A correction: how I fixed my mistake

Short abstract

Estimates of deaths of bicyclists attributable to not wearing a helmet are corrected, with explanation

In 2006, colleagues and I published a study of US traffic deaths during 1982–2001.¹ There were 858 741 deaths, and we estimated that (a) 366 607 could be attributed to alcohol use, (b) 259 239 to not wearing a seat belt, (c) 31 377 to lack of an air bag, (d) 12 095 to not wearing a motorcycle helmet, and (e) 10 552 to not wearing a bicycle helmet. Jointly, these factors accounted for 528 105 deaths, 61% of all the traffic deaths; this joint total was less than the sum of the five counts because some deaths could be assigned to more than one factor.

To estimate the counts above, we used attributable fractions.²,³,⁴,⁵ Imagine a hypothetical series of 100 unhelmeted motorcycle drivers who died; how many of those deaths would have been prevented if all the drivers had worn a helmet? The risk of death in a motorcycle crash has been reported to be greater for an unhelmeted motorcycle driver than for an otherwise similar driver who was helmeted: risk ratio (RR) 1.54.⁶ The fraction of motorcycle driver deaths that can be attributed to not wearing a helmet is (RR − 1)/RR  =  (1.54 − 1)/1.54  =  0.35. So, among the hypothetical 100 unhelmeted motorcycle drivers who died, 100 × 0.35  =  35 deaths were due to not wearing a helmet.

A few months after the study of traffic deaths was published,¹ I realized that I had made an error. To estimate deaths attributable to alcohol, no seat belt, no air bag, and no motorcycle helmet, I correctly used risk ratios for the outcome of death. But to estimate deaths of bicyclists resulting from not wearing a helmet, I used a risk ratio for brain injury, not death, when a helmet was not worn.⁷ Not all bicyclist deaths result from a brain injury. Whereas helmets may prevent some deaths from brain injury, it seems doubtful that helmets can prevent lethal chest or abdominal injuries. In retrospect, my mistake seems obvious; I cannot understand how I made it.

To fix my error, I searched for published estimates of the proportion of bicyclist deaths in vehicle collisions that were due to brain injury alone. Two studies were too small to be of use.⁸,⁹ One study of 4812 bicyclist deaths attributed 62% to a brain injury, but that estimate did not remove deaths that involved both a brain injury and other potentially lethal injuries.¹⁰

Figure 1 Corrected version of part of fig 3 from Cummings et al¹: trends in death rates for bicycle riders. The top line shows the observed rates and the fitted line for all crash deaths of bicycle riders. Also shown are the observed rates and fitted lines for deaths attributed to no bicycle helmet and for other deaths not attributed to that factor. The y‐axis uses a log scale so that convergence or divergence of changes in rates can be easily judged. Pointwise 95% confidence intervals are shaded.

I therefore used US multiple cause of death public‐use data for the years 1991–1994.¹¹ Among the 3015 bicyclists who died in a motor‐vehicle crash, 1727 (57%) had at least one code for head or brain injury, and 1058 (35%) had a code for head or brain injury and no code for other serious injury. The first of these proportions may approximate the upper limit for deaths due to a brain injury, whereas the second may estimate the lower limit. I averaged these to estimate the proportion of deaths that might have been avoided had there been no brain injury: (0.57 + 0.35)/2  =  0.46. I multiplied the attributable fraction of brain injuries that might be prevented by not wearing a bicycle helmet (0.65) by the proportion of bicyclist deaths that may be due to brain injury alone (0.46), to obtain a corrected attributable fraction for bicyclist deaths due to not wearing a helmet: 0.65 × 0.46  =  0.30.

Table 1 Corrected table 1 from Cummings et al¹: traffic crash deaths attributed to each risk factor, USA, 1982–2001.

