What is so odd about odds?

Abstract

In clinical studies, the relative likelihood of an event occurring between 2 groups is often expressed as the risk ratio (RR) or the odds ratio (OR). The RR is an intuitive parameter that is relatively easy to interpret. Quantitative interpretation of an OR is much more difficult and is often incorrectly equated to that of an RR. The problem is that OR may differ substantially from RR, especially when the outcome of interest is common in the study population. This article explains and clarifies controversial issues surrounding the use and interpretation of the OR. Theoretical concepts relating to ORs are illustrated by examples from the surgical literature. By reviewing articles from 5 surgical journals over a 5-year period, we show that the OR is often presented and misinterpreted as equivalent to the RR. When the discrepancy is large, using OR uncritically as an estimate of RR will strongly bias inferences about treatment effect or cause of disease by amplifying the apparent strength of an association between an exposure and an outcome.