11. A study to assess the relationship between smoking and lung cancer found that the odds ratio is 4. Using your own words, interpret the odds ratio.
The odds ratio of 4 means that individuals who smoke are 4 times more likely to develop lung cancer compared to individuals who do not smoke. In other words, the odds of developing lung cancer in smokers are four times higher than the odds of developing lung cancer in non-smokers.
To calculate the odds ratio, you need to know the number of individuals who smoke and develop lung cancer, as well as the number of individuals who smoke but do not develop lung cancer, and the number of individuals who do not smoke but develop lung cancer. The formula for calculating the odds ratio is:
Odds Ratio = (a / b) / (c / d)
Where:
- a is the number of individuals who smoke and develop lung cancer
- b is the number of individuals who smoke but do not develop lung cancer
- c is the number of individuals who do not smoke but develop lung cancer
- d is the number of individuals who do not smoke and do not develop lung cancer
By dividing the odds of smoking and developing lung cancer (a / b) by the odds of not smoking and developing lung cancer (c / d), the odds ratio provides a quantification of the association between smoking and lung cancer.