Risk factor	Affected population	All deaths in affected population (count)	Deaths attributed to each risk factor
			Count	Rate	%*
No bicycle helmet	Bicycle riders	16 473	10 552	0.21	64
No bicycle helmet	Bicycle riders	16 473	4854	0.09	29
All 5 risk factors	All traffic deaths	858 741	528 105	10.30	61
All 5 risk factors	All traffic deaths	858 741	524 099	10.22	61

Rates per 100 000 person‐years. Table is abridged to show only estimates that involved bicycle helmets. Corrected estimates, in bold font, based on corrected attributable fraction for no use of a bicycle helmet.

*%  =  100 × attributed deaths/deaths in affected population.

My next chore was to re‐estimate all the statistics in the 2006 paper¹ that required the bicycle helmet attributable fraction. This looked daunting: there were over 11 500 files which filled 14 gigabytes of hard‐drive space, including hundreds of files to create or transform variables, carry out multiple imputation, and analyze the data. Fortunately, I was helped by some of my work habits.¹² For a research project, I always create variables in one set of files, and perform analyses in another set. So I only needed to redo some of the analyses. And I always keep a computerized index of the analysis files, including a list of the electronic files of commands used to create each table and figure. I made copies of those command files, corrected the attributable fractions, and ran the statistical commands again. In a few days the work was done.

Corrected estimates are shown in abridged versions of tables 1 and 3. Part of fig 3 was also revised. Text on page 152 of the published paper¹ reported deaths prevented by increased use of bicycle helmets: the published estimate was 239, the corrected estimate 73. The published estimate of deaths prevented by changes in all five factors was 293 898, the corrected estimate 283 412. I also corrected Appendix 4, which is available online from Injury Prevention.

Table 2 Corrected table 3 from Cummings et al¹: rates (per 100 000 person‐years) and change in rates, for all deaths, deaths attributed to each risk factor, and other deaths not attributed to each risk factor*.

Risk factor	Rates
	1982†	2001†	Difference‡	Change (%)¶	95% CI
No bicycle helmet
All deaths	0.40	0.26	−0.14	−35	−40 to −30
Attributed deaths	0.26	0.16	−0.10	−39	−45 to −33
Attributed deaths	0.12	0.07	−0.05	−39	−45 to −33
Other deaths	0.14	0.10	−0.04	−28	−32 to −23
Other deaths	0.28	0.18	−0.09	−33	−38 to −28
All 5 risk factors
All deaths	19.57	14.39	−5.18	−26	−30 to −23
Attributed deaths	14.22	7.36	−6.85	−48	−51 to −45
Attributed deaths	14.12	7.30	−6.81	−48	−51 to −45
Other deaths	5.64	7.26	+1.62	+29	+18 to +41
Other deaths	5.74	7.32	+1.58	+28	+17 to +39

Table is abridged to show only estimates that involved bicycle helmets. Corrected estimates, in bold font, are based on corrected attributable fraction for no use of a bicycle helmet.

*Not all persons were considered exposed to all risk factors. For example, only vehicle occupants (not motorcyclists) were considered to be at risk for not wearing a seat belt, and only motorcycle riders were considered to be potential wearers of motorcycle helmets. Death rates attributed to each risk factor alone sum to more than rates attributed to all five risk factors, as some deaths can be attributed to more than one factor.

†Rates for 1982 and 2001 are from the fitted models.

‡Rate difference  =  2001 rate − 1982 rate.

¶Rate change  =  (2001 rate − 1982 rate)/(1982 rate).

When correcting a paper it is customary for authors to express regret for their errors. I feel regret for several reasons. Firstly, I do research in the hope that some of what I do may actually be useful in preventing future injuries; erroneous estimates cannot serve that purpose well. Secondly, I devote effort to finding and removing errors from my work before publication; it is discouraging and humbling when errors occur despite my precautions. However, I take some comfort from corrections; thanks to the cooperation of journals, it is possible to undo mistakes. I practiced medicine before starting a career in research; it is far easier to fix mistakes in research than in medical care.