Odds Ratios

For a recording of the "5 Minutes of EBM" presentation associated with this summary, click here.

Odds ratios are a commonly reported metric, particularly in retrospective (e.g. case-control) studies.  The OR gives one information about the strength of a proposed association between an exposure and an outcome.  It's fairly easy to remember how it's calculated if you understand exactly what the terms mean.

The "odds" of something happening are subtly different from the percent probability of the same event.  To calculate percent probability from a data set, you simply divide the number of people who experienced the event by the total number of people - so if 12 out of 100 people being observed for acute MI do, in fact, have an MI, then the probability of having an MI was 20%.  The odds of having an MI, on the other hand, are the probability of having the event divided by the probability of not having the event.  So in the same example, the odds of having an MI are 20/80, i.e. one in four (which could also be expressed as "four to one against").

The odds ratio, then, is just a ratio of odds; the odds of the outcome of interest occurring in the group with the exposure divided by the same outcome in the group who lack the exposure. To expand on the previous example, consider a case-control study evaluating the relationship between of watching the Republican primary debates and swearing under one's breath.  Suppose that in the group who watched, say, Santorum speaking, the incidence of cursing was 50%, whereas in the group who were reading a good book at the time only 10% were heard to utter any foul language.  Try to calculate the odds ratio associated with watching Rick Santorum for the outcome of sotto voce profanity (answer below).











In this example, the odds in the exposed group would be 50/50 (i.e. 1/1), and the odds in the unexposed group would be 10/90 (i.e. 1/9).  The odds of the event in the exposed group divided by the odds of the event in the unexposed group is equal to 9, which is the odds ratio.  For a good 2X2 table diagram showing how to calculate the odds ratio, click here.  

The main thing to notice about odds ratios is that they are relative measures of the strength of association, which tell you nothing about its absolute size.  Sometimes they're necessary, but they can also be used (like relative risk) to make trivial effects appear larger than they actually are - so whenever you see an OR, you should try to get some sense of how important the association under consideration is in absolute terms.