For this study, the odds ratio was: A. 1.0 B. 2.0 C. 3.0 D. Cannot be calculated from the information given

Steps to Solve

1. Set Up the Data

We need to organize the data into a 2x2 contingency table. The rows will represent the presence or absence of Kawasaki syndrome, and the columns will represent exposure to carpet shampoo.

Let:

• $A = \text{Children with Kawasaki syndrome exposed to carpet shampoo}$
• $B = \text{Children with Kawasaki syndrome not exposed to carpet shampoo}$
• $C = \text{Children without Kawasaki syndrome exposed to carpet shampoo}$
• $D = \text{Children without Kawasaki syndrome not exposed to carpet shampoo}$

2. Fill in the Data

Assuming we have the following hypothetical data:

• $A = 30$
• $B = 70$
• $C = 10$
• $D = 90$

3. Calculate the Odds for Cases and Controls

Calculate the odds of exposure for each group:

• Odds for cases (children with Kawasaki syndrome) is given by:

$$ \text{Odds}_{cases} = \frac{A}{B} $$

• Odds for controls (children without Kawasaki syndrome) is given by:

$$ \text{Odds}_{controls} = \frac{C}{D} $$

4. Calculate the Odds Ratio

The odds ratio (OR) is then calculated as:

$$ OR = \frac{\text{Odds}{cases}}{\text{Odds}{controls}} $$

5. Substitute the Values

Now, substitute the values we calculated into the formula for the odds ratio:

$$ OR = \frac{\frac{30}{70}}{\frac{10}{90}} $$

6. Simplify the Odds Ratio

Simplify the expression:

First, calculate the odds of exposure for both cases and controls:

$$ \text{Odds}{cases} = \frac{30}{70} = \frac{3}{7} $$ $$ \text{Odds}{controls} = \frac{10}{90} = \frac{1}{9} $$

Then substitute these into the odds ratio:

$$ OR = \frac{\frac{3}{7}}{\frac{1}{9}} = \frac{3}{7} \times \frac{9}{1} = \frac{27}{7} $$

7. Final Calculation

Now we can calculate the final odds ratio:

$$ OR = \frac{27}{7} \approx 3.86 $$