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On the need for the rare disease assumption in some case-control studies
  1. P Cummings,
  2. T D Koepsell
  1. Department of Epidemiology, School of Public Health and Community Medicine, University of Washington and the Harborview Injury Prevention and Research Center, 325 Ninth Ave, Box 359960, Seattle, Washington 98104–2499, USA peterc{at}u.washington.edu

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    Editor,—Several case-control studies have estimated the association between wearing of a bicycle helmet and head injury due to a bicycle crash.1 Hagel and Boivin recently argued that these studies do not need the rare disease assumption in order for us to accept the odds ratio as an estimate of the incidence rate ratio.2 In support of their argument, Hagel and Boivin described a hypothetical case-control study in which the study population is thought of as people riding bicycles.2 The cases were those who had a head injury after a crash. The controls were randomly sampled from all bicycle riders, regardless of whether or not they had just crashed. Such a study would seek to answer this question: if two bicycle riders, one helmeted and one not, set out on a ride, which is more likely to sustain a head injury? We agree with the contention of Hagel and Boivin that the odds ratio from such a study would estimate the incidence rate ratio, even if it were common for bicyclists to crash and sustain head injuries.

    None of the published studies, however, were designed in the manner described by Hagel and Boivin. Instead, all the published studies sought to address this question: if two bicycle riders, one helmeted and one not, crash while riding a bicycle, which is more likely to sustain a head injury? They restricted both cases and controls to the population of riders who had an incident crash. A rider entered the study population at the moment a crash began. Their experience in this population ended a fraction of a second later, when they either did or did not have a head injury.

    All of the published studies actually compared the head injured cases with bicycle crash victims who had an injury to a body site other than the head. As we have pointed out elsewhere, if helmet use neither increases nor decreases the risk of non-head injuries among cyclists who crash, then the helmet wearing prevalence among controls with non-head injuries should approximate the prevalence of helmet use among all cyclists who crashed and had no head injury.3 This study design compares cases with non-cases, the design that Hagel and Boivin refer to as a cumulative incidence case-control study. The odds ratio from such a study will closely approximate the relative risk of a head injury among the helmeted compared with the non-helmeted, only if this outcome is rare. We have little doubt that head injury is rare after a bicycle crash, so we think that the published studies used a reasonable design; we just wish to point out that it was not the design described by Hagel and Boivin. For further details about the design of bicycle helmet case-control studies, with numeric examples, we refer readers elsewhere.3

    One advantage of the design used by published case-control studies of bicycle helmet wearing and head injury, is that all the members of the study population had crashed. There was no need, therefore, to control for the propensity of riders to crash, which might confound a study of the type described by Hagel and Boivin.4

    When the goal of a case-control study is to assess the effects of a protective device among persons experiencing a brief event which might result in injury, such as a bicycle crash, a car crash, or a fall, it may be useful to limit the study population to persons who experience an incident event. In such as study, the odds ratio will closely approximate the relative risk only when the outcome is uncommon.

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