A. 2.25 – Explanation
| Odds – remember a ratio of the number of people who incur a particular outcome to the number of people who do not incur the outcome NOT a ratio of the number of people who incur a particular outcome to the total number of people |
The odds of asthmatics being exposed to passive smoking is 40 / 160 = 1 / 4
The odds of the controls being exposed to passive smoking is 20 / 180 = 1 / 9
The odds ratio is therefore 1/4 / 1/9 = 9/4 = 2.25
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 notincur 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.
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
