Odds Ratio
Definition: An odds ratio (OR) is defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a data-based estimate of that ratio. An odds ratio estimates the probability of disease given exposure to a specific factor by measuring the probability of exposure given the presence of disease.
An odds ratio can be calculated from a 2x2 table using the following formula:
Odds Ratio = (A / C) / (B / D) = (AD) / (BC)
| Disease Yes | Disease No | |
| Exposure Yes | A | B |
| Exposure No | C | D |
Example: At a recent UM football game, a terrorist group flew a crop duster over the stadium and dusted the western side of the stands with anthrax spores. Fortunately, the wind was blowing toward the west. Once cases were discovered, the investigation began.
A total of 100 people who sat on the eastern side developed disease and 1000 people who sat on the western side developed disease. Of the 100,000 people in attendance, 50,000 were sitting on the western side of the stadium and were considered to have been exposed.
From the given data, here is the 2x2 table and odds ratio calculation.
| Anthrax Yes | Anthrax No | |
| West (Exposure Yes) | 1000 | 49000 |
| East (Exposure No) | 100 | 49900 |
Odds Ratio = [(1000)(49,900)] / [(100)(49,000)] = 10.18
Interpretation: The odds of developing anthrax were 10 times higher for those sitting on the western side compared to those sitting on the eastern side of the stadium.
