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Old June 11th 04, 12:18 AM
Dorre
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Default Fundamental error in "Trends in serious head injuries..." Cook and Sheikh 2003Fundamental error in "Trends in serious head injuries..." Cook and Sheikh 2003

James Annan wrote in message ...
I sent the following to "Injury prevention on-line" over a week ago, but
it shows no sign of being published and my follow-up email has not been
answered. I guess someone might as well see it, typo and all. Isn't the
internet great for vanity publishing?


Sometimes these things take a little longer. Have you checked whether
you are in excess of the formal word limit?

The editor may also think that the nature of your criticism means he
should seek advice before publishing it. What you say is, of course,
correct. I was very suspicious when I first saw that claim and
thought I'd better write it out formally to check, but (shame on me!)
I never got round to it.

Below is a more formal way of expressing the same thing. I didn't
bother sending it to Injury Prevention. But if James or anyone else
thinks they can make use of it, feel free!

An alternative, more mathematical/formal way of making the same points
as James
----------------------------------------------------------------------------

There is a miscalculation in Cook and Sheikh's paper.[1]

From 1995/6 to 2000/1 the percentage of hospital admissions with head
injury (%HI) fell from 27.9% to 20.4% for cyclists and 26.9% to 22.8%
for pedestrians, declines of 7.5 and 4.1 percentage points.

Cook and Sheikh claimed that, because percent helmet wearing (%HW)
increased by 5.8% (from 16.0% to 21.8%) and %HI of cyclists fell by
3.6% more than pedestrians, helmets must prevent 3.6/5.8= 60% of head
injuries.

The above argument confuses percentages with percentage points. A
decline from 27.9 to 20.4 represents a fall of 27%. The predicted
fall in %HI of 3.6 percentage points more than pedestrians (25.9% to
22.3%, after subtracting pedestrian trends) represents a 13.9% drop in
numbers of head injuries. Could such a relatively large fall be
caused by an increase of just 5.8 percentage points in %HW?

A mathematical approach is needed to provide the answer.[2] If h and
n are the probabilities of head injury for helmet wearers and
non-wearers respectively, then:
%HI = %HW*h + (100-%HW)*n (1)
The predicted value of %HI at the midpoint of Cook and Sheikh's data
is 24.1%; with %HW of 18.9%. If helmets prevent 60% of head injuries,
h = 0.4n, so, from equation (1), n = 0.272.

Also from equation (1) with n = 0.272, increased %HW from 16.0% to
21.8% should decrease %HI from 24.59 to 23.64, 0.95 percentage points.
This is nowhere near the 3.6 percentage points reported by Cook and
Sheikh. Even if helmets prevented 100% of head injuries, %HI would
fall by only 1.7 percentage points.

Cook and Sheikh's estimate of 60% is therefore invalid. Increased
helmet wearing cannot explain the larger drop in %HI of cyclists
compared to pedestrians. Other factors must also have been involved,
such as gradual changes in the age composition of cyclists, or the
relative amounts of on vs off-road cycling. Cook and Sheikh's data
therefore provide no real evidence of reduced HI from increased helmet
wearing.

In Australia and New Zealand, helmet laws increased %HW dramatically,
in many cases from less than 30% to more than 80% of all cyclists in
less than a year, yet there were no large or obvious corresponding
changes in %HI over and above prevailing trends. In contrast to Cook
and Sheikh's analysis, this tells us a great deal about the benefits
of helmet laws.[3]

References
1. Cook A, Sheikh A. Trends in serious head injuries among English
cyclists and pedestrians. Inj Prev 2003; 9: 266–267.
2. Robinson DL. Head injuries and bicycle helmet laws. Accid Anal Prev
1996; 28: 463-475.
3. Robinson DL. Reasons for trends in cyclist injury data. Injury
Prevention 2004; 10: 126–127.
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