury" and the cases are "fatalities included in the coroner’s review for which the cause of death was a head injury" and the population being analysed is "cyclists who died in traffic accidents".

In the controls, 37/58 were not wearing a helmet (64%), while in the cases 58/71 (82%) were not wearing a helmet. It would have been better for the media to have also reported these raw figures.

The (unadjusted) odds ratio is then:

(58/71)/(1-58/71) / ((37/58)/(1-37/58)) = 2.53

Thus, of those cyclists who died, the odds of a non-helmeted cyclists dying of head injuries compared to helmeted cyclists dying of head injuries is 2.5 times higher than the odds of non-helmeted cyclists dying of other injuries compared to helmeted cyclists dying of other injuries (it is not a straightforward statistic!).

The "rare disease assumption" holds (thanks for pointing this out), if we consider the population to be everyone who has cycled in Ontario over the five year period.

But it does not hold if we consider the population to be those who died of injuries in the five year period, since in this case p=58/71, q=37/58, which are not small. Since it is these probabilities that are used to calculate the odds ratio, I would argue that it is misleading to interpret the odds ratio as relative risk for the entire population of cyclists over the five year period.

However, the news reports said that relative risk of non-helmeted cyclists dying of head injuries is 3 times higher, which implies an overall risk for the entire population of cyclists. This is what I meant by not interpreting odds ratio as relative risk (although I wasn't explicit enough).

The other point is that the risk for both groups is relatively low given the total number of cyclists: only 71 deaths from head injuries over 5 years, and only 43 deaths from only head injuries only over 5 years (compared with about 3700 total traffic fatalities over 5 years in Ontario).

The more convincing odds ratio is in fact 3.6 for cyclists who died of head injuries with no other injuries present.

This strongly suggests helmets are beneficial, although the uncertainty is very large due to the small sample size: [1.2, 10.2] 95% confidence interval, which suggests the need for a much larger follow-up study.

There are also questions about competing risk factors: what proportion of cyclists without helmets were riding drunk (this is a major factor in bike accidents)? Are they less law abiding and careful?

We also don't know for sure that helmets did provide protection: this can be assessed by seeing whether the foam actually compressed (rather than the helmet breaking). But this data was not considered.

My main problem is the leap from an odds ratio that shows that a cyclist who dies from a head injury is more likely not to be wearing a helmet to the strong assertion in the article that Ontario should introduce mandatory helmet laws for cyclists.

The international data on cycling accidents, helmet protection and the effect of helmet laws is extremely unclear and the article quotes only a single study from Australia that suggested helmet laws decreased the number of fatalities of all types.

The evidence suggests that there are other much more effective ways of reducing all cycling injuries and deaths (not just head injuries) and that mandatory cycle laws often have negative overall effects.

As this discussion shows, interpreting an odds ratio for a control group study is subtle, and the reporting of the article was confusing.

(Just to be clear: I always wear a helmet myself, but I am not convinced that the balance of benefits and risks is strong enough to force everyone to wear them, and forcing everyone to wear them could actually produce an overall negative outcome.)

Comment edited by kevlahan on 2012-10-17 12:35:10