The rare-disease assumption revisited. A critique of "estimators of relative risk for case-control studies"

Am J Epidemiol. 1986 Dec;124(6):869-83. doi: 10.1093/oxfordjournals.aje.a114476.


The extension of case-control methods to the study of common outcomes has led to the development of several design and analysis techniques which do not employ the rare-disease assumption. Unfortunately, the principles underlying valid application of these techniques are more subtle than those first considered by Cornfield in the rare-disease setting, and appear to be easily misunderstood. We especially wish to caution that: The unrestricted inclusion of prevalent cases in the control group (as described by Hogue et al. for estimation of the risk ratio) will not make the odds ratio an unbiased estimate of the risk ratio (or anything else). In their response to our article, following, Hogue et al. describe restrictions on prevalence and duration necessary for the odds ratio from a case-exposure design to unbiasedly estimate the risk ratio in a stable population; these conditions were not mentioned in their original article, and in their new paper Hogue et al. do not provide mathematical proof that the conditions are sufficient to guarantee unbiasedness. Exclusion ("decontamination") of incident cases from the control group (as recommended by Hogue et al. for testing and test-based interval estimation) will result in improperly narrow risk-ratio confidence intervals whether or not the population is stable, and, in unstable populations, will generally lead to an invalid test. Methods that replace the rare-disease assumption with the stable-population assumption (such as case-exposure designs applied to open populations) will not yield unbiased results when the source population is a fixed cohort. (Of course, this will not be an issue for methods that are not based on either assumption, such as the case-base design applied to fixed cohorts, and the matched density design.) As each case-control design has certain practical implications for selection and interviewing, in choosing a design one should carefully consider practical issues (such as vulnerability to recall bias and ease of control selection) in addition to the statistical issues discussed here. In general, however, one should be wary of methods of studying incidence that involve the use of prevalent cases (such as the approach of Hogue et al.): prevalence is influenced by factors related to treatment, recovery, and fatality, and thus any etiologic study employing prevalent cases may be biased by such factors.(ABSTRACT TRUNCATED AT 400 WORDS)

Publication types

  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Adult
  • Epidemiology*
  • Female
  • Gastrointestinal Diseases / etiology
  • Humans
  • Intrauterine Devices / adverse effects
  • Pelvic Inflammatory Disease / etiology
  • Risk
  • Statistics as Topic
  • Water Supply