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.^[1]

Case control studies are relatively inexpensive and less time-consuming than cohort studies.^{[citation needed]} 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.^[2] 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.^[3][4] Thus, the reliance on the rare disease assumption when discussing odds ratios as risk should be explicitly stated and discussed.