Which formula correctly represents the odds ratio?

The odds ratio is a measure used in epidemiology to determine the odds of an outcome occurring in one group compared to another group. It is typically calculated using a 2x2 contingency table that categorizes subjects based on exposure status and disease outcome.

The correct formula for the odds ratio is derived from the odds of exposure in cases to the odds of exposure in controls. Specifically, it is calculated as the ratio of the odds of exposure among cases (those who have the condition) to the odds of exposure among controls (those who do not have the condition). The formula for this is:

Odds Ratio (OR) = (Cases Exposed / Cases Not Exposed) / (Controls Exposed / Controls Not Exposed)

In expanded form, if we label:

• Cases Exposed = a

• Cases Not Exposed = b

• Controls Exposed = c

• Controls Not Exposed = d

The odds ratio would be represented as (a/b) / (c/d), and when simplified, this becomes (a * d) / (b * c).

In the chosen answer, the calculation of (# cases)(# controls not exposed)/(# cases not exposed)(# controls exposed) corresponds to this rearrangement and correctly represents