# New Zealand Cycling Fatalities and Bicycle Helmets

A colleague sent me an assessment of cycling fatalities in New Zealand. The report’s author is Dr Glen Koorey of the University of Canterbury. He’ll be one of the keynote speakers at the upcoming Velo-City Conference in Adelaide. In particular, I was tasked to comment about his section regarding bicycle helmets as they, in part, now form the basis of the Wikipedia page on Bicycle Helmets in New Zealand.

In the report, Koorey states

Only nine victims were noted as not wearing a helmet, similar to current national helmet-wearing rates (92%). This highlights the fact that helmets are generally no protection to the serious forces involved in a major vehicle crash; they are only designed for falls. In fact, in only one case did the Police speculate that a helmet may have saved the victim’s life. There is a suspicion that some people (children in particular) have been “oversold” on the safety of their helmet and have been less cautious in their riding style as a result.

On the surface, he has a point based on independence for probabilities. In mathematical terms, Koorey is stating

$P(helmet | fatality) \approx P(helmet)$

which is, by definition, independence (if they are equal). So, if the helmet wearing proportion among fatalities is equal to that in population, then helmet wearing is independent of fatality.

As I see it, the problem is in the interpretation as it is not a pure measure of helmet effectiveness. Helmets are a directed safety intervention, so they won’t protect body parts other than the head and you can certainly die from other injuries. It could very well be that helmet wearing is independent of fatalities, but the the sheer force of the collision makes other serious (and possibly fatal) injuries more likely negating any benefit to helmet wearing.

I searched through the publicly available data (found here) and asked around about what’s available in the complete data. In the end, there’s not enough information to identify location or severity of injuries. If we had all the data, a more appropriate probability to investigate would be

$P(helmet | \hbox{fatality due to head injury}) = P(helmet)$

When looking at the reported data, however, Koorey’s claim the proportion of fatalities wearing a helmet is “similar to current national helmet‐wearing rates (92%)” doesn’t appear justified.

First, he states there were 84 cycling fatalities between 2006-2012 in New Zealand. Of these, about 10% did not have information about helmet wearing. So, there is information on 76 fatalities and 9 of those were not wearing helmets. This gives us the proportion of non-helmet wearers among fatalities of 11.84% (9/76). This is not an estimate since this figure comes from all cycling fatalities in New Zealand.

Koorey wants to compare this to estimates of helmet wearing in New Zealand. Over this time frame, I compute a yearly average helmet wearing rate of 92.57%. So, the proportion of cyclists not wearing helmets is 7.43% during that time. This data could then be summarized by a $2 \times 2$ table as

 Helmet Yes No Death Yes a b No c d

From the data available, we do know $a=67$, $b=9$, $\frac{c}{c+d}=0.9257$ and $\frac{d}{c+d}=0.0743$. We would like to compute the risk of death for those wearing helmets versus those that do not; however, this is not possible using this summary data as we don’t really know how many cyclists there are.

Instead, we can compute the odds ratio (OR) which is a good estimate of relative risk for rare events (cycling deaths are certainly rare). The odds ratio is

$OR=\dfrac{ad}{bc}=\dfrac{a\frac{d}{c+d}}{b\frac{c}{c+d}}=0.598$

If helmet wearing were identical among fatalities and the general population, as Koorey has suggested, the odds ratio would be 1. Instead of being similar, the risk of death is 40% less among helmeted NZ cyclists versus those without a helmet. This figure is consistent with the latest re-re-analysis of a meta-analysis from case-control studies, although this is likely a conservative figure since head (or any other) injuries were not identified.

Statistical significance would be hard to come by here considering we don’t have the exact counts of cyclists from those surveys (or from the general population). However, the asymptotic variance of the log(OR) is

$\widehat{var}(log(OR)) \approx 1/a + 1/b + 1/c + 1/d$

The last available helmet use survey came from over 4600 cyclists (that is 7*4600 over the study period). Since this is such a sizable number, the last two terms of the variance formula do not contribute much.

Using only the fatalities in the variance formula gives us an asymptotic confidence interval for the odds ratio of

$OR\times e^{\pm 1.96 \times s.e.} = (0.298, 1.198)$

where the $s.e. = \sqrt{1/a + 1/b}$ (this assumes both $1/c$ and $1/d$ are small). Note this result is not statistically significant; however, this is due to having relatively few cycling fatalities (which is good and having less would be better).

There’s also the issue regarding the effect of missing data. One method is to recompute the odds ratio assuming all missings did not wear helmets and repeat assuming all missings did wear helmets giving a range of possible values. The odds ratios are 0.316 and 0.669 respectively. So, at worst, there is an estimated 33% decrease in the risk of death when wearing a helmet versus not.

Koorey’s claims are therefore not justified as the risk of death was much less among helmeted cyclists.This is even without specific information about cause of death and properly assessing helmet effectiveness to lower the risk of a fatality.

I also take issue with Koorey’s statement “This highlights the fact that helmets are generally no protection to the serious forces involved in a major vehicle crash; they are only designed for falls.” A recently published article in Accident Analysis and Prevention states

Considering a realistic bicycle accident scenario documented in the literature (Fahlstedt et al., 2012) where a cyclist was thrown at 20 km/h (i.e. 5.6 m/s which corresponds to a drop height of approximately 1.5 m), our analysis indicates that a helmeted cyclist in this situation would have a 9% chance of sustaining the severe brain and skull injuries noted above whereas an unhelmeted cyclist would have sustained these injuries with 99.9% certainty. In other words, a helmet would have reduced the probability of skull fracture or life threatening brain injury from very likely to highly unlikely.

I also published a paper last year where we found helmets reduced the odds of severe head injury by up to 74% (these were NSW cyclists hospitalised after a motor vehicle crash and reported to the police from 2001-2009). Severe injuries included “Open wound of head with intracranial injury” (S01.83), “Multiple fractures involving skull and facial bones” (S02.7), “Fracture of skull and facial bones, part unspecified” (S02.9), “Loss of consciousness [30 mins-24hrs]” (S06.03), “Loss of consciousness prolonged without return of consciousness ” (S06.05), “Traumatic cerebral oedema” (S06.1), “Diffuse brain injury” (S06.2), “Other diffuse cerebral & cerebellar injury” (S06.28), “Traumatic subdural haemorrhage” (S06.5), “Traumatic subarachnoid haemorrhage” (S06.6), “Other intracranial injuries” (S06.8), and “Intracranial injury, unspecified” (S06.9). None of these are minor injuries.

Using available data, the evidence does suggest helmet wearing mitigates cycling fatalities and serious injury. It does not appear as though the public have been oversold on the benefits of bicycle helmets.

Update: The original version focused on the relative risk of helmet wearing among fatalities and helmet wearing surveys in New Zealand. This made the wording quite strange and difficult to interpret. However, the odds ratio isn’t as problematic and is a good estimate of relative risk of death in this instance.