Odds Ratio

The odds ratio, or cross-product ratio, is the ratio of the odds that a disease occurs upon exposure to a risk factor to the odds that the same disease occurs in the absence of that exposure.

The odds ratio can be interpreted as a ratio of the odds of the presence or absence of a disease given exposure to the risk factor.

Mathematically, the odds ratio is expressed as follows:

For instance, to understand the association between smoking and the development of lung cancer, the odds ratio is calculated as follows.

 This result means that the odds of developing lung cancer in smokers are 4.75 times the odds for non-smokers.

The odds ratio does not determine causality; instead, it only measures the strength of the association.

Additionally, when data are based on small samples or in the case of a rare disease, calculating the odds ratio is advised as relative risk may overestimate the outcome.