Chapter 12.2

### Odds in Ordinary Life

You might be most familiar with odds in the context of sporting events, when bookmakers or newspaper commentators quote the odds for and against a horse, a boxer, or a tennis player winning a particular event. In the context of games, suppose you have a typical die that has 6 faces. What is the probability (likelihood or chance) of rolling a 4 on a single throw? The answer is 1/6. What is the probability of rolling a number other than 4? The answer is 5/6.

Gamblers generally think in terms of odds. Odds refer to the probability of a particular event occurring vs the probability of that particular event not occurring. What are the odds of rolling a 4 on a single throw? The answer is (1/6)/(5/6), or 1:5. What are the odds of rolling a number other than 4? The answer is (5/6)/(1/6), which is 5:1.

### The 2 × 2 Table

As clinicians, we are interested less in rolling dice than in treating patients. We are also more accustomed to thinking in terms of probabilities than in terms of odds. Because odds vs probabilities provide certain advantages in statistical analyses, however, we frequently encounter odds in reading medical journal articles. Thus, we may read about the odds of experiencing vs avoiding a given outcome after a certain intervention.

Alternatively, in the context of case-control studies, we may be interested in knowing the odds of having a previous exposure vs not having that exposure. When we compare odds from 2 groups, we end up with the ratio of 2 odds, not surprisingly called an odds ratio (OR). In Chapter 9, Does Treatment Lower Risk? Understanding the Results, in which we discuss ways of presenting the magnitude of a treatment effect, such as the relative risk (RR), we introduced the concept of the OR. Compared with RR, which focuses on the risk (probability or likelihood) of an event among all exposed (ratio of events/total at risk of event), the OR is based on an estimate of odds of an event (ratio of having event/not having event). To help understand this concept, we present once again the 2 × 2 table (Table 12.2-1) and the results from ligation vs sclerotherapy of bleeding esophageal varices (Table 12.2-2), the example from Chapter 9.1

TABLE 12.2-1

The 2 × 2 Table

TABLE 12.2-2

Results From a Randomized Trial of Endoscopic Sclerotherapy Compared With Endoscopic Ligation for Bleeding Esophageal ...

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