Understanding Odds Ratio Calculation

This problem requires calculating the Odds Ratio (OR) from a case-control study. The OR estimates the odds of exposure (obesity) among cases (breast cancer patients) compared to the odds of exposure among controls (women without breast cancer).

Case-Control Study Data Setup

First, let's define the groups and exposure status:

• Cases: Women with breast cancer (Total = 300)
• Controls: Women without breast cancer (Total = 300)
• Exposure: Obesity

Constructing the 2x2 Contingency Table

We can represent the data in a 2x2 table, where 'a' and 'c' represent the number of exposed individuals (obese) in cases and controls, respectively, and 'b' and 'd' represent the number of unexposed individuals (not obese) in cases and controls, respectively.

• Number of obese cases (a) = 120
• Number of obese controls (c) = 60
• Number of non-obese cases (b) = Total cases - Obese cases = 300 - 120 = 180
• Number of non-obese controls (d) = Total controls - Obese controls = 300 - 60 = 240

The table is structured as follows:

Calculating the Odds Ratio (OR)

The formula for the Odds Ratio in a case-control study is:

$ OR = \frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}} = \frac{a/b}{c/d} = \frac{ad}{bc} $

Substitute the values from the table:

$ OR = \frac{120 \times 240}{180 \times 60} $

Now, simplify the calculation:

$ OR = \frac{28800}{10800} $

Simplify the fraction:

$ OR = \frac{288}{108} $

Divide both numerator and denominator by their greatest common divisor (which is 36):

$ OR = \frac{288 \div 36}{108 \div 36} = \frac{8}{3} $

Conclusion

The odds ratio of developing breast cancer among obese women is 8/3.