Odds and odds ratio
Odds are a ratio of the number of people who incur a particular outcome to the number of people who do not incur the outcome. The odds ratio may be defined as the ratio of the odds of a particular outcome with experimental treatment and that of control.
In contrast, probability is the fraction of times you'd expect to see an event in many trials. When expressed as a single number probability is always between 0 and 1. So, if we take the example of rolling a dice:
Odds ratios are the usual reported measure in case-control studies. It approximates to relative risk if the outcome of interest is rare.
For example, if we look at a trial comparing the use of paracetamol for dysmenorrhoea compared to placebo we may get the following results
The odds of achieving significant pain relief with paracetamol = 40 / 20 = 2
The odds of achieving significant pain relief with placebo = 30 / 60 = 0.5
Therefore the odds ratio = 2 / 0.5 = 4
Odds vs. probability
In contrast, probability is the fraction of times you'd expect to see an event in many trials. When expressed as a single number probability is always between 0 and 1. So, if we take the example of rolling a dice:
- the probability of rolling a six is 1/6 or 0.166666
- the odds of rolling a six is 1/5 or 0.2
Odds ratios are the usual reported measure in case-control studies. It approximates to relative risk if the outcome of interest is rare.
For example, if we look at a trial comparing the use of paracetamol for dysmenorrhoea compared to placebo we may get the following results
| Total number of patients | Achieved = 50% pain relief | |
|---|---|---|
| Paracetamol | 60 | 40 |
| Placebo | 90 | 30 |
The odds of achieving significant pain relief with paracetamol = 40 / 20 = 2
The odds of achieving significant pain relief with placebo = 30 / 60 = 0.5
Therefore the odds ratio = 2 / 0.5 = 4