Rare disease assumption

The rare disease assumption is a mathematical assumption in epidemiologic case-control studies where the hypothesis tests the association between an exposure and a disease. It is assumed that, if the prevalence of the disease is low, then the odds ratio (OR) approaches the relative risk (RR). The idea was first demonstrated by Jerome Cornfield.

Case control studies are relatively inexpensive and less time-consuming than cohort studies. Since case control studies don't track patients over time, they can't establish relative risk. The case control study can, however, calculate the exposure-odds ratio, which, mathematically, is supposed to approach the relative risk as prevalence falls.

Sander Greenland showed that if the prevalence is 10% or less, the disease can be considered rare enough to allow the rare disease assumption. Unfortunately, the magnitude of discrepancy between the odds ratio and the relative risk is dependent not only on the prevalence, but also, to a great degree, on two other factors. Thus, the reliance on the rare disease assumption when discussing odds ratios as risk should be explicitly stated and discussed.