Odds Ratio
Ratio of the odds of exposure among cases versus controls in a case-control study.
Formula
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Example
a=40, b=20, c=10, d=30 → OR = (40×30)/(20×10) = 6
How it works
The odds ratio compares how strongly an exposure is associated with a disease outcome by looking at the odds of being exposed in cases versus controls. In a 2×2 table, the cross-product formula (a×d)/(b×c) comes from simplifying the ratio of those two odds, so it uses all four cells while avoiding the need to compute separate odds first. An OR of 1 suggests no association, above 1 suggests the exposure is more common among cases, and below 1 suggests it may be protective.
When to use it
Use this in case-control studies, especially when you start with people who already have the outcome and people who do not, then compare prior exposure. It is also common in logistic regression output, where the exponentiated coefficient is interpreted as an odds ratio.
Worked example, step by step
Suppose a case-control study records: exposed cases (a) = 18 exposed controls (b) = 12 unexposed cases (c) = 30 unexposed controls (d) = 40 Step 1: Multiply the diagonal cells: a × d = 18 × 40 = 720 Step 2: Multiply the other diagonal cells: b × c = 12 × 30 = 360 Step 3: Divide the two products: OR = (a × d) / (b × c) = 720 / 360 = 2 Final answer: the odds ratio is 2, meaning the odds of exposure are twice as high among cases as among controls.
Common mistakes to avoid
- Swapping odds ratio with risk ratio, which are not the same in case-control studies
- Putting the cells in the wrong positions and calculating a different cross-product
- Interpreting the odds ratio as a direct probability or percentage increase
Did You Know?
For rare diseases (prevalence < 10 %), the odds ratio closely approximates the relative risk.
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