Question

In a case-control study, among the cases there are 60 exposed and 20 unexposed individuals, while among the controls there are 40 exposed and 80 unexposed individuals. What is the odds ratio of exposure?

• A. 6
• B. 3
• C. 1.5
• D. 0.17

Hint:

Odds ratio = cross-product ad/bc of the 2×2 table.

Answer 1

The Correct Option is A

Step 1: Lay out the 2 × 2 table. Let a = exposed cases = 60, b = exposed controls = 40, c = unexposed cases = 20, d = unexposed controls = 80.

Step 2: Recall the odds ratio formula. For a case-control study the odds ratio (OR) is the cross-product ratio:
\[ OR = \frac{a \times d}{b \times c} \]

Step 3: Substitute the values.
\[ OR = \frac{60 \times 80}{40 \times 20} = \frac{4800}{800} = 6 \]

Step 4: Interpret. An OR of 6 means the odds of exposure among cases are 6 times the odds among controls, indicating a strong positive association between the exposure and the disease (OR > 1).

Step 5: Why the others are wrong. 3, 1.5 and 0.17 arise from mis-pairing the cells (e.g. using a/c ÷ b/d incorrectly or inverting the cross-product). The correct diagonal cross-product is (60 × 80)/(40 × 20).

Key fact: OR = (ad)/(bc) = (60 × 80)/(20 × 40) = 6.